###### Abstract

The Compact Linear Collider (CLIC) is a multi-TeV high-luminosity linear
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
collider under development. For an optimal exploitation of its physics
potential, CLIC is foreseen to be built and operated in a staged approach with
three centre-of-mass energy stages ranging from a few hundred GeV up to 3 TeV.
The first stage will focus on precision Standard Model physics, in particular
Higgs and top-quark measurements. Subsequent stages will focus on measurements
of rare Higgs processes, as well as searches for new physics processes and
precision measurements of new states, e.g. states previously discovered at LHC
or at CLIC itself. In the 2012 CLIC Conceptual Design Report, a fully
optimised 3 TeV collider was presented, while the proposed lower energy stages
were not studied to the same level of detail. This report presents an updated
baseline staging scenario for CLIC. The scenario is the result of a
comprehensive study addressing the performance, cost and power of the CLIC
accelerator complex as a function of centre-of-mass energy and it targets
optimal physics output based on the current physics landscape. The optimised
staging scenario foresees three main centre-of-mass energy stages at 380 GeV,
1.5 TeV and 3 TeV for a full CLIC programme spanning 22 years. For the first
stage, an alternative to the CLIC drive beam scheme is presented in which the
main linac power is produced using X-band klystrons.

CERN–2016–00412 August 2016

Updated baseline for a stagedCompact Linear Collider

GENEVA2016

ISBN | 978–92–9083–432–8 (paperback)
---|---
ISBN | 978–92–9083–433–5 (PDF)
ISSN | 0007–8328
DOI | http://dx.doi.org/10.5170/CERN-2016-004

Available online at https://publishing.cern.ch and https://cds.cern.ch

Copyright © CERN, 2016

Creative Commons Attribution 4.0

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This report is indexed in: CERN Document Server (CDS), INSPIRE.

This report should be cited as:

Updated baseline for a staged Compact Linear Collider, edited by P.N. Burrows,
P. Lebrun, L. Linssen, D. Schulte, E. Sicking, S. Stapnes, M.A. Thomson,
CERN–2016–004 (CERN, Geneva, 2016), http://dx.doi.org/10.5170/CERN-2016-004

Abstract

> Corresponding editors

Philip N. Burrows (University of Oxford), Philippe Lebrun (CERN),

Lucie Linssen (CERN), Daniel Schulte (CERN), Eva Sicking (CERN),

Steinar Stapnes (CERN), Mark A. Thomson (University of Cambridge)

The CLIC and CLICdp collaborations

M.J. Boland, U. Felzmann, P.J. Giansiracusa, T.G. Lucas, R.P. Rassool
_University of Melbourne, Melbourne, Australia_

C. Balazs, T.K. Charles
_Monash University, Melbourne, Australia_

K. Afanaciev, I. Emeliantchik, A. Ignatenko, V. Makarenko, N. Shumeiko1
_Belarusian State University, Minsk, Belarus_

A. Patapenka, I. Zhuk
_Joint Institute for Power and Nuclear Research - Sosny, Minsk, Belarus_

A.C. Abusleme Hoffman, M.A. Diaz Gutierrez, M. Vogel Gonzalez2
_Pontificia Universidad Católica de Chile, Santiago, Chile_

Y. Chi, X. He, G. Pei, S. Pei, G. Shu, X. Wang, J. Zhang, F. Zhao, Z. Zhou
_Institute of High Energy Physics, Beijing, China_

H. Chen, Y. Gao, W. Huang, Y.P. Kuang, B. Li, Y. Li, J. Shao, J. Shi, C. Tang,
X. Wu
_Tsinghua University, Beijing, China_

L. Ma, Y. Han
_Shandong University, Jinan, China_

W. Fang, Q. Gu, D. Huang, X. Huang, J. Tan, Z. Wang, Z. Zhao
_Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai,
China_

T. Laštovička
_Institute of Physics, Academy of Sciences, Prague, Czech Republic_

U. Uggerhoj, T.N. Wistisen
_Aarhus University, Aarhus, Denmark_

A. Aabloo, K. Eimre, K. Kuppart, S. Vigonski, V. Zadin
_University of Tartu, Tartu, Estonia_

M. Aicheler, E. Baibuz, E. Brücken, F. Djurabekova3, P. Eerola3, F. Garcia, E.
Haeggström3, K. Huitu3, V. Jansson3, V. Karimaki, I. Kassamakov3, A.
Kyritsakis, S. Lehti, A. Meriläinen3, R. Montonen3, T. Niinikoski, K.
Nordlund3, K. Österberg3, M. Parekh3,4, N.A. Törnqvist, J. Väinölä, M. Veske
_Helsinki Institute of Physics, University of Helsinki, Helsinki, Finland_

W. Farabolini, A. Mollard, O. Napoly, F. Peauger, J. Plouin
_CEA, Gif-sur-Yvette, France_

P. Bambade, I. Chaikovska, R. Chehab, M. Davier, W. Kaabi, E. Kou, F.
LeDiberder, R. Pöschl, D. Zerwas
_Laboratoire de l’Accélérateur Linéaire, Université de Paris-Sud XI,
IN2P3/CNRS, Orsay, France_

B. Aimard, G. Balik, J.-P. Baud, J.-J. Blaising, L. Brunetti, M. Chefdeville,
C. Drancourt, N. Geoffroy, J. Jacquemier, A. Jeremie, Y. Karyotakis, J.M.
Nappa, S. Vilalte, G. Vouters
_LAPP, Université de Savoie, IN2P3/CNRS, Annecy, France_

A. Bernard, I. Peric
_Karlsruhe Institute for Technology, Karlsruhe, Germay_

M. Gabriel, F. Simon, M. Szalay, N. van der Kolk
_Max-Planck-Institut für Physik, Munich, Germany_

T. Alexopoulos, E.N. Gazis, N. Gazis, E. Ikarios, V. Kostopoulos5, S.
Kourkoulis
_National Technical University of Athens, Athens, Greece_

P.D. Gupta, P. Shrivastava
_Raja Ramanna Centre for Advanced Technology, Department of Atomic Energy,
Indore, India_

H. Arfaei, M.K. Dayyani, H. Ghasem6, S.S. Hajari, H. Shaker6
_The School of Particles and Accelerators, Institute for Research in
Fundamental Sciences, Tehran, Iran_

Y. Ashkenazy
_Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem,
Israel_

H. Abramowicz, Y. Benhammou, O. Borysov, S. Kananov, A. Levy, I. Levy, O.
Rosenblat
_School of Physics & Astronomy, Tel Aviv University, Tel Aviv, Israel_

G. D’Auria, S. Di Mitri
_Elettra Sincrotrone Trieste, Trieste, Italy_

T. Abe, A. Aryshev, T. Higo, Y. Makida, S. Matsumoto, T. Shidara, T. Takatomi,
Y. Takubo, T. Tauchi, N. Toge, K. Ueno, J. Urakawa, A. Yamamoto6, M. Yamanaka
_High Energy Accelerator Research Organization, KEK, Tsukuba, Japan_

R. Raboanary
_University of Antananarivo, Antananarivo, Madagascar_

R. Hart, H. van der Graaf
_Nikhef, Amsterdam, Netherlands_

G. Eigen, J. Zalieckas
_Department of Physics and Technology, University of Bergen, Bergen, Norway_

E. Adli6, R. Lillestøl, L. Malina6, J. Pfingstner, K.N. Sjobak6
_University of Oslo, Oslo, Norway_

W. Ahmed, M.I. Asghar, H. Hoorani
_National Centre for Physics, Islamabad, Pakistan_

S. Bugiel, R. Dasgupta, M. Firlej, T.A. Fiutowski, M. Idzik, M. Kopec, M.
Kuczynska, J. Moron, K.P. Swientek
_AGH University of Science and Technology, Krakow, Poland_

W. Daniluk, B. Krupa, M. Kucharczyk, T. Lesiak, A. Moszczynski, B. Pawlik, P.
Sopicki, T. Wojtoń, L. Zawiejski
_Institute of Nuclear Physics PAN, Krakow, Poland_

J. Kalinowski, M. Krawczyk, A.F. Żarnecki
_University of Warsaw, Warsaw, Poland_

E. Firu, V. Ghenescu, A.T. Neagu, T. Preda, I-S. Zgura
_Institute of Space Science, Bucharest, Romania_

A. Aloev, N. Azaryan, J. Budagov, M. Chizhov, M. Filippova, V. Glagolev, A.
Gongadze, S. Grigoryan, D. Gudkov, V. Karjavine, M. Lyablin, A. Olyunin6, A.
Samochkine, A. Sapronov, G. Shirkov, V. Soldatov, A. Solodko6, E. Solodko6, G.
Trubnikov, I. Tyapkin, V. Uzhinsky, A. Vorozhtov
_Joint Institute for Nuclear Research, Dubna, Russia_

E. Levichev, N. Mezentsev, P. Piminov, D. Shatilov, P. Vobly, K. Zolotarev
_Budker Institute of Nuclear Physics, Novosibirsk, Russia_

I. Bozovic-Jelisavcic, G. Kacarevic, S. Lukic, G. Milutinovic-Dumbelovic, M.
Pandurovic
_Vinca Institute of Nuclear Sciences, University of Belgrade, Belgrade,
Serbia_

U. Iriso, F. Perez, M. Pont
_CELLS-ALBA, Barcelona, Spain_

J. Trenado
_University of Barcelona, Barcelona, Spain_

M. Aguilar-Benitez, J. Calero, L. Garcia-Tabares, D. Gavela, J.L. Gutierrez,
D. Lopez, F. Toral
_Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas
(CIEMAT), Madrid, Spain_

D. Moya, A. Ruiz-Jimeno, I. Vila
_Instituto de Física de Cantabria (CSIC-UC), Santander, Spain_

T. Argyropoulos6, C. Blanch Gutierrez, M. Boronat, D. Esperante6, A. Faus-
Golfe, J. Fuster, N. Fuster Martinez, N. Galindo Muñoz, I. García, J. Giner
Navarro6, E. Ros, M. Vos
_Instituto de Física Corpuscular (CSIC-UV), Valencia, Spain_

R. Brenner, T. Ekelöf, M. Jacewicz, J. Ögren , M. Olvegård, R. Ruber, V.
Ziemann
_Uppsala University, Uppsala, Sweden_

D. Aguglia, N. Alipour Tehrani7, A. Andersson, F. Andrianala8, F. Antoniou, K.
Artoos, S. Atieh, R. Ballabriga Sune, M.J. Barnes, J. Barranco Garcia, H.
Bartosik, C. Belver-Aguilar, A. Benot Morell9, D.R. Bett, S. Bettoni10, G.
Blanchot, O. Blanco Garcia, X.A. Bonnin, O. Brunner, H. Burkhardt, S.
Calatroni, M. Campbell, N. Catalan Lasheras, M. Cerqueira Bastos, A. Cherif,
E. Chevallay, B. Constance, R. Corsini, B. Cure, S. Curt, B. Dalena11, D.
Dannheim, G. De Michele, L. De Oliveira, N. Deelen, J.P. Delahaye, T. Dobers,
S. Doebert, M. Draper, F. Duarte Ramos, A. Dubrovskiy, K. Elsener, J. Esberg,
M. Esposito, V. Fedosseev, P. Ferracin, A. Fiergolski, K. Foraz, A. Fowler, F.
Friebel, J-F. Fuchs, C.A. Fuentes Rojas, A. Gaddi, L. Garcia Fajardo12, H.
Garcia Morales, C. Garion, L. Gatignon, J-C. Gayde, H. Gerwig, A.N. Goldblatt,
C. Grefe13, A. Grudiev, F.G. Guillot-Vignot, M.L. Gutt-Mostowy, M. Hauschild,
C. Hessler, J.K. Holma, E. Holzer, M. Hourican, D. Hynds, Y. Inntjore
Levinsen, B. Jeanneret, E. Jensen, M. Jonker, M. Kastriotou, J.M.K. Kemppinen,
R.B. Kieffer, W. Klempt, O. Kononenko, A. Korsback, E. Koukovini Platia, J.W.
Kovermann, C-I. Kozsar, I. Kremastiotis14, S. Kulis, A. Latina, F. Leaux, P.
Lebrun∗, T. Lefevre, L. Linssen∗, X. Llopart Cudie, A.A. Maier, H. Mainaud
Durand, E. Manosperti, C. Marelli, E. Marin Lacoma, R. Martin, S. Mazzoni, G.
Mcmonagle, O. Mete, L.M. Mether, M. Modena, R.M. Münker15, T. Muranaka, E.
Nebot Del Busto, N. Nikiforou, D. Nisbet, J-M. Nonglaton, F.X. Nuiry, A.
Nürnberg, M. Olvegard, J. Osborne, S. Papadopoulou, Y. Papaphilippou, A.
Passarelli, M. Patecki, L. Pazdera, D. Pellegrini, K. Pepitone, E. Perez
Codina, A. Perez Fontenla, T.H.B. Persson, M. Petrič, F. Pitters16, S. Pittet,
F. Plassard, R. Rajamak, S. Redford10, Y. Renier17, S.F. Rey, G. Riddone, L.
Rinolfi, E. Rodriguez Castro, P. Roloff, C. Rossi, V. Rude, G. Rumolo, A.
Sailer, E. Santin, D. Schlatter, H. Schmickler, D. Schulte∗, N. Shipman, E.
Sicking∗, R. Simoniello, P.K. Skowronski, P. Sobrino Mompean, L. Soby, M.P.
Sosin, S. Sroka, S. Stapnes∗, G. Sterbini, R. Ström, I. Syratchev, F. Tecker,
P.A. Thonet, L. Timeo, H. Timko, R. Tomas Garcia, P. Valerio18, A.L. Vamvakas,
A. Vivoli, M.A. Weber, R. Wegner, M. Wendt, B. Woolley W. Wuensch, J.
Uythoven, H. Zha, P. Zisopoulos
_CERN, Geneva, Switzerland_

M. Benoit, M. Vicente Barreto Pinto
_Département de physique nucléaire et corpusculaire, Université de Genève,
Geneva, Switzerland_

M. Bopp, H.H. Braun, M. Csatari Divall, M. Dehler, T. Garvey, J.Y. Raguin, L.
Rivkin19, R. Zennaro
_Paul Scherrer Institut, Villigen, Switzerland_

A. Aksoy, Z. Nergiz20, E. Pilicer21, I. Tapan21, O. Yavas
_IAT, Ankara University, Ankara, Turkey_

V. Baturin, R. Kholodov, S. Lebedynskyi, V. Miroshnichenko, S. Mordyk, I.
Profatilova6, V. Storizhko
_Institute of Applied Physics, National Academy of Sciences of Ukraine, Sumy,
Ukraine_

N. Watson, A. Winter
_School of Physics and Astronomy of the University of Birmingham, Birmingham,
United Kingdom_

J. Goldstein
_University of Bristol, Bristol, United Kingdom_

S. Green, J.S. Marshall, M.A. Thomson∗, B. Xu
_Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom_

W.A. Gillespie, R. Pan, M.A Tyrk
_University of Dundee, Dundee, United Kingdom_

D. Protopopescu, A. Robson
_University of Glasgow, Glasgow, United Kingdom_

R. Apsimon22, I. Bailey22, G. Burt22, D. Constable22, A. Dexter22, S.
Karimian22, C. Lingwood22
_Lancaster University, Lancaster, United Kingdom_

