# Design of a Space-based Near-Solar Neutrino Detector for the vSOL Experiment

N. Solomey111Email<EMAIL_ADDRESS>J. Folkerts222Email:
<EMAIL_ADDRESS>Mailing address: Jonathan Folkerts, Wichita
State University, Campus box 32, 1845 Fairmount St., Wichita, KS 67260
Telephone: (316) 978-3991 H. Meyer333Email<EMAIL_ADDRESS>C. Gimar
J. Novak444Email<EMAIL_ADDRESS>B. Doty555Email:
<EMAIL_ADDRESS>T. English666Email<EMAIL_ADDRESS>L. Buchele  A. Nelsen  R. McTaggart777Email<EMAIL_ADDRESS>M.
Christl888Email<EMAIL_ADDRESS>
###### Abstract

The concept of putting a neutrino detector in close orbit of the sun has been
unexplored until very recently. The primary scientific return is to vastly
enhance our understanding of the solar interior, which is a major NASA goal.
Preliminary calculations show that such a spacecraft, if properly shielded,
can operate in space environments while taking data from neutrino
interactions. These interactions can be distinguished from random background
rates of solar electromagnetic emissions, galactic charged cosmic-rays, and
gamma-rays by using a double pulsed signature. Early simulations of this
project have shown this veto schema to be successful in eliminating background
and identifying the neutrino interaction signal in upwards of 75% of gamma ray
interactions and nearly 100% of other interactions. Hence, we propose a new
instrument to explore and study our sun. Due to inverse square scaling, this
instrument has the potential to outperform earth-based experiments in several
domains such as making measurements not accessible from the earth’s orbit.

###### keywords:

neutrino , gallium , double-pulse , solar , scintillating crystal

††journal: Nuclear Physics A

[inst1]organization=Wichita State University, addressline=1845 Fairmount St.,
city=Wichita, postcode=67260, state=Kansas, country=United States of America

[inst2]organization=South Dakota State University, addressline=175 Medary
Avenue, city=Brookings, postcode=57006, state=South Dakota, country=United
States of America

[inst3]organization=NASA Marshall Space Flight Center, addressline=Martin Rd
SW, city=Huntsville, postcode=35808, state=Alabama, country=United States of
America

Research highlight 1

Research highlight 2

##  1 Introduction

Since neutrinos interact only weakly they are hard to detect; nevertheless,
within the last ten years neutrino detectors on earth have started to reliably
detect neutrinos from the fusion reactions in the interior of the sun and
scientists have started to use this information to investigate the sun’s
nuclear furnace. These neutrino detectors are normally very large and deep
underground. They are large because they need as much mass as possible to
capture more neutrinos, and they are underground to reduce background rates.
If a neutrino detector could operate in space, what advantages would it have
to perform unique science? Clearly to just take a neutrino detector into space
may not bring any new science unless the possibility for dramatically
enhancing the neutrino flux was associated with this endeavor, but it could
also be of interest if it can dramatically reduce solar neutrino backgrounds
to see other processes such as dark matter or galactic neutrinos currently
hidden by a large solar neutrino presence at the earth.

We propose three distinct possibilities for science using the Neutrino Solar
Observatory ($\nu$SOL):

  1. 1.

Going closer to the sun, see Table 1, the $1/r^{2}$ neutrino flux would
provide 1,000x more neutrino rates at seven solar radii distance where the
current NASA Parker Solar Probe operates and 10,000x more neutrino rate at
three solar radii where some NASA scientists think it is possible to go [1].
Here new science would be a larger statistical observation of solar neutrino
emission, the study of the size of the fusion emission region, and particle
physics looking for the transition from coherent to de-coherent neutrino
oscillations. The sun’s gravitational well could trap dark matter in its core
and this would displace the solar fusion region and would be a way to search
for dark matter’s presence without direct detection [1].

  2. 2.

Because the neutrino has a non-zero mass, which we know from the existence of
neutrino oscillations, the sun bends space to create a gravitational focus,
but for neutrinos this gravitational focus would be very close to us at 20 to
40 AU: a distance easily reachable with current technology, unlike the
gravitational focus for light which is 450 to 750 AU away [2]. This solar
neutrino focus could be a testing ground for gravitational lens ideas. The
galactic core is 27,000 light years away from us and is about two times larger
than the moon when viewed from earth and is the 2nd largest neutrino source in
the sky after the sun[3, 4, 5]. The galactic core not only has many neutrino-
producing stars, but also 10,000 neutron stars and black holes in the central
cubic parsec of the core. Matter falling into these objects is crushed,
producing neutrons and isotropically emitted neutrinos of higher energy than
solar fusion neutrinos. A detector at the solar neutrino focus would permit
imaging of the galactic core and just finding the neutrino gravitational focus
of the sun would be a new way to measure the neutrino mass.