M.D. Buckland, G. Casse, J. Vossebeld
_University of Liverpool, Liverpool, United Kingdom_

A. Bosco, P. Karataev, K. Kruchinin, K. Lekomtsev, L. Nevay, J. Snuverink, E.
Yamakawa
_The John Adams Institute for Accelerator Science, Royal Holloway, University
of London, Egham, United Kingdom_

V. Boisvert, S. Boogert, G. Boorman, S. Gibson, A. Lyapin, W. Shields, P.
Teixeira-Dias, S. West
_Royal Holloway, University of London, Egham, United Kingdom_

R. Jones, N. Joshi
_University of Manchester, Manchester, United Kingdom_

R. Bodenstein, P.N. Burrows∗, G.B. Christian, D. Gamba6, C. Perry, J. Roberts6
_John Adams Institute, Department of Physics, University of Oxford, Oxford,
United Kingdom_

J.A. Clarke22, N.A. Collomb, S.P. Jamison22, B.J.A. Shepherd22, D. Walsh22
_STFC Daresbury Laboratory, Warrington, United Kingdom_

M. Demarteau, J. Repond, H. Weerts, L. Xia
_Argonne National Laboratory, Argonne, USA_

J.D. Wells
_Physics Department of the University of Michigan, Ann Arbor, USA_

C. Adolphsen, T. Barklow, M. Breidenbach, N. Graf, J. Hewett, T. Markiewicz,
D. McCormick, K. Moffeit, Y. Nosochkov, M. Oriunno, N. Phinney, T. Rizzo, S.
Tantawi, F. Wang, J. Wang, G. White, M. Woodley
_SLAC National Accelerator Laboratory, Menlo Park, USA_

1Deceased

2Now at Bergische Universität Wuppertal, Wuppertal, Germany

3Also at Department of Physics, University of Helsinki, Helsinki, Finland

4Also at Department of Mechanical Engineering, Aalto University, Espoo,
Finland

5Also at University of Patras, Patras, Greece

6Also at CERN, Geneva, Switzerland

7Also at ETH Zürich, Zurich, Switzerland

8Also at University of Antananarivo, Antananarivo, Madagascar

9Also at IFIC, Valencia, Spain

10Now at PSI, Villigen, Switzerland

11Now at CEA, Gif-sur-Yvette, France

12Now at LBNL, Berkeley CA, USA

13Now at University of Bonn, Bonn, Germany

14Also at KIT, Karlsruhe, Germany

15Also at University of Bonn, Bonn, Germany

16Also at Vienna University of Technology, Vienna, Austria

17Now at DESY, Zeuthen, Germany

18Now at Université de Genève, Geneva, Switzerland

19Also at EPFL, Lausanne, Switzerland

20Also at Physics Department, Nigde University, Turkey

21Also at Physics Department, Uludag University, Turkey

22Also at The Cockcroft Institute, Daresbury, United Kingdom

∗Editors<EMAIL_ADDRESS>
###### Contents

  1. 1 Introduction
  2. 2 CLIC physics
    1. 2.1 CLIC detector and experimental conditions
    2. 2.2 CLIC energy stages and their impact on the physics potential
    3. 2.3 Higgs physics
      1. 2.3.1 Combined Higgs fits
    4. 2.4 Top-quark physics
      1. 2.4.1 Top-quark mass
      2. 2.4.2 Top quark as a probe of BSM physics
    5. 2.5 Physics beyond the Standard Model
      1. 2.5.1 Direct searches for BSM physics
      2. 2.5.2 Sensitivity of precision measurements to BSM physics
    6. 2.6 Summary of physics requirements for the CLIC energy stages
  3. 3 CLIC post-CDR accelerator optimisation
    1. 3.1 Overview
    2. 3.2 Ingredients for the optimisation procedure
      1. 3.2.1 Beam parameters
      2. 3.2.2 RF structure design
      3. 3.2.3 Cost and power models
    3. 3.3 Optimisation procedure and results
      1. 3.3.1 Optimum at 3 TeV
      2. 3.3.2 Optimum at 380 GeV
      3. 3.3.3 Staging strategy
  4. 4 CLIC staging baseline
    1. 4.1 Description and performance parameters
    2. 4.2 Operating scenario and luminosities
    3. 4.3 Power and energy consumption
      1. 4.3.1 Additional energy-saving options
    4. 4.4 Cost estimate
  5. 5 Alternative klystron-based scenario for the first CLIC stage
  6. 6 Summary and outlook

##  1 Introduction

The Compact Linear Collider (CLIC) is a multi-TeV high-luminosity linear
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
collider under development by the international CLIC collaboration [1]. It is
based on a novel two-beam acceleration technique with accelerating gradients
at the level of 100 MV/m. Feasibility studies for the CLIC accelerator have
systematically and successfully addressed the main technical challenges of the
accelerator concept, while detailed detector and physics studies, carried out
by the CLIC detector and physics (CLICdp) collaboration [2], have confirmed
the ability to perform high-precision measurements at CLIC. The results have
been documented in the CLIC Conceptual Design Report (CDR) [3, 4, 5].

The CDR was finalised in 2012, just before the discovery of the Higgs boson at
the Large Hadron Collider (LHC) [6, 7]. Hence, for the CDR the Higgs mass was
not fully taken into account in the choice of the CLIC energy staging. The CDR
presented an accelerator complex optimised for 3 TeV with two initial lower-
energy stages, projected at 500 GeV and 1.4/1.5 TeV [5], which were not
technically optimised to the same degree.

Since then comprehensive studies have addressed performance, cost and power
optimisation of the accelerator complex as a function of energy. In parallel
further Higgs and top-quark physics studies have been carried out [8, 9, 10],
in particular for the initial-energy stage.

Recent implementation studies for CLIC have converged towards a staged
approach offering a comprehensive physics programme that may span several
decades of exploration. In this scheme, CLIC would provide high-luminosity
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
collisions covering a centre-of-mass energy range from 380 GeV to 3 TeV. For a
given nominal centre-of-mass energy, the energy can be tuned down by up to a
third, with limited loss of luminosity performance [5]. As additional LHC data
are collected, new physics results may call for further adjustment of the two
envisaged higher energy stages of CLIC.

In line with the European Strategy for Particle Physics, the ongoing CLIC
study aims to provide for the next Strategy update (expected to take place in
2019–2020) a project implementation plan for CLIC construction.

This report presents an updated CLIC staging scenario, where the initial
stages are adapted to the currently-known physics landscape and for which a
more thorough technical optimisation has been carried out.

The first stage is proposed to be at 380 GeV. It gives access to Higgs boson
measurements through the Higgsstrahlung and
$\mathup{{{W}}}\mathup{{{W}}}$-fusion production processes, thereby providing
accurate model-independent measurements of Higgs couplings to both fermions
and bosons [8]. This stage also addresses precision top-quark physics and
includes devoting approximately 15% of the running time to a threshold scan of
top pair production in the vicinity of 350 GeV.

The second stage around 1.5 TeV opens the energy frontier, allowing for the
discovery of new physics phenomena, while also giving access to additional
Higgs and top-quark properties such as the top-Yukawa coupling, the Higgs
self-coupling and rare Higgs branching ratios. The third stage at 3 TeV
further enlarges the CLIC physics potential. It will give direct access to the
discovery and accurate measurements of pair-produced particles, typically with
a mass up to 1.5 TeV or single particles with a mass up to 3 TeV. New
electroweak particles or dark matter candidates are of special interest, as
they may be easier to observe at CLIC than at the LHC. Furthermore, the 3 TeV
stage provides the best sensitivity to new physics processes at much higher
energy scales via indirect searches. Beam polarisation (80%
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$ polarisation) can help to
constrain the underlying physics.

A staged implementation of CLIC as described here offers an impressive energy
frontier physics programme that reaches beyond the LHC. It is an excellent
option for a post-LHC facility at CERN.

Section 2 of this report summarises the physics potential of CLIC for Higgs,
top quark and Beyond-Standard Model (BSM) physics and justifies the choice of
380 GeV for the initial energy stage. Section 3 describes the methodology of
the accelerator optimisation study performed after the CDR. Section 4
describes the implementation of the improved CLIC staging baseline with 380
GeV as the first energy stage. It includes detailed descriptions of the
accelerator layout and estimates of the energy consumption and cost. Further
plans towards additional optimisations of the accelerator design are also
outlined. Section 5 describes an alternative klystron-based scenario for the
first CLIC energy stage. Section 6 concludes with a summary and outlook.

##  2 CLIC physics

###  2.1 CLIC detector and experimental conditions

CLIC has a broad physics potential covering precision Higgs boson and top-
quark physics, direct searches for BSM physics as well as indirect BSM
searches through precision observables. This potential has been assessed
through the simulation and reconstruction of benchmark physics processes in
two dedicated CLIC detector concepts and results have been reported in several
summary documents [4, 5, 11]. These detector concepts, CLIC_SiD and CLIC_ILD,
are based on the SiD [12] and ILD [13] detector concepts for the International
Linear Collider (ILC) [14] and have been adapted to the experimental
environment at CLIC, which is characterised by challenging conditions imposed
by the high centre-of-mass energies and by the CLIC accelerator technology. In
the multi-TeV region this leads to an environment with beam-induced background
levels that are relatively high for a lepton collider.

CLIC will deliver bunch trains with a repetition rate of 50 Hz. Each bunch
train consists of 312 individual bunches, with 0.5 ns between bunch crossings
at the interaction point. The beam-crossing angle is 20 mrad in the horizontal
plane. On average there is less than one
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
interaction per bunch-train crossing. However, for CLIC operation at
$\sqrt{s}\,>\,1\,$$\mathrm{\,Te\kern-1.00006ptV}$ the crossing of highly-
focussed intense-beams leads to significant radiation of photons. This
“beamstrahlung” process results in high rates of incoherent electron-positron
pairs and low-$p_{\text{T}}$ $t$-channel
$\mathup{}\mathup{}\to\mathrm{hadrons}$ events. In addition, the energy loss
through beamstrahlung generates a long lower-energy tail to the luminosity
spectrum [3, 4]. The CLIC detector design and the event reconstruction
techniques employed are both optimised to mitigate the influence of these
backgrounds. The accelerator design foresees 80% electron polarisation.
Provisions are made for adding the equipment for positron polarisation if
required.

The CLIC detector concepts are optimised for the precise reconstruction of
complex final states in the multi-TeV region and in an environment with high
background levels. For most sub-detector systems, the 3 TeV detector design is
suitable also for the lower-energy stages, with one notable exception being
the inner tracking and vertex detectors. The lower backgrounds at sub-TeV
energies enable these detectors to be placed at a smaller radius with respect
to the beam [4], offering enhanced capabilities for jet flavour tagging. The
key performance parameters of the CLIC detector concepts are:

  * •

excellent track-momentum resolution, at the level of
$\sigma_{p_{\text{T}}}/p_{\text{T}}^{2}\lesssim 2\cdot
10^{-5}\leavevmode\nobreak\ \textrm{GeV}^{-1}$ ;

  * •

precise impact-parameter resolution, at the level of
$\sigma^{2}_{d_{0}}=(5\leavevmode\nobreak\
\upmu\mathrm{m})^{2}+(15\leavevmode\nobreak\
\upmu\mathrm{m}\,\text{GeV})^{2}/p^{2}\sin^{3}{\theta}$, to provide accurate
vertex reconstruction, enabling flavour-tagging with clean $\mathup{{{b}}}$-,
$\mathup{{{c}}}$\- and light-quark jet separation;

  * •

jet-energy resolution $\sigma_{E}/E\lesssim 3.5\%$ for jet energies in the
range 100 GeV to 1 TeV ($\lesssim 5\%$ at 50 GeV);

  * •

detector coverage for electrons and photons extending to very low polar angles
($\sim$10 mrad) with respect to the outgoing beam axes , e.g. to maximise
background rejection.

A main design driver for the CLIC and ILC detector concepts is the required
jet-energy resolution. As a result, the CLIC detector concepts CLIC_SiD and
CLIC_ILD are based on fine-grained electromagnetic and hadronic calorimeters,
optimised for particle-flow analysis techniques [15, 16]. In the particle-flow
approach, the aim is to reconstruct the individual, visible final-state
particles within a jet using information from the tracking detectors combined
with that from the highly granular calorimeters. In addition, particle-flow
event reconstruction provides a powerful tool for the rejection of beam-
induced backgrounds [4]. The CLIC detector concepts employ strong central
solenoid magnets, located outside the hadronic calorimeter, providing an axial
magnetic field of 5 T in CLIC_SiD and 4 T in CLIC_ILD. The CLIC_SiD concept
employs central silicon-strip tracking detectors, whereas CLIC_ILD assumes a
large central gaseous Time Projection Chamber. In both concepts the central
tracking system is augmented with silicon-based inner vertex and tracking
detectors. The LumiCal and BeamCal, two compact electromagnetic calorimeters,
allow the measurement of electrons and photons down to approximately 10 mrad
in polar angle. The two detector concepts each have an overall height of 14 m
and a length of 13 m; they are described in more detail in [4].

A study is almost completed to define a single optimised CLIC detector. The
new concept incorporates lessons learnt from CLIC_SiD and CLIC_ILD and will be
used for future benchmark CLIC physics studies.

###  2.2 CLIC energy stages and their impact on the physics potential

For optimal exploitation of its physics capabilities CLIC is foreseen to
follow a staged construction and operation scenario [5]. The aim is to choose
the energy stages such that the luminosity performance and physics potential
are maximised. Therefore a comprehensive set of physics benchmark studies at
the energies listed in Table 1 was performed. Based on the current physics
landscape and the results of the physics benchmark studies and accelerator
optimisation studies, the optimal choice for the CLIC energy stages is shown
to be 380 GeV, 1.5 TeV and 3 TeV (see Section 2.6), with some additional
running time at the first stage devoted to a
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ threshold scan near 350
GeV.

Table 1:  CLIC energy stages investigated in the physics benchmark studies discussed in Section 2.3, Section 2.4 and Section 2.5. The optimal staging scenario resulting from these studies is presented in Section 2.6, Table 7. Stage |  $\sqrt{s}$ (GeV) |  $\mathcal{L}_{\text{int}}$ ($\text{fb}^{-1}$)
---|---|---
1 | $250/350/380/420/500$ | $500+100$
2 | 1400 | 1500
3 | 3000 | 2000

The first energy stage should give access to Standard Model (SM) Higgs physics
and top-quark physics and should provide the possibility of performing a
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ threshold scan. The
second energy stage should offer direct sensitivity to many BSM models. It
provides higher Higgs statistics, allowing for measurements of rare Higgs
decays, $\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}\mathup{{{H}}}$
production and double-Higgs production. The third energy stage gives the best
sensitivity to new physics and double-Higgs production, therefore allowing for
improved measurements of the Higgs self-coupling and
$\mathup{{{H}}}\mathup{{{H}}}\mathup{{{W}}}\mathup{{{W}}}$ quartic coupling.

For the physics benchmark studies integrated luminosities of
$500\,\mbox{\,fb}^{-1}$, $1.5\,\mbox{\,ab}^{-1}$ and $2\,\mbox{\,ab}^{-1}$
were assumed for the three energy stages (Table 1). Near the
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ production threshold,
around 350 $\mathrm{\,Ge\kern-1.00006ptV}$, $100\,\mbox{\,fb}^{-1}$ was
assumed for an energy scan for an accurate measurement of the top-quark mass.
These integrated luminosities correspond to CLIC operation for 4 to 5 years at
each stage, with additional time reserved at each stage for accelerator
commissioning and luminosity ramp up in the first years [5].

To characterise the CLIC physics performance, physics events were generated
using the CLIC_SiD and CLIC_ILD detectors, taking realistic experimental
conditions into account. These include the luminosity spectrum at different
collision energies and the pileup of $\mathup{}\mathup{}\to\mathrm{hadrons}$
events according to the time structure of the CLIC beam [4]. The WHIZARD 1.95
event generator [17, 18] was employed in most cases, followed by PYTHIA 6.4
[19] for hadronisation and TAUOLA [20] for tau decays. The effects of Initial
State Radiation (ISR) are included in WHIZARD. GEANT4 [21, 22] was used to
simulate the detector response. The MARLIN [23] framework was used for the
digitisation and reconstruction of events simulated with the CLIC_ILD
detector, while the org.lcsim [24] framework was used to digitise detector
hits and perform track reconstruction in the CLIC_SiD detector. Particle flow
reconstruction was performed using PandoraPFA [15, 16]. FASTJET was used for
jet clustering [25], where the longitudinally invariant $k_{\text{T}}$
algorithm [26, 27] in the exclusive mode, which includes two additional beam
jets, was found to give good performance. LCFIPlus [28] was used for flavour-
tagging. The event simulation and reconstruction of the large data samples
used in the studies was performed using the iLCDirac grid submission tools
[29].

The results of these physics benchmark studies are presented in Section 2.3
(Higgs physics), in Section 2.4 (top physics) and in Section 2.5 (BSM
scenarios). The collective results allowed us to select an optimal staging
scenario based on our current knowledge. This is presented in Section 2.6 and
in Section 4. The staging scenario can be further adapted to future
discoveries from the LHC or elsewhere.

###  2.3 Higgs physics

A high-energy
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
collider provides a clean experimental environment to study the properties of
the Higgs boson with high precision [8]. The evolution of the leading-order
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
SM Higgs production cross sections with the centre-of-mass energy is shown in
Figure 1 for a Higgs boson mass of 126 GeV [30].

Figure 1: The centre-of-mass dependencies of the cross sections for the main
Higgs production processes at an
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
collider. The values shown correspond to unpolarised beams and do not include
the effect of beamstrahlung.

The Feynman diagrams for the three highest cross section Higgs production
processes are shown in Figure 2. Around $\sqrt{s}=350\,\text{GeV}$ the
Higgsstrahlung process
($\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{Z}}}\mathup{{{H}}}$)
has the largest cross section, but the $\mathup{{{W}}}\mathup{{{W}}}$-fusion
process
($\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$)
is also significant. The combined study of these two processes probes the
Higgs boson properties (width and branching ratios) in a model-independent
manner. Around $\sqrt{s}=1.4$ TeV and at 3 TeV Higgs production is dominated
by the $\mathup{{{W}}}\mathup{{{W}}}$-fusion process, with the
$\mathup{{{Z}}}\mathup{{{Z}}}$-fusion process
($\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{H}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$)
also becoming significant. Here the relatively large
$\mathup{{{W}}}\mathup{{{W}}}$-fusion cross section, combined with the high
luminosity of CLIC, results in large data samples, allowing precise
(${\cal{O}}(1\%)$) measurements of the couplings of the Higgs boson to both
fermions and gauge bosons. In addition, rarer processes such as
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}\mathup{{{H}}}$
and
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{H}}}\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$
(Figure 3) provide access to the top Yukawa coupling and the Higgs trilinear
self-coupling as determined by the parameter $\lambda$ in the Higgs potential.
In the SM, the Higgs boson originates from a doublet of complex scalar fields
$\phi$ described by the potential

$V(\phi)=\mu^{2}\phi^{\dagger}\phi+\lambda(\phi^{\dagger}\phi)^{2}\,,$ (1)

where $\mu$ and $\lambda$ are the parameters of the Higgs potential.

./Figures/Physics/Higgs/higgs_production/eezh (25,20) i1,i2 o1,o2
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$i1
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}$i2 $\mathup{{{Z}}}$o2
$\mathup{{{H}}}$o1 photon,tension=1.0,label=$\mathup{{{Z}}}$v1,v2
fermion,tension=1.0i1,v1,i2 photon,tension=1.0o2,v2 dashes,tension=1.0v2,o1 v1
v2 ./Figures/Physics/Higgs/higgs_production/eevvh (25,20) i1,i2 o1,oh,o2
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$i1
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}$i2
$\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$o2
$\mathup{{{H}}}$oh
$\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$o1 fermion,
tension=2.0i1,v1 fermion, tension=1.0v1,o1 fermion, tension=1.0o2,v2 fermion,
tension=2.0v2,i2 photon,
lab.side=right,lab.dist=1.5,label=$\mathup{{{W}}}$,tension=1.0v1,vh photon,
lab.side=right, lab.dist=1.5,label=$\mathup{{{W}}}$,tension=1.0vh,v2 dashes,
tension=1.0vh,oh vh ./Figures/Physics/Higgs/higgs_production/eeeeh (25,20)
i1,i2 o1,oh,o2 $\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$i1
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}$i2
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}$o2 $\mathup{{{H}}}$oh
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$o1 fermion, tension=2.0i1,v1
fermion, tension=1.0v1,o1 fermion, tension=1.0o2,v2 fermion, tension=2.0v2,i2
photon, lab.side=right,lab.dist=1.5,label=$\mathup{{{Z}}}$,tension=1.0v1,vh
photon, lab.side=right, lab.dist=1.5,label=$\mathup{{{Z}}}$,tension=1.0vh,v2
dashes, tension=1.0vh,oh vh

Figure 2: The three highest cross section Higgs production processes at CLIC.

./Figures/Physics/Higgs/higgs_production/eetth (25,20) i1,i2 o1,oh,o2
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$i1
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}$i2 $\mathup{{{t}}}$o2
$\mathup{{{H}}}$oh $\mathup{{\overline{{\mathup{{{t}}}}}}}$o1
photon,label=$\mathup{{{Z}}}$,tension=2.0v1,v2 fermion,tension=1.0i1,v1,i2
phantom,tension=1.0o1,v2,o2 fermion,tension=1.0o1,v2
fermion,tension=1.0v2,vh,o2 dashes,tension=0.0vh,oh vh
./Figures/Physics/Higgs/higgs_production/eevvhh (25,20) i1,i2 o1,oh1,oh2,o2
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$i1
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}$i2
$\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$o2
$\mathup{{{H}}}$oh1 $\mathup{{{H}}}$oh2
$\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$o1 fermion,
tension=2.0i1,v1 fermion, tension=1.0v1,o1 fermion, tension=1.0o2,v2 fermion,
tension=2.0v2,i2 photon,
label=$\mathup{{{W}}}$,label.dist=1.5,tension=1.0v1,vh photon,
label=$\mathup{{{W}}}$,label.dist=1.5,tension=1.0v2,vh dashes,
label=$\mathup{{{H}}}$, label.dist=1.5,tension=2.0vh,vh1 dashes,
tension=1.0oh1,vh1,oh2 vh1 ./Figures/Physics/Higgs/higgs_production/ghhww
(25,20) i1,i2 o1,oh1,oh2,o2 $\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$i1
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}$i2
$\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$o2
$\mathup{{{H}}}$oh1 $\mathup{{{H}}}$oh2
$\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$o1 fermion,
tension=2.0i1,v1 fermion, tension=1.0v1,o1 fermion, tension=1.0o2,v2 fermion,
tension=2.0v2,i2 photon,
label=$\mathup{{{W}}}$,label.side=right,label.dist=1.5, tension=1.0vh,v1
photon, label=$\mathup{{{W}}}$,label.sde=right,label.dist=1.5,
tension=1.0v2,vh dashes, tension=1.0oh1,vh,oh2 vh

Figure 3: The main processes at CLIC involving the top Yukawa coupling
$g_{\mathup{{{H}}}\mathup{{{t}}}\mathup{{{t}}}}$, the Higgs boson trilinear
self-coupling $\lambda$ and the quartic coupling
$g_{\mathup{{{H}}}\mathup{{{H}}}\mathup{{{W}}}\mathup{{{W}}}}$.

Table 2 shows the cross sections and the expected numbers of
$\mathup{{{H}}}\mathup{{{Z}}}$,
$\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$
and
$\mathup{{{H}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
events for the three studied energy stages. These numbers account for the
effect of beamstrahlung and ISR, which result in a tail in the distribution of
the effective centre-of-mass energy $\sqrt{s^{\prime}}$.

Table 2: The leading-order Higgs unpolarised cross sections for the Higgsstrahlung, $\mathup{{{W}}}\mathup{{{W}}}$-fusion, and $\mathup{{{Z}}}\mathup{{{Z}}}$-fusion processes for $m_{\mathup{{{H}}}}=126\,\text{GeV}$ at the three centre-of-mass energies studied. The quoted cross sections include the effects of ISR but do not include the effects of beamstrahlung. Also listed are the numbers of expected events including the effects of the CLIC beamstrahlung spectrum and ISR. The cross sections and expected numbers do not take into account the enhancements possible with polarised beams.  $\sqrt{s}$ | 350 GeV | 1.4 TeV | 3 TeV
---|---|---|---
$\mathcal{L}_{\text{int}}$ | 500 $\text{fb}^{-1}$ | 1.5 $\text{ab}^{-1}$ | 2 $\text{ab}^{-1}$
$\sigma(\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{Z}}}\mathup{{{H}}})$ | 133 fb | 8 fb | 2 fb
$\sigma(\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}})$ | 34 fb | 276 fb | 477 fb
$\sigma(\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{H}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}})$ | 7 fb | 28 fb | 48 fb
# $\mathup{{{H}}}\mathup{{{Z}}}$ events | 68,000 | 20,000 | 11,000
# $\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$ events | 17,000 | 370,000 | 830,000
# $\mathup{{{H}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$ events | 3,700 | 37,000 | 84,000

Table 2 does not take beam polarisation into account. In fact, the majority of
CLIC Higgs physics studies have been performed assuming unpolarised
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}$ and
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$ beams. However, for the
baseline CLIC design the electron beam can be 80% polarised. The accelerator
design is compatible with introducing positron polarisation at a lower level
but this is not currently part of the baseline design. By selecting different
beam polarisations it is possible to enhance or suppress different physical
processes. The chiral nature of the weak coupling can offer significant
enhancements in $\mathup{{{W}}}\mathup{{{W}}}$-fusion Higgs production, as
indicated in Table 3. The potential gains for the Higgsstrahlung process
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{Z}}}\mathup{{{H}}}$
and the $\mathup{{{Z}}}\mathup{{{Z}}}$-fusion process
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{H}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
however are less significant (Table 3). In practice, the balance between
operation with different beam polarisations will depend on the CLIC physics
programme taken as a whole, including the searches for BSM particles. For
example, based on current knowledge one could imagine similar running times
with both negative and positive longitudinal electron polarisation at the
first energy stage in order to optimise top-quark asymmetry measurements (see
Section 2.4). At the higher energy stages, principal running with negative
electron polarisation is likely to be favoured in view of the significant
enhancement of Higgs statistics.

Table 3: The dependence of the event rates for the $s$-channel $\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{Z}}}\mathup{{{H}}}$ process and the pure $t$-channel $\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$ and $\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{H}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$ processes for three example beam polarisations. The numbers are only approximate as they do not account for interference between $\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\\!\to\mathup{{{H}}}\mathup{{{Z}}}\\!\to\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$ and $\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\\!\to\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$.  Polarisation | Enhancement factor
---|---
$P(\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}):P(\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}})$ | $\\!\\!\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\\!\to\mathup{{{Z}}}\mathup{{{H}}}\\!\\!$ | $\\!\\!\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\\!\to\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\\!\\!$ | $\\!\\!\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\\!\rightarrow\mathup{{{H}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\\!\\!$
unpolarised | 1.00 | 1.00 | 1.00
$-80\%\,:\phantom{+3}\,0\%$ | 1.12 | 1.80 | 1.12
$+80\%\,:\phantom{+3}\,0\%$ | 0.88 | 0.20 | 0.88

Polar-angle distributions for single Higgs production at the three studies
CLIC energy stages are shown in Figure 4. At $350\,\text{GeV}$ most Higgs
bosons are produced in the central parts of the detector, whereas at centre-
of-mass energies above $1\,\text{TeV}$ they are mainly produced in the forward
regions, therefore requiring good forward detection capabilities.

Figure 4: Polar angle distributions for single Higgs production at the three
studied CLIC energy stages. All distributions include the effects of the CLIC
beamstrahlung spectrum and ISR. All distributions are normalised to unit area.

The choice of the CLIC energy stages is motivated by the desire to pursue a
programme of precision Higgs and top physics, as well as to operate the
accelerator above 1 TeV at the earliest possible time. The lower-energy
operation is partly motivated by the Higgsstrahlung process, as it provides
the opportunity to measure the couplings of the Higgs boson in a model-
independent manner, as further described below. This is unique to an electron-
positron collider. The clean experimental environment, and the relatively low
SM cross sections for background processes, allow
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{Z}}}\mathup{{{H}}}$
events to be selected based solely on the measurement of the four-momentum of
the $\mathup{{{Z}}}$ boson through its decay products.

The most distinct event topologies occur for
$\mathup{{{Z}}}\to\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
and
$\mathup{{{Z}}}\to\mathup{{}^{\scriptstyle{+}}}\mathup{{}^{\scriptstyle{-}}}$
decays, each with a branching ratio of about 3.4% [30], which can be
identified by requiring that the di-lepton invariant mass is consistent with
$m_{\mathup{{{Z}}}}$. The four-momentum of the system recoiling against the
$\mathup{{{Z}}}$ boson can be obtained from
$E_{\mathrm{rec}}=\sqrt{s}-E_{\mathup{{{Z}}}}$ and
$\vec{p}_{\mathrm{rec}}=-\vec{p}_{\mathup{{{Z}}}}$. In
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{Z}}}\mathup{{{H}}}$
events the invariant mass of this recoiling system will peak at
$m_{\mathup{{{H}}}}$, allowing the $\mathup{{{H}}}\mathup{{{Z}}}$ events to be
selected based only on the observation of the leptons from the
$\mathup{{{Z}}}$ boson decay, providing a model-independent measurement of the
Higgs coupling to the $\mathup{{{Z}}}$ boson,
$g_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{{{Z}}}}$.

The hadronic decay channel
$\mathup{{{Z}}}\rightarrow\mathup{{{q}}}\mathup{{\overline{{\mathup{{{q}}}}}}}$
with a branching ratio of $\sim$70% [30] has a less distinct event topology,
but it provides a statistically more precise measurement of recoil mass
analysis. The combination of the leptonic and hadronic decay channels allows
$g_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{{{Z}}}}$ to be determined in a model-
independent way with a precision of 0.8% at 350 GeV [9]. In addition, the
recoil mass from
$\mathup{{{Z}}}\rightarrow\mathup{{{q}}}\mathup{{\overline{{\mathup{{{q}}}}}}}$
decays provides a direct search for possible Higgs decays to invisible final
states, and can be used to constrain the invisible decay width of the Higgs,
$\Gamma_{\text{invis}}$, to less than 1% at 90% confidence level [9].

As the HZ Higgsstrahlung production process with the Z boson decaying to
$\mathup{{{q}}}\mathup{{\overline{{\mathup{{{q}}}}}}}$ provides the best
accuracy for the $g_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{{{Z}}}}$ measurement,
it is important to understand its dependence on the CLIC centre-of-mass
energy. The study was hence performed for three different centre-of-mass
energies: 250 GeV, 350 GeV and 420 GeV for the same integrated luminosity of
500 $\text{fb}^{-1}$ at each energy [9]. Among these, the 350 GeV case
provides the best precision, as shown in Table 4.

Table 4: Statistical precision achievable on $\sigma(\mathup{{{H}}}\mathup{{{Z}}})$ from the hadronic recoil mass analysis for $\sqrt{s}=250$ GeV, 350 GeV and 420 GeV, assuming for each energy 500 $\text{fb}^{-1}$ and unpolarised beams [9]. $\sqrt{s}$ | $\sigma(\mathup{{{H}}}\mathup{{{Z}}})$ | $\Delta\,\sigma(\mathup{{{H}}}\mathup{{{Z}}})$
---|---|---
250 GeV | 136 fb | $\pm 3.7\,\%$
350 GeV | 93 fb | $\pm 1.8\,\%$
420 GeV | 68 fb | $\pm 2.6\,\%$

This can be understood as a trade-off between recoil mass resolution, HZ
production cross section and signal-to-background ratio. In the hadronic
channel, the recoil mass resolution degrades with increasing centre-of-mass
energy, due to the $\sqrt{s^{\prime}}$ dependence of the recoil mass itself,
combined with detector resolution trends. On the other hand, the signal-to-
noise ratio is significantly less favourable near the HZ production threshold
at 250 $\mathrm{\,Ge\kern-1.00006ptV}$, where one of the dominant background
processes
($\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\rightarrow\mathup{{{q}}}\mathup{{\overline{{\mathup{{{q}}}}}}}\mathup{{{q}}}\mathup{{\overline{{\mathup{{{q}}}}}}}$)
can easily mimic HZ events. Therefore, despite the fact that the HZ production
cross section is higher at 250 $\mathrm{\,Ge\kern-1.00006ptV}$, the optimal
$\sqrt{s}$ choice for this measurement is in the region near 350
$\mathrm{\,Ge\kern-1.00006ptV}$.

The statistical accuracy of the Higgs mass determined through the recoil mass
measurement for leptonic $\mathup{{{Z}}}$-decays in Higgsstrahlung events is
110 MeV. This accuracy will be improved further by including the Higgs
invariant mass reconstruction for Higgs decay channels with large branching
fractions.

By identifying the individual final states for different Higgs decay modes,
and by taking advantage of the accessibility of both Higgsstrahlung and Higgs
production through $\mathup{{{W}}}\mathup{{{W}}}$-fusion, precise measurements
of the Higgs boson branching ratios (BR) can be made. Although the cross
section is lower, the $t$-channel $\mathup{{{W}}}\mathup{{{W}}}$-fusion
process
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$
is an important part of the Higgs physics programme around
$\sqrt{s}=350\,\text{GeV}$.

Once the Higgs coupling to the $\mathup{{{Z}}}$ boson,
$g_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{{{Z}}}}$, is known, the Higgs coupling
to the $\mathup{{{W}}}$ boson can be determined from, for example, the ratios
of Higgsstrahlung to $\mathup{{{W}}}\mathup{{{W}}}$-fusion cross sections,

$\frac{\sigma(\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{Z}}}\mathup{{{H}}})\times\text{BR}(\mathup{{{H}}}\to\mathup{{{b}}}\mathup{{\overline{{\mathup{{{b}}}}}}})}{\sigma{(\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{{H}}})}\times\text{BR}(\mathup{{{H}}}\to\mathup{{{b}}}\mathup{{\overline{{\mathup{{{b}}}}}}})}\propto\left(\frac{g_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{{{Z}}}}}{g_{\mathup{{{H}}}\mathup{{{W}}}\mathup{{{W}}}}}\right)^{2}\,.$

In order to determine absolute measurements of the other Higgs couplings, the
Higgs total decay width needs to be inferred from the data. For the Higgs
boson mass of 126 GeV, the total Higgs decay width in the SM
($\Gamma_{\mathup{{{H}}}}$) is less than $5\,\text{MeV}$ and cannot be
measured directly. However, given that the absolute couplings of the Higgs
boson to the $\mathup{{{Z}}}$ and $\mathup{{{W}}}$ bosons can be obtained as
described above, the total decay width of the Higgs boson can be determined
from $\mathup{{{H}}}\to\mathup{{{W}}}\mathup{{{W}}}^{*}$ or
$\mathup{{{H}}}\to\mathup{{{Z}}}\mathup{{{Z}}}^{*}$ decays. For example, the
measurement of the Higgs decay to $\mathup{{{W}}}\mathup{{{W}}}^{*}$ in the
$\mathup{{{W}}}\mathup{{{W}}}$-fusion process determines

$\sigma(\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}})\times\text{BR}(\mathup{{{H}}}\to\mathup{{{W}}}\mathup{{{W}}}^{*})\propto\frac{g^{4}_{\mathup{{{H}}}\mathup{{{W}}}\mathup{{{W}}}}}{\Gamma_{\mathup{{{H}}}}}\,,$

and thus the total width can be determined utilising the model-independent
measurement of $g_{\mathup{{{H}}}\mathup{{{W}}}\mathup{{{W}}}}$. In practice a
fit (see Section 2.3.1) was performed to all of the experimental measurements
involving Higgs boson couplings. For the first CLIC energy stage the fit is
based on the 350 GeV data set. At the higher energies significantly more Higgs
data from the $\mathup{{{W}}}\mathup{{{W}}}$-fusion process become available,
profiting from the fact that this Higgs production process as well as the CLIC
luminosity increase with $\sqrt{s}$. These data also provide a more accurate
measurement of the Higgs mass, for example through invariant mass
reconstruction in
$\mathup{{{H}}}\to\mathup{{{b}}}\mathup{{\overline{{\mathup{{{b}}}}}}}$
decays. This allows determination of the Higgs mass with a statistical
accuracy of $47\,\text{MeV}$ at 1.4 TeV centre-of-mass energy and
$44\,\text{MeV}$ at 3 TeV. Combining these results yields a statistical
accuracy of $32\,\text{MeV}$, or $24\,\text{MeV}$ when using 80% electron beam
polarisation [8].

Although the $\mathup{{{W}}}\mathup{{{W}}}$-fusion process has the largest
cross section for Higgs production above 1 TeV, other processes are also
important. For example, measurements of the
$\mathup{{{Z}}}\mathup{{{Z}}}$-fusion process provide further constraints on
the $g_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{{{Z}}}}$ coupling. Furthermore,
operation at $\sqrt{s}=1.4\,\mathrm{\,Te\kern-1.00006ptV}$ enables a
determination of the top Yukawa coupling from the process
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}\mathup{{{H}}}\to\mathup{{{b}}}\mathup{{{W}}}^{+}\mathup{{\overline{{\mathup{{{b}}}}}}}\mathup{{{W}}}^{-}\mathup{{{H}}}$
in which a top quark radiates a Higgs boson. In the SM this coupling is the
strongest Higgs-fermion coupling, as the top quark is the most massive
fermion. At 1.4 TeV this coupling can be determined with a statistical
accuracy of 4.1% [31] when using 80% electron beam polarisation.

Finally, the self-coupling of the Higgs boson at the
$\mathup{{{H}}}\mathup{{{H}}}\mathup{{{H}}}$ vertex is measurable in
$1.4\,\mathrm{\,Te\kern-1.00006ptV}$ and $3\,\mathrm{\,Te\kern-1.00006ptV}$
operation. After spontaneous symmetry breaking the form of the Higgs potential
given in Equation 1 gives rise to a trilinear Higgs self-coupling of strength
proportional to $\lambda v$, where $v$ is the vacuum expectation value of the
Higgs potential. The measurement of the strength of the Higgs self-coupling
therefore provides direct access to the coupling $\lambda$ assumed in the
Higgs mechanism. This measurement is an essential part of experimentally
establishing the Higgs mechanism as described by the SM. The measurement of
the Higgs boson self-coupling at the LHC will be extremely challenging even
with $3000\,\text{fb}^{-1}$ of data (see for example [32]). At a linear
collider, the trilinear Higgs self-coupling can be measured through the
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{Z}}}\mathup{{{H}}}\mathup{{{H}}}$
and
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{H}}}\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$
processes. The achievable precision has been studied for the
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{Z}}}\mathup{{{H}}}\mathup{{{H}}}$
process at $\sqrt{s}=500\,\text{GeV}$ in the context of the ILC, where the
results show that a very large integrated luminosity is required to reach even
a moderate precisions of approximately 30% [33]. For this reason, the most
favourable channel for the measurement of the Higgs self-coupling is the
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\to\mathup{{{H}}}\mathup{{{H}}}\mathup{{{\mathup{}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}\mathup{{\overline{{\mathup{}}}}{}_{\scriptstyle{\\!\mathup{{{e}}}}}}$
process at $\sqrt{s}\geq 1\,\text{TeV}$. In this channel, the sensitivity
increases with increasing centre-of-mass energy. The measurement of the Higgs
boson self-coupling forms a central part of the CLIC Higgs physics programme;
ultimately a precision of approximately 10% on $\lambda$ can be achieved [8].

####  2.3.1 Combined Higgs fits

From the Higgs cross section and branching ratio measurements at the three
studied CLIC energy stages, the Higgs coupling parameters and total width are
extracted by a global fit [34, 8]. Here, a $-80\%$ electron polarisation is
assumed at $1.4\,\text{TeV}$ and $3\,\text{TeV}$, while no beam polarisation
is assumed at 350 GeV. The corresponding increase in cross section is taken
into account by multiplying the event rates by a factor of 1.8 (see Table 3).
This approach is conservative since it assumes that all backgrounds including
those from $s$-channel processes, which do not receive the same enhancement by
polarisation, scale by the same factor.

Some of the Higgs cross section and branching ratio analyses in the
$\mathup{{{W}}}\mathup{{{W}}}$-fusion and
$\mathup{{{Z}}}\mathup{{{Z}}}$-fusion processes were so far only performed for
1.4 TeV centre-of-mass energy. For these channels, the uncertainties on the
measurements estimated at 1.4 TeV were extrapolated to 3 TeV, based on scaling
of the integrated luminosity. In addition to this scaling, the signal fraction
within the detector acceptance, which changes between the centre-of-mass
energies, is taken into account for each Higgs decay channel individually.

Two types of fits were used: a model-independent fit making no additional
assumptions, and a model-dependent fit following the strategies used for the
interpretation of LHC Higgs results. To obtain the precision expected at CLIC,
it was assumed that the value expected in the SM has been observed throughout.
In the fit only statistical uncertainties were used. Correlations between
measurements were taken into account in cases where they are expected to be
large. This applies to the measurements of $\sigma\times\text{BR}$ for
$\mathup{{{H}}}\to\mathup{{{b}}}\mathup{{\overline{{\mathup{{{b}}}}}}},\mathup{{{c}}}\mathup{{\overline{{\mathup{{{c}}}}}}},\mathup{{{g}}}\mathup{{{g}}}$
in Higgsstrahlung and $\mathup{{{W}}}\mathup{{{W}}}$-fusion events at 350 GeV,
which were extracted simultaneously from the data in a combined fitting
procedure.

The model-independent fit was performed with eleven free parameters: the Higgs
couplings $g_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{{{Z}}}}$,
$g_{\mathup{{{H}}}\mathup{{{W}}}\mathup{{{W}}}}$,
$g_{\mathup{{{H}}}\mathup{{{b}}}\mathup{{{b}}}}$,
$g_{\mathup{{{H}}}\mathup{{{c}}}\mathup{{{c}}}}$,
$g_{\mathup{{{H}}}\mathup{}\mathup{}}$,
$g_{\mathup{{{H}}}\mathup{}\mathup{}}$,
$g_{\mathup{{{H}}}\mathup{{{t}}}\mathup{{{t}}}}$, the Higgs total width,
$\Gamma_{\mathup{{{H}}}}$, as well as the three effective couplings
$g^{\dagger}_{\mathrm{\mathup{{{H}}}\mathup{{{g}}}\mathup{{{g}}}}}$,
$g^{\dagger}_{\mathup{{{H}}}\mathup{}\mathup{}}$ and
$g^{\dagger}_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{}}$. The latter three
parameters were treated in the same way as the physical Higgs couplings in the
fit.

Table 5:  Results of the model-independent Higgs fit. Values marked “$-$” can not be measured with sufficient precision at the given energy. The three effective couplings $g^{\dagger}_{\mathup{{{H}}}\mathup{{{g}}}\mathup{{{g}}}}$, $g^{\dagger}_{\mathup{{{H}}}\mathup{}\mathup{}}$ and $g^{\dagger}_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{}}$ are also included in the fit.  Parameter | Relative precision
---|---
| $350\,\text{GeV}$ | \+ $1.4\,\text{TeV}$ | \+ $3\,\text{TeV}$
| $500\,\text{fb}^{-1}$ | \+ $1.5\,\text{ab}^{-1}$ | \+ $2\,\text{ab}^{-1}$
$g_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{{{Z}}}}$ | 0.8% | 0.8% | 0.8%
$g_{\mathup{{{H}}}\mathup{{{W}}}\mathup{{{W}}}}$ | 1.3% | 0.9% | 0.9%
$g_{\mathup{{{H}}}\mathup{{{b}}}\mathup{{{b}}}}$ | 2.8% | 1.0% | 0.9%
$g_{\mathup{{{H}}}\mathup{{{c}}}\mathup{{{c}}}}$ | 6.0% | 2.3% | 1.9%
$g_{\mathup{{{H}}}\mathup{}\mathup{}}$ | 4.2% | 1.7% | 1.4%
$g_{\mathup{{{H}}}\mathup{}\mathup{}}$ | $-$ | 14.1% | 7.8%
$g_{\mathup{{{H}}}\mathup{{{t}}}\mathup{{{t}}}}$ | $-$ | 4.4% | 4.4%
$g^{\dagger}_{\mathup{{{H}}}\mathup{{{g}}}\mathup{{{g}}}}$ | 3.6% | 1.7% | 1.4%
$g^{\dagger}_{\mathup{{{H}}}\mathup{}\mathup{}}$ | $-$ | 5.7% | 3.2%
$g^{\dagger}_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{}}$ | $-$ | 15.6% | 9.1%
$\Gamma_{\mathup{{{H}}}}$ | 6.4% | 3.7% | 3.6%
Figure 5: Illustration of the precision of the Higgs couplings of the studied
three-stage CLIC programme determined in a model-independent fit.

The fit was performed in three stages, taking the statistical uncertainties
obtainable from CLIC at the three considered energy stages successively into
account. The fits for subsequent stages also include all measurements of the
previous stages. Table 5 summarises the results. They are graphically
illustrated in Figure 5. Since the model-independence of the analysis hinges
on the absolute measurement of $\sigma(\mathup{{{Z}}}\mathup{{{H}}})$ at
$350\,\text{GeV}$, which provides the coupling
$g_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{{{Z}}}}$, the precision of all other
couplings is ultimately limited by this uncertainty.

For the model-dependent fit, it is assumed that the Higgs decay properties can
be described by ten independent parameters
$\kappa_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{{{Z}}}}$,
$\kappa_{\mathup{{{H}}}\mathup{{{W}}}\mathup{{{W}}}}$,
$\kappa_{\mathup{{{H}}}\mathup{{{b}}}\mathup{{{b}}}}$,
$\kappa_{\mathup{{{H}}}\mathup{{{c}}}\mathup{{{c}}}}$,
$\kappa_{\mathup{{{H}}}\mathup{}\mathup{}}$,
$\kappa_{\mathup{{{H}}}\mathup{}\mathup{}}$,
$\kappa_{\mathup{{{H}}}\mathup{{{t}}}\mathup{{{t}}}}$,
$\kappa_{{\mathup{{{H}}}\mathup{{{g}}}\mathup{{{g}}}}}$,
$\kappa_{\mathup{{{H}}}\mathup{}\mathup{}}$ and
$\kappa_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{}}$. These factors are defined by
the ratio of the Higgs partial width divided by the partial width expected in
the Standard Model as

$\kappa_{i}^{2}=\Gamma_{i}/\Gamma_{i}^{\text{SM}}\,.$ (2)

In this scenario the total width is given by the sum of the ten partial widths
considered, which is equivalent to assuming no invisible Higgs decays. The
variation of the total width from its SM value is thus given by

$\frac{\Gamma_{\mathup{{{H}}},\text{model
dependent}}}{\Gamma_{\mathup{{{H}}}}^{\text{SM}}}=\sum_{i}\kappa_{i}^{2}\
\text{BR}_{i},$ (3)

where $\text{BR}_{i}$ is the SM branching ratio for the respective final
state. To obtain these branching ratios, a fixed value for the Higgs mass has
to be imposed. The theoretical uncertainties on the branching ratios taken
from [35] are ignored. To exclude effects from numerical rounding errors, the
sum of the BRs was normalised to unity.

Since at the first energy stage of CLIC no significant measurements of the
$\mathup{{{H}}}\to\mathup{{}^{\scriptstyle{+}}}\mathup{{}^{\scriptstyle{-}}}$,
$\mathup{{{H}}}\to\mathup{}\mathup{}$ and
$\mathup{{{H}}}\to\mathup{{{Z}}}\mathup{}$ decays are possible, the fit is
reduced to six free parameters with an appropriate rescaling of the branching
ratios used in the total width for $350\,\text{GeV}$.

Table 6: Results of the model-dependent global Higgs fit. Values marked “$-$” cannot be measured with sufficient precision at the given energy. The uncertainty of the total width is calculated from the fit results, taking the parameter correlations into account.  Parameter | Relative precision
---|---
| $350\,\text{GeV}$ | \+ $1.4\,\text{TeV}$ | \+ $3\,\text{TeV}$
| $500\,\text{fb}^{-1}$ | \+ $1.5\,\text{ab}^{-1}$ | \+ $2\,\text{ab}^{-1}$
$\kappa_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{{{Z}}}}$ | 0.57% | 0.37% | 0.34%
$\kappa_{\mathup{{{H}}}\mathup{{{W}}}\mathup{{{W}}}}$ | 1.1% | 0.21% | 0.14%
$\kappa_{\mathup{{{H}}}\mathup{{{b}}}\mathup{{{b}}}}$ | 2.0% | 0.41% | 0.24%
$\kappa_{\mathup{{{H}}}\mathup{{{c}}}\mathup{{{c}}}}$ | 5.9% | 2.2% | 1.7%
$\kappa_{\mathup{{{H}}}\mathup{}\mathup{}}$ | 3.9% | 1.5% | 1.1%
$\kappa_{\mathup{{{H}}}\mathup{}\mathup{}}$ | $-$ | 14.1% | 7.8%
$\kappa_{\mathup{{{H}}}\mathup{{{t}}}\mathup{{{t}}}}$ | $-$ | 4.3% | 4.3%
$\kappa_{\mathup{{{H}}}\mathup{{{g}}}\mathup{{{g}}}}$ | 3.2% | 1.6% | 1.2%
$\kappa_{\mathup{{{H}}}\mathup{}\mathup{}}$ | $-$ | 5.6% | 3.1%
$\kappa_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{}}$ | $-$ | 15.6% | 9.1%
$\Gamma_{\mathup{{{H}}},\text{md,derived}}$ | 1.6% | 0.41% | 0.28%
Figure 6: Illustration of the precision of the Higgs couplings determined in a
model-dependent fit in the studied three-stage CLIC programme. Note the
reduced $y$-axis range with respect to Figure 5.

As in the model-independent case the fit was performed in three stages, taking
the statistical errors at the three considered energy stages
($350\,\text{GeV}$, $1.4\,\text{TeV}$, $3\,\text{TeV}$) successively into
account. Each new stage also includes all measurements of the previous stages.
The total width is not a free parameter of the fit. Instead, its uncertainty,
based on the assumption given in Equation 3, is calculated from the fit
results, taking the full correlation of all parameters into account. Table 6
summarises the results of the model-dependent fit, and Figure 6 illustrates
the evolution of the precision over the full CLIC programme.

These results show that the CLIC Higgs physics programme, interpreted with a
combined fit of the couplings to fermions and gauge bosons as well as the
total width, and combined with the measurement of the self-coupling, will
provide a comprehensive picture of the Higgs properties. Each of the CLIC
stages contributes significantly to the total precision, with the first stage
near $350\,\text{GeV}$ providing the model-independent “anchor” of the
coupling to the $\mathup{{{Z}}}$ boson as well as a first measurement of the
total width and coupling measurements to most fermions and bosons. The higher-
energy stages add direct measurements of the coupling to top quarks, to muons
and photons as well as overall improvements of the branching ratio
measurements. Hence, they improve the uncertainties of the total widths and
all couplings except the one to the $\mathup{{{Z}}}$ boson already measured
with best precision in the first stage. They also provide a measurement of the
self-coupling of the Higgs boson. In a model-dependent analysis, the
improvement with increasing energy is even more significant than in the model-
independent fit, since the overall limit on all couplings imposed by the
model-independent measurement of the $\mathup{{{H}}}\mathup{{{Z}}}$ recoil
process is removed. With these results on Higgs couplings at the percent
level, CLIC will have strong capabilities to detect possible deviations from
the SM Higgs properties. It will thereby have a powerful handle on pinning
down influences of possible BSM phenomena [36, 37].

###  2.4 Top-quark physics

In addition to a broad and comprehensive Higgs physics programme, CLIC also
provides the opportunity to study the top quark with unprecedented precision
via production of $\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ pairs
in
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
collisions. Measurements of the top-quark properties are of special interest
as it is the heaviest elementary particle of the SM. Due to its mass, the top
quark couples strongest to the Higgs field and it has a central role in many
BSM models. Precision measurements of top-quark properties at
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
colliders promise therefore to be highly sensitive to physics beyond the SM.

In the following, two areas of top-quark physics at CLIC are described. The
first set of measurements will focus on the top-quark mass. The second will
explore the potential of measurements of other top-quark properties as probes
for BSM physics, for instance the top-quark coupling to $\mathup{{{Z}}}$ and .

####  2.4.1 Top-quark mass

Together with the Higgs mass, the top-quark mass is a key input parameter to
studies of the SM vacuum stability. With the precision of the Higgs mass as
measured by ATLAS and CMS [38], the uncertainty on the top-quark mass [39, 40,
41, 42] currently remains the leading uncertainty in tests of the SM vacuum
stability [43, 44]. While the statistical top-quark mass precision expected
for High-Luminosity LHC (HL-LHC) is in the order of 10 MeV, significant
systematic uncertainties of the direct mass measurement are expected in the
order of 600 MeV [45], for instance due to the ambiguity in the interpretation
of the top-quark mass parameter in the Monte Carlo event generators in terms
of the field theoretical mass scheme [46].

For CLIC two complementary techniques to measure the top-quark mass were
investigated. The first and more precise option is a scan of the top pair-
production cross section at several centre-of-mass energies close to the
threshold of approximately $\sqrt{s}=350$ $\mathrm{\,Ge\kern-1.00006ptV}$,
from which the top-quark mass can be extracted using a fit to the threshold
shape. The second option is the reconstruction of the top invariant mass from
its decay products.

Both techniques have been studied using full CLIC detector simulations [47]
including beam-induced and
non-$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ physics backgrounds
as well as a realistic CLIC luminosity spectrum. An input top-quark mass of
$m_{\mathup{{{t}}}}=174.0$ $\mathrm{\,Ge\kern-1.00006ptV}$ and a width of
$\Gamma_{\mathup{{{t}}}}=1.37$ $\mathrm{\,Ge\kern-1.00006ptV}$ were assumed.
The two dominant $\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ decay
modes corresponding to a branching ratio of 75% were considered. These are the
fully-hadronic decay mode
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}\to\mathup{{{\mathup{{{W}}}}}^{\scriptstyle{+}}}\mathup{{{b}}}\mathup{{{\mathup{{{W}}}}}^{\scriptstyle{-}}}\mathup{{\overline{{\mathup{{{b}}}}}}}\to\mathup{{{q}}}\mathup{{\overline{{\mathup{{{q}}}}}}}\mathup{{{b}}}\mathup{{{q}}}\mathup{{\overline{{\mathup{{{q}}}}}}}\mathup{{\overline{{\mathup{{{b}}}}}}}$
and the semi-leptonic decay mode
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}\to\mathup{{{\mathup{{{W}}}}}^{\scriptstyle{+}}}\mathup{{{b}}}\mathup{{{\mathup{{{W}}}}}^{\scriptstyle{-}}}\mathup{{\overline{{\mathup{{{b}}}}}}}\to\mathup{{{q}}}\mathup{{\overline{{\mathup{{{q}}}}}}}\mathup{{{b}}}\mathup{{{l}}}\mathup{}\mathup{{\overline{{\mathup{{{b}}}}}}}$
excluding final states. The top pair reconstruction and identification used
flavour tagging, kinematic fitting, and multivariate background rejection,
resulting in clean signal event samples.

##### Threshold scan

(a)

(b)

Figure 7:  a: $\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ cross
section as a function of centre-of-mass energy for
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ production simulated in
a scan of ten data sets of $10\,\mbox{\,fb}^{-1}$ each in steps of 1
$\mathrm{\,Ge\kern-0.90005ptV}$ around
$\sqrt{s}=350\,\mathrm{\,Ge\kern-0.90005ptV}$ [47]. b: Correlation between the
top-quark mass $m_{\mathup{{{t}}}}$ and the strong coupling constant
$\alpha_{s}$ extracted from the threshold scan [47].

Dedicated operation during the first CLIC energy stage would enable a
threshold scan of $\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$
production [47]. By collecting ten data sets of $10\,\mbox{\,fb}^{-1}$ each in
steps of 1 $\mathrm{\,Ge\kern-1.00006ptV}$ around
$\sqrt{s}=350\,\mathrm{\,Ge\kern-1.00006ptV}$, the
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ production cross
section can be measured as a function of centre-of-mass energy as shown in
7(a). In this centre-of-mass energy range, the
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ cross section rises
from 50 fb to about 500 fb amounting to several tens of thousands of
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ events. A study of the
threshold shape as discussed here can not be performed at hadron colliders,
where the parton-parton centre-of-mass energy is not known.

Theoretical evaluations of the evolution of the top pair production cross
section close to the threshold are since recently available at next-to-next-
to-next-to leading order (NNNLO), allowing for an accurate extraction of the
top-quark mass in the theoretically well-defined 1S mass scheme with an
uncertainty of the order of tens of MeV [48, 49]. Using a two-dimensional
template fit to the threshold, the 1S mass of the top quark and the strong
coupling constant $\alpha_{s}$ can be extracted simultaneously (see 7(b)). The
statistical uncertainty on the measured 1S top-quark mass using this method is
33 MeV. The total uncertainty, including also the theoretical uncertainty and
systematic uncertainties on the beam energy, the luminosity spectrum and the
background subtraction, amounts to approximately 50 MeV.

The 1S mass of the top quark extracted in this threshold scan can be
transformed into the $\overline{\text{MS}}$ mass scheme commonly used in
precision calculations. Even with the current world average value of
$\alpha_{s}$ [30] taken as external input for this conversion, this results
only into an additional theory uncertainty of the order of 10 MeV [50].

##### Invariant mass

The invariant mass measurement of the top quark has been studied for CLIC at
$\sqrt{s}=500\,$$\mathrm{\,Ge\kern-1.00006ptV}$, for an integrated luminosity
of 100 fb-1 [47]. With a top pair-production cross section of 530 fb at
$\sqrt{s}=500\,$$\mathrm{\,Ge\kern-1.00006ptV}$ this results in 53000
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ events. By using
maximum likelihood fits to the reconstructed invariant mass distributions,
shown in Figure 8 for fully-hadronic events, a top-quark mass compatible with
the input value was extracted that had a statistical precision of $80$ MeV
[47]. Relevant systematic uncertainties, for instance including the
uncertainty on the jet energy scale, are limited to a similar level as the
statistical uncertainty. The extracted top width is compatible with the input
value and it has a statistical uncertainty of 220 MeV.

Figure 8:  Distribution of reconstructed top-quark mass for events classified
as fully-hadronic [47]. The data points include signal and background events
for an integrated luminosity of 100 fb-1 at $\sqrt{s}=500$
$\mathrm{\,Ge\kern-0.90005ptV}$. The pure background contribution is shown by
the green solid histogram. The top-quark mass is extracted through a fit to a
probability density function (pdf) that includes detector resolution effects.

An advantage of the top-quark invariant-mass measurement is that it can be
performed at any centre-of-mass energy above the top pair production
threshold. The top-quark mass is then obtained in the context of the event
generator used in the comparison to data. Uncertainties when translating the
measured mass to the $\overline{\text{MS}}$ scheme could however be large.
These systematic uncertainties are expected to be larger than the experimental
uncertainties listed above [47, 46].

####  2.4.2 Top quark as a probe of BSM physics

For top-quark measurements as probes of BSM physics, a trade-off has to be
made between centre-of-mass energies optimised for available statistics, or
for small uncertainties on theoretical predictions, or for the expected
magnitude of BSM effects on the top sector. Details of these considerations
are described in the following, with example measurements at the first stage
of CLIC and an outlook on measurements at the subsequent energy stages.

##### Impact of initial CLIC energy stage on top BSM physics reach

The production of $\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$
events in
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
collisions sets on at approximately $\sqrt{s}=350$
$\mathrm{\,Ge\kern-1.00006ptV}$, and the cross section exhibits a steep rise
until a maximum of approximately 640 fb is reached near 420
$\mathrm{\,Ge\kern-1.00006ptV}$. Above this energy the cross section decreases
following an $1/s$ dependence. To record
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ events with high
statistics, operation close to the maximum in the
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ production cross
section is favourable.

In the threshold region, non-relativistic QCD leads to an uncertainty of 3%
[48]. Far away from the threshold, the uncertainty of NLO predictions is much
lower, for example 0.5% at $\sqrt{s}=500$ GeV [51]. Hence, a comparison of
data with theory predictions is more stringent at higher energies. In the
transition region around 380 GeV the matching between both approaches is
currently being worked on.

Taking into account that, in addition, relative contributions from many BSM
effects in the top sector are expected to increase as a function of the
centre-of-mass energy, operation at energies substantially above the top pair
production threshold is favourable.

The choice of the centre-of-mass energy of the initial stage of CLIC has to
take these considerations into account, while also considering the Higgs
physics reach discussed in Section 2.3.

##### Top-quark form-factor measurement at 380 GeV

At energies above the top pair production threshold,
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ pairs are produced
through s-channel processes via $\mathup{{{Z}}}$ boson or exchange. The
relative contributions of $\mathup{{{Z}}}$ boson and exchange to the
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ production depend on
the beam polarisation as well as on the top-quark polarisation. Hence the
couplings to $\mathup{{{Z}}}$ boson and can be extracted from forward-backward
and polarisation asymmetries of the produced top quarks. Since CLIC provides
the possibility of $\pm 80$% $\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
beam polarisation and since the top quarks decay before hadronisation, such
that their polarisation can be measured by studying their decay products, the
top-quark couplings to the electroweak gauge bosons can be studied in detail.

Figure 9: Uncertainties on the top-quark form factors (assuming SM values for
the remaining form factors), comparing estimations for HL-LHC, ILC and CLIC
[10]. The form factors are extracted from the measured forward backward
asymmetry and cross section. For the ILC, $\pm 80\%$
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$ polarisation and $\mp 30\%$
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}$ polarisation are considered
and for CLIC, $\pm 80\%$ $\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
polarisation is considered.

Simulation studies of the measurements of the top-quark form factors [51],
extracted from the top pair-production cross section and top forward-backward
asymmetries, have been performed for CLIC at 380
$\mathrm{\,Ge\kern-1.00006ptV}$ [10]. Figure 9 shows a comparison of the
uncertainties on the top-quark form factors between HL-LHC at 14
$\mathrm{\,Te\kern-1.00006ptV}$ [52, 53], ILC at 500
$\mathrm{\,Ge\kern-1.00006ptV}$ [54, 33, 55] and CLIC at 380
$\mathrm{\,Ge\kern-1.00006ptV}$. At ILC and CLIC, the top couplings to the
electroweak gauge bosons can be extracted with precisions at the percent
level, well beyond those projected for HL-LHC. Since the theory uncertainties
are not yet calculated at 380 $\mathrm{\,Ge\kern-1.00006ptV}$, the CLIC
uncertainties include a theory uncertainty of 3%, corresponding to the maximal
theory uncertainty on the
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ production cross
section at the threshold [51]. This is a very conservative upper limit.

As all couplings between top quarks and electroweak gauge bosons are predicted
to high precision by the SM, a stringent comparison between the observed and
the predicted couplings can be performed. In many BSM models the top couplings
to the electroweak interaction are substantially modified. This is the case,
for example, in composite Higgs models or extra dimension models, where
coupling modifications are of the order of 10% [56, 55, 46], resulting in a
large discovery potential for future
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}$
colliders. Additional information can also be extracted from an analysis of
the top-quark decays [57].

##### Top BSM physics outlook for subsequent CLIC stages

In addition to the measurements performed at the initial centre-of-mass energy
stage, CLIC allows for measurements at centre-of-mass energies of $\sim$1.4
$\mathrm{\,Te\kern-1.00006ptV}$ and 3 $\mathrm{\,Te\kern-1.00006ptV}$. This
offers an extended BSM physics potential in the top sector at CLIC in
comparison to ILC.
For operations above approximately 420 GeV, where the
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ production has its
maximum, the $\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ production
cross section decreases, resulting in a decreasing statistical precision in
the measurement of the top-quark properties. However, this might be
compensated by two effects. At higher collision energies the top quarks have
an increased boost resulting in a better separation between the decay products
of the two top quarks, leading most likely to an improved reconstruction of
the top-quark properties. Moreover, the relative contribution from new physics
in many BSM models increases with the centre-of-mass energy following
$s/\Lambda^{2}$, where $\Lambda$ is the scale of the new physics.
Dedicated simulation studies focussing on top-quark measurements at the CLIC
higher-energy stages are performed at the moment.

###  2.5 Physics beyond the Standard Model

Strategies for studying BSM physics at CLIC follow two different approaches,
depending on the nature of the new physics involved [11]. Direct detection of
new particles is possible up to the kinematic limit, typically up to
$\sqrt{s}/2$ for particles produced in pairs and $\sqrt{s}$ for single
particle production. In this area CLIC is particularly sensitive to
electroweak states and therefore complementary to the LHC. Much higher mass
scales are attainable through indirect searches, where precision measurements
of observables are compared with SM expectations. Both approaches have been
assessed for CLIC and the current findings are summarised below.

####  2.5.1 Direct searches for BSM physics

Based on the detector concepts described in Section 2.1 direct studies of the
BSM physics potential were performed at 1.4 $\mathrm{\,Te\kern-1.00006ptV}$
and 3 $\mathrm{\,Te\kern-1.00006ptV}$. Several of these studies make use of
SUSY models containing sparticles with masses within the kinematic limit.
Whether addressing sleptons, gauginos, squarks or heavy Higgs-like particles,
the studies confirm that CLIC can measure them accurately, typically to 1%
accuracy on their mass and up to the kinematic limit of typically $\sqrt{s}/2$
[4, 5, 58, 59, 60, 61]. These direct searches use SUSY particles as an
example. As SUSY provides a very wide range of states, all with different
signatures in the detector, these studies have a wide applicability to physics
scenarios in addition to SUSY.

####  2.5.2 Sensitivity of precision measurements to BSM physics

In many cases new physics beyond the kinematic limit of CLIC can still be
detected due to its effects on SM observables. Given their high masses,
precision measurements of Higgs and top are very powerful in this context, as
already indicated in the previous subsections. Various other indirect studies
are described in [4, 5, 11], among which are the two examples illustrated in
Figure 10. In 10(a) the process
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\rightarrow\mathup{{}^{\scriptstyle{+}}}\mathup{{}^{\scriptstyle{-}}}$
is studied at 1.4 $\mathrm{\,Te\kern-1.00006ptV}$ and 3
$\mathrm{\,Te\kern-1.00006ptV}$. This process is sensitive to the presence of
a high-mass $\mathup{{{\mathup{{{Z}}}}}^{\scriptstyle{\prime}}}$ boson.
Observables such as the total cross section, the forward-backward asymmetry
and the left-right asymmetry with $\pm 80\%$ electron polarisation are used in
the study. Depending on the effective parameters of the underlying theory (in
this case the minimal anomaly-free
$\mathup{{{\mathup{{{Z}}}}}^{\scriptstyle{\prime}}}$ model), a discovery reach
up to tens of $\mathrm{\,Te\kern-1.00006ptV}$ is attainable at CLIC.
Alternatively, if a high-mass
$\mathup{{{\mathup{{{Z}}}}}^{\scriptstyle{\prime}}}$ boson were discovered
earlier at the LHC, CLIC would be able to pin down its properties to high
accuracy [11, 62].

Another possibility concerns composite Higgs models, in which the Higgs boson
exists as a composite state of bound fermions. Using measurements of double-
Higgs production and single-Higgs production, CLIC could significantly reduce
the parameter space. At 3 $\mathrm{\,Te\kern-1.00006ptV}$ with
$1\,\mbox{\,ab}^{-1}$ of data it would provide an indirect probe up to a Higgs
composite scale of 20 $\mathrm{\,Te\kern-1.00006ptV}$ and 70
$\mathrm{\,Te\kern-1.00006ptV}$ respectively [11, 58], (see 10(b)).

An additional example is the study of triple gauge couplings in
$\mathup{{{\mathup{{{W}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{W}}}}}^{\scriptstyle{-}}}$
production, where coupling accuracies at the level of 10-4 are predicted [4],
thereby providing relevant input on BSM physics. Furthermore vector boson
scattering ($\mathup{{{W}}}$, $\mathup{{{Z}}}$) can be studied where the
sensitivity rises quickly with $\sqrt{s}$ [63].

Similarly, large numbers of $\mathup{{{W}}}$ bosons will be produced in
$\mathup{{{e}}}\mathup{{{e}}}\rightarrow\mathup{{{W}}}\mathup{{{W}}}$ and
$\mathup{{{e}}}\mathup{{{e}}}\rightarrow\mathup{{{e}}}\mathup{{{W}}}\mathup{}$
events at CLIC. For example, it was found in a generator-level study of
$\mathup{{{e}}}\mathup{{{e}}}\rightarrow\mathup{{{e}}}\mathup{{{W}}}\mathup{}$
events that the number of hadronic $\mathup{{{W}}}$ decays within the detector
volume is expected to be around $10^{7}$ at 1.4
$\mathrm{\,Te\kern-1.00006ptV}$ and $1.5\times 10^{7}$ at 3
$\mathrm{\,Te\kern-1.00006ptV}$. These samples provide the potential for a
measurement of the $\mathup{{{W}}}$ boson mass from its hadronic decays with a
few-MeV statistical accuracy. A full simulation study is foreseen to study the
impact of systematic effects, such as the uncertainty of the jet energy scale,
on this measurement [11].

(a)

(b)

Figure 10:  a: $\mathup{{{\mathup{{{Z}}}}}^{\scriptstyle{\prime}}}$ mass
discovery limit at $5\sigma$ from the measurement of
$\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{+}}}\mathup{{{\mathup{{{e}}}}}^{\scriptstyle{-}}}\rightarrow\mathup{{}^{\scriptstyle{+}}}\mathup{{}^{\scriptstyle{-}}}$
as a function of the integrated luminosity and for different coupling values
in the minimal anomaly-free
$\mathup{{{\mathup{{{Z}}}}}^{\scriptstyle{\prime}}}$ model. For more details
see [11, 62]. b: Summary plot of the current constraints (orange curves and
brown region) and prospects for direct and indirect probes at LHC and CLIC
(horizontal regions) of the strong interactions triggering electroweak
symmetry breaking. $m_{\rho}$ is the mass of the vector resonances and
$\xi=(v/f)^{2}$ measures the strengths of the Higgs interactions. For more
details see [11, 58].

###  2.6 Summary of physics requirements for the CLIC energy stages

With the above assessment of the CLIC physics potential for Higgs, top-quark
and BSM physics, one has the ingredients to reflect on the optimal choice for
the future CLIC energy stages.

A choice of 350 $\mathrm{\,Ge\kern-1.00006ptV}$ for the first energy stage
turns out to be close to optimal for initial precision Higgs studies. As
explained in Section 2.3 it gives access to the Higgs boson in the
$\mathup{{{H}}}\mathup{{{Z}}}$ production process, thereby providing a model-
independent measurement of the
$g_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{{{Z}}}}$ coupling of the Higgs to the
$\mathup{{{Z}}}$ boson. This measurement forms the cornerstone of all other
Higgs coupling measurements and determines the ultimate accuracy with which
Higgs couplings can be measured in a model-independent way at CLIC. As
discussed in Section 2.3 the $g_{\mathup{{{H}}}\mathup{{{Z}}}\mathup{{{Z}}}}$
coupling is best measured in events where the $\mathup{{{Z}}}$ decays to
$\mathup{{{q}}}\mathup{{\overline{{\mathup{{{q}}}}}}}$ at centre-of-mass
energies near 350 $\mathrm{\,Ge\kern-1.00006ptV}$. This centre-of-mass energy
is also favourable for the high-accuracy measurement of the top-quark mass
through a threshold scan, as shown in Section 2.4. However, a $\sqrt{s}$
choice above the $\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$
threshold, e.g. near 400 $\mathrm{\,Ge\kern-1.00006ptV}$, offers clear
advantages for the measurement of top-quark kinematic variables and forward-
backward asymmetry due to the additional boost of the produced top quarks.
Taking all these arguments together, a centre-of-mass energy of 380
$\mathrm{\,Ge\kern-1.00006ptV}$ appears to be a more optimal choice for the
first CLIC energy stage, as it combines favourable conditions for both Higgs
and top-quark physics. At this energy CLIC would collect $500\mbox{\,fb}^{-1}$
of data, complemented with $100\,\mbox{\,fb}^{-1}$ for a
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}$ threshold scan near 350
$\mathrm{\,Ge\kern-1.00006ptV}$.

At the higher energies, above 1 $\mathrm{\,Te\kern-1.00006ptV}$, Higgs and
top-quark physics continue to provide guaranteed precision physics cases.
Profiting from the increased cross sections at higher centre-of-mass energies,
combined with larger instantaneous luminosities, Higgs production through WW
and ZZ fusion yields significantly improved statistical accuracies, thereby
also giving access to rare Higgs decay modes. The measurement of the top
Yukawa coupling, through
$\mathup{{{t}}}\mathup{{\overline{{\mathup{{{t}}}}}}}\mathup{{{H}}}$
production, provides optimal accuracy in the range 1
$\mathrm{\,Te\kern-1.00006ptV}$ to 1.5 $\mathrm{\,Te\kern-1.00006ptV}$ [64,
31]. The measurement of the Higgs self-coupling profits greatly from
increasing rates at high $\sqrt{s}$, providing a unique opportunity for CLIC
to measure the self coupling down to the 10% level at
$\sqrt{s}=3\,\mathrm{\,Te\kern-1.00006ptV}$. Top pair production at the higher
CLIC energies has the potential of being a sensitive probe for BSM physics
(see Section 2.4). Overall the high-energy reach of CLIC provides significant
potential for studying BSM phenomena, either through accurate measurements of
new states previously discovered at LHC or by acting as a discovery machine in
its own right. For new particles produced in pairs direct detection is
possible up to the kinematic limit of $\sqrt{s}/2$. Indirect detection through
precision observables profits from high $\sqrt{s}$ in many cases as well, as
illustrated with the $\mathup{{{\mathup{{{Z}}}}}^{\scriptstyle{\prime}}}$ and
composite Higgs examples of Section 2.5.

Based on the current knowledge, CLIC delivers optimal physics potential when
constructed and operated in three main energy stages: 380
$\mathrm{\,Ge\kern-1.00006ptV}$, 1.5 $\mathrm{\,Te\kern-1.00006ptV}$ and 3
$\mathrm{\,Te\kern-1.00006ptV}$. Here, the low-energy stage is chosen for
optimal Higgs and top-quark physics reach, while 3 TeV is the maximum which
can presently be envisaged. The choice of the intermediate energy stage at 1.5
$\mathrm{\,Te\kern-1.00006ptV}$ is driven by the fact that this is the maximum
energy that can be reached with a single CLIC drive-beam complex.
Realistically, one can assume that CLIC will operate for the equivalent of 125
days per year at 100% efficiency (see Section 4.3). A period of luminosity
ramp-up will be necessary at each stage of CLIC. Together with the expected
peak luminosity at the different energies (see Section 4) this results in the
integrated luminosities listed in Table 7.

Table 7: Proposed CLIC energy staging scenario for optimal physics performance, assuming between 5 and 7 years of running including luminosity ramp-up at each of the three energy stages as described in Section 4.2. Stage |  $\sqrt{s}$ (GeV) |  $\mathcal{L}_{\text{int}}$ ($\text{fb}^{-1}$)
---|---|---
1 | 380 | 500
350 | 100
2 | 1500 | 1500
3 | 3000 | 3000

##  3 CLIC post-CDR accelerator optimisation

###  3.1 Overview

A first optimisation of the parameters for a 3 TeV CLIC accelerator complex
was performed as early as 2008, based on performance and cost models developed
at that time. During the years leading to the CDR in 2012 [3, 5], a large
number of simulation studies and R&D tests validated most aspects of the CLIC
design. In parallel, more detailed models of power consumption and cost of a 3
TeV CLIC facility were developed for the CDR. The results of those studies,
together with physics scenarios envisaged at the time, provided the basis for
the proposal to build CLIC in energy stages. In the CDR [5], an example of the
implementation and operation of CLIC in three energy stages is described.
During the past years more high-gradient tests of the main linac accelerating
structures have been made, which allow a review of the performance limitations
that are used in the optimisation. The gradient $G$ which can be achieved in
these structures is largely limited by vacuum arcing, otherwise known as radio
frequency (RF) breakdowns. For a reliable operation of CLIC, RF breakdowns
must occur during less than 1% of the RF pulses in any of the installed
structures along the entire length of the main linacs. This translates into
the specification of “fewer than $3\times 10^{-7}$ breakdowns per pulse and
per metre of accelerating structure”.

Designing structures with the required low breakdown rates at the design
gradient is done by constraining certain RF parameters, such as the maximum
local power along the surface of the structure when an RF pulse is sent
through. Experiments and long-term testing of CLIC RF structures are ongoing.
To first approximation, these tests confirm the assumptions for the RF
constraints used for the CDR. For example, an RF structure which does not have
features necessary for higher-order-mode damping (damping will be required for
the operation of the structures with intense beam trains) reached a gradient
well above the nominal 100 MV/m for an RF pulse of 180 ns, complying with the
parameters assumed in the CDR. Other RF structures that include the features
needed for damping fell slightly short of the goal stated in the CDR.
Presently, incremental improvements in the design and production of the RF
structures are being implemented, aiming to have “damped” structures
performing at the same high level as “undamped” ones. Given the observations
on performance of the RF structures, a scale $S$111also referred to as safety
factor or safety margin describing the RF limits has been introduced as a
parameter in the optimisation models used for the CLIC re-baselining. A value
of $S=1.0$ corresponds to the already achieved performance using RF structures
with damping features, whereas e.g. $S=1.1$ assumes that there will be a 10%
improvement of the gradient while maintaining the low breakdown rates (i.e.
corresponding approximately to the current performance of “undamped”
structures)222occasionally, a range of values from $S=0.8$ to $S=1.2$ is used
to demonstrate parameter dependencies.

In a scenario of construction of CLIC in energy stages, a reasonably
conservative assumption is $S=1.0$ for the first stage, when limited
experience on RF structures is available. In addition we will see in
subsequent sections that the optimum gradient for lower energy stages is in
any case lower than 100 MV/m. For the second and third energy stages, the
additional development time, production and operational experience are
expected to contribute to improved structure performance.

In the present re-baselining study, the first (380 GeV) and final (3 TeV)
stages are being considered at the outset, and the nominal gradient in the RF
structures of 100 MV/m is assumed for CLIC at 3 TeV. The parameters chosen for
the intermediate energy stage are then, to a large extent, given by the
initially defined parameters for the 380 GeV and the 3 TeV CLIC accelerator.
Within this approach, three different strategies emerge for designing a staged
construction and operation of CLIC:

In the first strategy, priority is given to optimising the cost of the 380 GeV
energy stage. In such a strategy, one would use an RF structure design and RF
pulse length fully optimised for the first energy stage, without taking
parameter optimisation for the higher energy stages into account. As a
consequence, for the upgrades to higher energies, all RF structures would have
to be replaced by new ones, i.e. by the structures optimised for the 3 TeV
energy stage. In such an “unconstrained” scenario, one would be free to change
the length of drive beam decelerating sectors, and hence the RF pulse length,
when moving from the first energy stage to higher energies. Note that this
scenario would allow optimisation of the first energy stage (i.e. having the
lowest initial cost), however with the consequence of the highest overall cost
for the three energy stages of the overall CLIC project.

In the second strategy, priority is given to the overall optimisation of the
CLIC project with its three energy stages. In this strategy, structure design
and RF pulses are optimised for the final energy stage. This implies that the
initial 380 GeV stage will already be built using RF structures designed for
the final high energy stage, using also the gradient and RF pulse length
designed for 3 TeV. While this scenario minimises the total CLIC cost for the
three stages, it compromises the performances and increases the cost of the
initial low-energy stage. Moreover, since high-performance high-gradient RF
structures are required from the outset, this scenario does not allow
advantage to be taken of continuing improvements in the design and performance
of RF structures during the operation of the first energy stage.

The third strategy compromises between the other two. Different compromise
solutions between the two strategies outlined above may be considered.

As detailed below, we have chosen a staging scenario where an optimised design
of RF structures is chosen for the first CLIC stage at 380 GeV, and structures
of a different design are added for the energy upgrades (i.e. the structures
used for the first stage can be re-used in the later stages). The same RF
pulse length has been chosen for the first and the later energy stages,
allowing one to avoid major modifications to the drive beam generation when
upgrading to later stages.

The following subsections describe the details of the methodology used in the
recent CLIC optimisation for a staged construction. A full description of the
staging implementation chosen, including the corresponding parameters, is
presented in Section 4.

###  3.2 Ingredients for the optimisation procedure

A systematic methodology was developed for determining the main beam
parameters and subsequently the cost and power consumption of an optimised
CLIC design, (a) for a given physics performance goal and (b) for a given main
linac accelerating structure.

The physics performance goal is parametrised by the centre-of-mass energy, the
luminosity and the fraction of luminosity above 99% of the nominal centre-of-
mass energy. Physics benchmark studies have shown that the impact of beam-
induced backgrounds can efficiently be minimised through optimised detector
design and the application of selection criteria during event reconstruction
[4]. Therefore background considerations are not part of the accelerator
optimisation process.

The accelerating structure is parameterised by the number of cells, the phase
advance per cells, the loaded gradient and the iris radius and thickness of
the first and the last cell. The iris radius and thickness are assumed to
decrease linearly along the structure.

####  3.2.1 Beam parameters

The possible choices of the beam parameters and their interdependence have
been established by detailed beam dynamics studies. This allows one to select
the optimum beam parameters for a given main linac structure design. The main
constraints are:

  * •

The bunch charge and length at the collision point and the bunch spacing are
limited by wakefield effects in the main linac, in particular by the
accelerating structure design.

  * •

The horizontal emittance is determined mainly by the damping ring as a
function of the bunch charge; the ring to main linac transport system and main
linac slightly increase this value.

  * •

The vertical emittance is given by the damping ring, the ring to main linac
transport systems, the main linac and the beam delivery system.

  * •

The vertical beta-function at the interaction point is determined by the final
focus system.

  * •

The horizontal beta-function has two sources for the lower limit. One limit
arises from the final focus system. The other limit arises from the
beamstrahlung. It depends on the bunch charge and the required quality of the
luminosity spectrum.

  * •

The minimum spacing between the bunches is determined by the long-range
wakefields in the main linac.

  * •

The number of bunches in each train is finally determined by the luminosity
target and the integrated luminosity per bunch. A repetition rate of 50 Hz for
the pulses is assumed. This allows to lock the RF to the frequency of the
mains power and reduces pulse-to-pulse variations of the RF and of potential
stray fields.

####  3.2.2 RF structure design

One of the key elements which has made the overall optimisation of the CLIC
accelerator complex possible is the parameterisation of the full RF properties
of the accelerating structures [65, 66] including fundamental RF parameters
(the ratio of impedance over stored energy $R/Q$, the group velocity, the beam
loading, the efficiency, etc.) and higher-order-mode properties. The high-
gradient parameterisation makes a gradient and breakdown rate performance
prediction based on the structure geometry for a given fabrication technology.
The prediction is based on geometry and RF pulse length through a number of
quantities including peak surface electric field, peak surface magnetic field,
overall power-flow and a local power flow. The limiting values for these
quantities are based on many test results from prototype structures with
different geometries used in the high-gradient testing programme carried out
in the context of the CLIC study. The highest achieved values in different
tests indicate that the baseline CLIC 3 TeV structure CLIC_G described in the
CDR (its properties will be listed in Table 8) should perform above 100 MV/m
including the power overhead needed for beam loading. Currently, 3 TeV-type
prototype baseline structures (TD26CC in the test structure nomenclature) are
being tested and the results are being analysed. The results for the
prototypes give gradients very close to 100 MV/m at the target breakdown rate
of $3\times 10^{-7}\,\text{pulse}^{-1}\,\text{m}^{-1}$ when power overhead for
beam loading is included [67]. The high-gradient field values derived from
these tests alone imply that a minor re-design would give the full 100 MV/m.
Higher gradients at low breakdown rates have already been achieved with
undamped structures (the T24 structure). In addition, a number of fabrication
issues have been uncovered in the prototypes, such as excessive radii on cell
walls for waveguide damped structures [67]. Moreover, a number of improvements
to the individual cells have been identified, e.g. optimised damping waveguide
width [68], and the RF conditioning process is far better understood [69]. A
new generation of prototypes which implement these improvements is now under
preparation and we expect that they will fully meet the 100 MV/m
specification. In order to make comparison to past results as direct as
possible, it was decided to maintain the current basic parameters for the test
structures (e.g. iris aperture radius range and number of cells). The baseline
design is also left unchanged to maintain consistency between the design and
the testing programme. Finally, changing the baseline design now, based on
partial high-gradient testing results with many improvements expected for the
near future, does not seem appropriate.

####  3.2.3 Cost and power models

The cost model for the re-baselining is based on the cost estimates for the
CDR, with some updates for the drive beam complex. The cost of the drive beam
complex and the main linac have been included in the model. In addition to the
technical equipment, the main linac tunnel, the turn-arounds in the main linac
and the building housing the drive beam accelerator are included. This model
reflects most of the dependence of the cost on the accelerating structure
design and on the beam parameters. For example, the cost of the beam delivery
system does not depend on the structure design. The main beam injector cost
will depend on the beam parameters. However, for a given luminosity this
dependence will be very weak.

The cost model includes in particular:

  * •

The cost of the main linac takes the total length into account and the impact
of the accelerating structure length; longer structures lead to lower cost.

  * •

The cost of the drive beam accelerator is based on detailed cost models for
the modulators, the klystrons, the RF waveguides and the accelerating
structures.

  * •

The cost of the building housing the drive beam accelerator and of the
associated infrastructure are scaled according to the peak power of the drive
beam klystrons. This ensures that the building can house the RF units of the
drive beam complex also when the modulators are upgraded to the full drive
beam pulse length for 3 TeV, in order to provide enough pulses. In contrast to
the CDR, the buildings and infrastructure for additional RF units will not be
provided from the start but will be upgraded once the higher energy stages are
realised.

  * •

The other components, such as the combiner rings and turn-arounds are assumed
to have a fixed unit cost, independent of the CLIC centre-of-mass energy.

The power consumption model is based on the CDR [3, 70]. It includes the whole
accelerator complex. The power is calculated separately for the RF components
and the magnets. In addition the power consumption of the cooling water and
air cooling are calculated based on the power consumption for RF and magnets
and taking into account the CDR models of the distribution of these power
losses in each sub-system.

The following parts of the accelerator complex are covered:

  * •

The drive beam generation complex. For the drive beam RF power the model is
analytic and based on the updated designs of the modulators, klystrons and
accelerating structures. For the magnets of the drive beam complex, the power
consumption is scaled according to the drive beam energy.

  * •

Drive beam frequency multiplication. The power consumption is scaled according
to the beam energy.

  * •

Drive beam distribution system. The power consumption is scaled according to
system length, number of turn-arounds and beam energy.

  * •

Main beam injector complex. The RF power consumptions of the main beam
injectors, the predamping rings, the damping rings and the booster linac are
scaled with the total average beam current. The power for magnets is constant.

  * •

Main Linac. The power for the magnets is proportional to the linac length.

  * •

Beam delivery system. Its power consumption does not depend on the simulation
parameters.

###  3.3 Optimisation procedure and results

The parameter optimisation has been performed by defining the target energy
and luminosity. A scan was performed over a large number of different
parameter points, each consisting of a specific main linac accelerating
structure and loaded gradient, see Figure 11.

In the optimisation procedure, each structure is described by its frequency
$f$, length $L_{\text{structure}}$ and phase advance per cell $\phi$ as well
as by the initial and final cell iris aperture radii and thicknesses ($a_{1}$,
$a_{2}$, $d_{1}$ and $d_{2}$, respectively) [71]. It is assumed that the
structure cells are linearly tapered between these initial and final cells.
For each loaded gradient $G$, the RF parameters are used to determine the beam
parameters. This allows to determine the number of bunches per train to reach
the luminosity target and hence the RF pulse length. A final check is
performed on whether this operation point respects the RF limitations, in
which case the cost of the accelerator complex is calculated and the parameter
set is stored. Here, the parameter $S$ is taken into account in the definition
of the RF limits.

Figure 11: An illustration of the accelerator parameter derivation based on
the parameters of the main linac accelerating structure.

In the optimisation scans, after some exploratory scans the most interesting
ranges of parameters were studied. The gradients $G$ range typically from 50
to 120 MV/m, the accelerating structure length $N_{\text{c}}$ from 20 to 60
cells, the aperture radii $a_{1}$ and $a_{2}$ each from $0.08\lambda$ to
$0.18\lambda$ (where $\lambda$ is the RF wavelength) and the thicknesses
$d_{1}$ and $d_{2}$ range each from 0.11 to 0.39 of the cell length.

####  3.3.1 Optimum at 3 TeV

Figure 12: Possible average aperture radii $a$ normalised to the RF wavelength
$\lambda$ and number of cells $N_{\text{c}}$ for the structures that meet the
luminosity goal at 3 TeV (in yellow). The most efficient structures, which do
not require more than 1%, 3% or 5% higher power consumption than the best, are
indicated by blue, purple and orange colours. For all parameter combinations
without a point, no structure solution is found. The spot “$\times$” indicates
the parameters of the CDR structure (“CLIC_G”). Left: The solutions based on
the current state of the conservative RF limits. Right: The solutions for
$S=1.2$.

Figure 13: The RF pulse length $\tau_{\text{RF}}$ and number of bunches
$n_{\text{b}}$ for the most power efficient structures at 3 TeV. The different
colours indicate the relative cost increase $\Delta\,c$ with respect to the
minimum cost. Comparison with the reference line shows that for equal pulse
length fewer bunches are needed when better RF performance is assumed. Left:
For the conservative RF limits ($S=1.0$) and a gradient of $G=100$ MV/m.
Right: For $S=1.2$ and a gradient of $G=120$ MV/m.

The possible structure parameters for a 3 TeV design are shown in Figure 12.
On the left-hand side, the options for $S=1.0$ are shown. The optimum
structure has the same aperture radii as CLIC_G, the structure of the CLIC
design documented in the CDR, but it is shorter by four cells. On the right-
hand side, the options for $S=1.2$ are shown. Again the optimum structure is
similar to CLIC_G, though slightly longer.

In Figure 13, the optimum pulse lengths and number of bunches per train are
shown for the conservative RF limits and $G=100$ MV/m. The current pulse
length of $\tau_{\text{RF}}=244\,\text{ns}$ is well within this optimum range.
If larger gradients can be reached, this optimum does not shift by very much,
as can be seen on the right-hand side of the figure. Here, a somewhat
optimistic value of $S=1.2$ and a gradient of $G=120$ MV/m are used for the
demonstration.

While experimental results from various other structure tests are positive, it
still remains to be demonstrated that CLIC_G can reach the fully loaded
gradient of 100 MV/m. Other structures can reach this gradient using more
pessimistic assumptions about the RF limits. Designs based on these structures
require similar RF pulse lengths and number of bunches per train as the CDR
design. Hence an RF pulse length of $\tau_{\text{RF}}=244\,\text{ns}$ remains
a good choice for the staged design. This remains true even if larger
gradients can be reached in the future.

####  3.3.2 Optimum at 380 GeV

Figure 14: Left: Cost and power consumption of the different possible designs
at a centre-of-mass energy of 380 GeV and a luminosity of $L=1.5\times
10^{34}\,\text{cm}^{-2}\text{s}^{-1}$. Different safety margins for the
gradient are used. Right: Cost and power consumption with a gradient safety
margin of 10% ($S=1.1$) for different luminosities (in units of
$10^{34}\text{cm}^{-2}\text{s}^{-1}$).

The cost and power consumption of the different designs at 380 GeV are shown
in Figure 14. In all cases, the cheapest variants of CLIC have a power
consumption close to the minimum. Hence the cheapest design will always be
used as the optimum choice. The safety margin in the gradient has a small
impact on the cost. The choice of 10% margin therefore does not lead to a
significant cost or power consumption increase.

Aiming at higher instantaneous luminosities leads to somewhat higher cost and
power consumption. On the other hand, reducing the luminosity below the target
value of $L=1.5\times 10^{34}\text{cm}^{-2}\text{s}^{-1}$ would only result in
minor cost saving.

####  3.3.3 Staging strategy

Figure 15: One of the potential staging concepts. In this solution, the
modules at the beginning of the previous main linac are moved to the new
beginning during the upgrade.

The concept of the staging is illustrated in Figure 15. In the first stage,
the linac consists of accelerating structures that are optimised for this
energy range, while respecting the constraints for the energy upgrade. When
upgrading to higher energy, the modules containing these structures will be
moved to the beginning of the new linac and the remaining space is filled with
new structures that are optimised for 3 TeV. Alternatively the old structures
could be evenly distributed along the new linac.

This scheme places additional constraints on the first energy stage. In order
to minimise modifications of the drive beam complex, the RF pulse length of
the first stage is chosen to be the same as for the subsequent energy stages.
In particular the turn-arounds in the main linac can be reused. Within the
main beam pulses the bunches have the same spacing at all energy stages to
minimise the impact on the main beam production complex. To be able to
accelerate the full train of the final stage, the fill time of the first-stage
structures must be shorter and the bunch charge limit higher than in the final
stage.

Figure 16: The minimum cost of the first energy stage as a function of the
luminosity target. The fully optimised (opt.) case and the one adapted for the
upgrade (match.) are shown.

Figure 16 illustrates the minimum cost of the first stage as a function of the
luminosity. The values for the fully optimised case and for the solution using
the constraints from the 3 TeV stage are shown. As can be seen, the cost
difference is rather small, though slightly increasing towards higher
luminosities. For the target value of $L=1.5\times
10^{34}\,\text{cm}^{-2}\text{s}^{-1}$ at 380 GeV, the cost increases from 3.45
to 3.5 in arbitrary units.

The gradient of the structures for the first stage is 72 MV/m. Consequently
four decelerator stages are required per main linac in the first stage. The
upgrade to 3 TeV requires an additional 21 decelerator stages.

The structure parameters of the optimised structure for the first energy
stage, in the following called “DB244” as it is optimised for drive beam
acceleration and a 244 ns RF pulse length, are shown in Table 8. For
comparison the parameters of the CDR structure CLIC_G are also listed.

Table 8: The parameters for the CLIC_G and the DB244 structure designs.  Parameter | Symbol | Unit | CLIC_G | DB244
---|---|---|---|---
Frequency | $f$ | GHz | 12 | 12
Acceleration gradient | $G$ | MV/m | 100 | 72
RF phase advance per cell | $\Delta\phi$ | ∘ | 120 | 120
Number of cells | $N_{\text{c}}$ |  | 28 | 33
First iris radius / RF wavelength | $a_{1}/\lambda$ |  | 0.126 | 0.1625
Last iris radius / RF wavelength | $a_{2}/\lambda$ |  | 0.094 | 0.104
First iris thickness / cell length | $d_{1}/L_{\text{c}}$ |  | 0.200 | 0.303
Last iris thickness / cell length | $d_{2}/L_{\text{c}}$ |  | 0.120 | 0.172
Number of particles per bunch | $N$ | $10^{9}$ | 3.7 | 5.2
Number of bunches per train | $n_{\text{b}}$ |  | 312 | 352
Pulse length | $\tau_{\text{RF}}$ | ns | 244 | 244
Peak input power into the structure | $P_{\text{in}}$ | MW | 61.3 | 59.5

##  4 CLIC staging baseline

Figure 17: CLIC footprints near CERN, showing the three implementation stages.

The proposed CLIC staging scenario is described in the following sections. The
accelerator is foreseen to be built in three stages with centre-of-mass
energies of 380 GeV, 1.5 TeV and 3 TeV. An implementation plan for the three
CLIC stages at CERN is shown in Figure 17.

###  4.1 Description and performance parameters

The CLIC accelerator can be built in energy stages, re-using existing
equipment for subsequent stages. At each energy stage the centre-of-mass
energy can be tuned to lower values, down to a third of the nominal energy,
with limited loss of luminosity performance [5]. The key parameters of the
present scenario, with stages at 380 GeV, 1.5 TeV and 3 TeV are given in Table
9. In this scenario the first and second stages use a single drive-beam
generation complex to feed both linacs, while in the third stage two drive
beam complexes are needed. The schematic layouts of the CLIC accelerator
complex at 380 GeV and 3 TeV are shown in Figure 18 and Figure 19.

Table 9: Parameters for the CLIC energy stages. The power consumptions for the 1.5 and 3 TeV stages are from the CDR; depending on the details of the upgrade they can change at the percent level. Parameter | Symbol | Unit | Stage 1 | Stage 2 | Stage 3
---|---|---|---|---|---
Centre-of-mass energy | $\sqrt{s}$ | GeV | 380 | 1500 | 3000
Repetition frequency | $f_{\text{rep}}$ | Hz | 50 | 50 | 50
Number of bunches per train | $n_{b}$ |  | 352 | 312 | 312
Bunch separation | $\Delta\,t$ | ns | 0.5 | 0.5 | 0.5
Pulse length | $\tau_{\text{RF}}$ | ns | 244 | 244 | 244
Accelerating gradient | $G$ | MV/m | 72 | 72/100 | 72/100
Total luminosity | $\mathcal{L}$ | $10^{34}\;\text{cm}^{-2}\text{s}^{-1}$ | 1.5 | 3.7 | 5.9
Luminosity above 99% of $\sqrt{s}$ | $\mathcal{L}_{0.01}$ | $10^{34}\;\text{cm}^{-2}\text{s}^{-1}$ | 0.9 | 1.4 | 2
Main tunnel length |  | km | 11.4 | 29.0 | 50.1
Number of particles per bunch | $N$ | $10^{9}$ | 5.2 | 3.7 | 3.7
Bunch length | $\sigma_{z}$ | $\upmu\mathrm{m}$ | 70 | 44 | 44
IP beam size | $\sigma_{x}/\sigma_{y}$ | nm | 149/2.9 |  $\sim$ 60/1.5 |  $\sim$ 40/1
Normalised emittance (end of linac) | $\epsilon_{x}/\epsilon_{y}$ | nm | 920/20 | 660/20 | 660/20
Normalised emittance (at IP) | $\epsilon_{x}/\epsilon_{y}$ | nm | 950/30 | — | —
Estimated power consumption | $P_{\text{wall}}$ | MW | 252 | 364 | 589
Figure 18: Overview of the CLIC layout at $\sqrt{s}=380$ GeV. Only one drive
beam complex is needed for the first (and second) stage of CLIC.  Figure 19:
Overview of the CLIC layout at $\sqrt{s}=3$ TeV.

###  4.2 Operating scenario and luminosities

The CLIC project as outlined is an ambitious long-term programme, with an
initial 7 year construction period [5] and three energy stages each lasting 7,
5 and 6 years respectively to achieve the integrated luminosity goals,
interrupted by 2-year upgrade periods. The overall duration of the three-stage
programme is 22 years from the start of operation. The operating scenario
currently foreseen for the complete CLIC programme is sketched in Figure 20
and Figure 21 in terms of the luminosity and integrated luminosity as a
function of the year of operation. The duration of each stage is defined by
the integrated luminosity targets of 500 fb-1 at 380 GeV, 1.5 ab-1 at 1.5 TeV
and 3 ab-1 at 3 TeV collision energy. During the first stage a top threshold
scan will be performed near 350 GeV. For this scan an additional integrated
luminosity of 100 fb-1 will be collected during a few months of CLIC
operation.

Figure 20: Luminosity per year in the considered staging scenario. Years are
counted from the start of beam commissioning. This figure includes luminosity
ramp-up of four years (5%, 10%, 25%, 50%) in the first stage and two years
(25%, 50%) in subsequent stages. Figure 21: Integrated luminosity in the
considered staging scenario. Years are counted from the start of beam
commissioning. The luminosity ramp-up corresponds to what is described in
Figure 20.

###  4.3 Power and energy consumption

The nominal power consumption of CLIC at 380 GeV centre-of-mass energy has
been estimated using the parametric model [70] derived from the estimates of
the CDR [3]. This yields a total of 252 MW for all accelerator systems and
services, including experimental area and detectors and taking into account
network losses for transformation and distribution on site. The breakdowns of
this value per domain of the CLIC accelerator complex and per technical system
are shown graphically in Figure 22. Most of the power is used in the drive-
beam and main-beam injector complexes, comparatively little in the main
linacs. Among the technical systems, the RF represents the major consumer.

Figure 22: Estimated power consumption of CLIC in MW at a centre-of-mass
energy of 380 GeV. The contributions add up to a total of 252 MW. Left:
breakdown of power consumption between different domains of the accelerator
complex. Right: breakdown of power consumption between different technical
systems.

Table 10 shows the nominal power consumption of CLIC at the different stages,
as well as the residual values for two modes corresponding to short (“waiting
for beam”) and long (“stop”) beam interruptions. At any stage the power
consumption has a large volatility, allowing CLIC to be operated as a peak-
shaving facility for the electrical network, matching not only seasonal, but
also daily fluctuations of the demand. This particular feature constitutes a
strong asset towards optimal energy management, a necessary approach in view
of the large values of power consumption of the CLIC complex during nominal
operation.

Table 10: CLIC estimated power consumption for the updated staging scenario. Values at the 1.5 TeV and 3 TeV centre-of-mass energy stages are taken from the CDR [3].  $\sqrt{s}$ [TeV] | $P_{\textrm{nominal}}[\textrm{MW}]$ | $P_{\textrm{waiting for beam}}[\textrm{MW}]$ | $P_{\textrm{stop}}[\textrm{MW}]$
---|---|---|---
0.38 | 252 | 168 | 30
1.5 | 364 | 190 | 42
3.0 | 589 | 268 | 58

Estimating yearly energy consumption from the power numbers requires an annual
operational scenario (Figure 23). In any “normal” year, i.e. once CLIC will
have been fully commissioned, we consider a 90-day annual shutdown, and an
additional 50 days of scheduled maintenance stops (typically 1 day per week
and 1 week after every 2 months of running). Out of the remaining 225 days, we
assume 80% availability, i.e. 45 days of fault-induced stops. This leaves 180
days for operation, of which 55 days are allocated to machine development and
tuning runs, thus yielding 125 days for physics data taking (“luminosity
runs”). This is the assumption used for estimating the build-up of integrated
luminosity in Figure 21.

Figure 23: Operation schedule in “normal” year (days/year).

For energy consumption, one also has to consider reduced operation in the
first years at each energy stage, similar to what was done in the CDR [3]. For
example, at 380 GeV centre-of-mass energy a single positron target is used for
the first three years (10 MW less with respect to nominal).

During the first year at each centre-of-mass energy, we consider the 180 days
of operation to be composed of three periods of 60 days each. In the first
period, only one bunch train is produced in order to commission the drive-beam
generation complex, and then to commission each decelerator in turn, one at a
time. In the second period, the main linacs are commissioned, one at a time.
Nominal operation occurs during the third period at nominal power. The energy
is the power integrated over time, including the period without beam. During
operation with beam, an additional down-time of 50% is taken into account in
the first year.

During the second year at each centre-of-mass energy, we consider the 180 days
of operation to be composed of two periods of 90 days. In the first period,
only one main linac is powered at a time and the additional down-time is taken
at 30%. Nominal conditions are assumed in the second period. The third and
following years are nominal in all centre-of-mass energy stages. The evolution
of electrical energy consumption over the years is illustrated in Figure 24.
For comparison, CERN’s energy consumption in 2015 was approximately 1.3 TWh,
of which the accelerator complex used approximately 90%.

Figure 24: Estimated yearly energy consumption of CLIC.

####  4.3.1 Additional energy-saving options

Several paths of development aiming at saving power and energy have been
identified and are under investigation. The first one consists in achieving
power sobriety by re-design, possibly trading operation expenditure against
investment costs. This is what was done for the re-optimisation of the
accelerating structures described under Section 3.3. Other possibilities are
lower current density in normal-conducting magnets and cables, use of
permanent or ”super-ferric” magnets [72] and reduction of heat loads to the
ventilation system through enhanced use of water cooling. A second path aims
at improving efficiency in the use of electrical energy, e.g. by improving
network-to-RF power conversion profiting from ongoing developments of more
efficient modulators and klystrons [73]. Overall, at 380 GeV the total
potential for such power savings is estimated to be around 30 MW, thus
lowering the nominal power consumption to approximately 220 MW (see Table 10).
In addition, waste heat recovery may also constitute an interesting option in
view of the large power rejected into water, provided that the heat rejection
temperature is high enough to be utilised and that associated needs exist in
the neighbourhood.

###  4.4 Cost estimate

The CDR [5] presented value estimates of CLIC at 500 GeV centre-of-mass energy
for two staging scenarios, A and B. In scenario A the 500
$\mathrm{\,Ge\kern-1.00006ptV}$ stage deploys dedicated RF structures with a
gradient of 80 MV/m, whereas scenario B uses identical RF structures with 100
MV/m gradient at all energy stages. Scenario A has a better luminosity
performance at 500 $\mathrm{\,Ge\kern-1.00006ptV}$, while scenario B is more
cost effective. These value estimates were built bottom-up from unit costs and
quantities for components to subdomains to complete domains, following the
work breakdown structure of the project. “On-the-shelf” spare components were
not included as they would be charged to the operation budget rather than the
construction budget. However, “hot spares”, i.e. spare components installed
and operational to provide on-line redundancy were part of the value
estimates. Unit costs were obtained from prices paid for other similar
supplies or scaled from them after adequate escalation, and from specific
industrial studies when the former were not available. Uncertainties stemming
from technical and commercial risks were also quantified, the latter from a