  3. 3.

Any neutrino-detecting space probe could take advantage of a flight towards
the sun to observe the shape of the solar neutrino changes due solely to the
distance from a non-point source of solar neutrinos inside the sun, while when
traveling away from the sun, deviations from the expected $1/r^{2}$ curve are
an indication of the direct observation of dark matter or galactic neutrinos
[1].

Although operating a neutrino detector in space will be challenging, we
believe we have found a way to do just so. Our technique would permit
operation and detection in space, would be a major advance for astrophysics
and heliophysics, and would allow for new ways to make elementary particle
physics fundamental measurements, all of great importance.

Distance from Sun | Flux relati | ve to Earth
---|---|---
696342 km ($R_{\odot}$) | 46200 |
1500000 km ($\sim 3R_{\odot}$) | 10000 |
4700000 km ($\sim 7R_{\odot}$) | 1000 |
15000000 km | 100 |
47434000 km | 10 |
Mercury | 6 | .4
Venus | 1 | .9
Earth | 1 |
Mars | 0 | .4
Asteroid Belt | 0 | .1
Jupiter | 0 | .037
Saturn | 0 | .011
Uranus | 0 | .0027
Neptune | 0 | .00111
Pluto | 0 | .00064
KSP | 0 | .0002
Voyager 1 (2015) | 0 | .00006
Table 1: Intensity of solar neutrinos at various distances from the sun.

##  2 Neutrino Physics in Space

###  2.1 Disadvantages

The most obvious disadvantage of a space-based detector is the harsh
environment of space. Most neutrino detectors have the luxury of being built
deep underground in order to eliminate most cosmic backgrounds. A space-based
detector will have to contend with the full flux of energetic cosmic gamma
rays, electrons, protons, and heavier nuclei. The first level of shielding for
these events comes from the outermost iron shell.

The first significant source of background events in space is the gamma
ray/x-ray background. Our passive shield can stop the energy of gamma rays up
to 600 keV with better than $2\cdot 10^{-4}$ attenuation [6]. This should be
more than sufficient to shield against the gamma ray background. The total
gamma background can be seen in Figure 1 from 0.5 keV to 2.5 GeV. The
sufficiently energetic gammas, in the energy range of 500 keV and above,
create a background of approximately 130 m-2 sr-1 s-1 [7]. Our electronics are
being designed so that they are sufficient to deal with this noise on the
order of 500 Hz.

Figure 1: Cosmic gamma ray spectrum vs photon energy. Fermi gamma-ray data
extends to 100 GeV, but the contribution to the total rate is small [7].

There are two major sources of electrons in terms of space conditions. The
solar wind electrons have a characteristic temperature of 12 eV at the earth
[8]. This temperature will increase, using the worst case of Boldyrev, Forest,
and Egedal, to a maximum temperature of 130 eV [9]. These are both well below
energies at which any significant fraction of electrons might penetrate the
satellite’s shielding. The second source is the cosmic background electrons.
These background electrons, Figure 2, have been measured with a total rate of
approximately 50 m-2 sr-1 s-1 on the MeV-TeV regime. The iron shield will
moderate electrons and, in the continuously slowing down approximation (CSDA),
the shielding will be 100% effective at energies up to 15 MeV [10]. At
energies beyond this, there will begin to be penetration, and we will rely on
active veto rejection techniques.

Figure 2: Cosmic electron differential flux vs electron kinetic energy. [11]

Similar to electrons, the solar wind and cosmic background are the primary
sources of positively charged particles. The solar wind protons have a
normative temperature of 18 eV, and the maximum temperature measurement of the
DSCOVR solar wind warning probe in the earth-sun L1 point has measured maximum
proton temperatures of approximately 86 eV. These energies are well below the
MeV scales of the passive shielding [12]. The total cosmic flux of protons and
heavier nuclei is well measured, and the total flux is on the order of 3000
m-2 sr-1 s-1 from 100 MeV and up [13]. In the CSDA, the shield will be able to
stop protons of energy up to 80 MeV, and it will be able to stop alpha
particles up to 300 MeV.

Figure 3: Fluxes of nuclei of the primary cosmic radiation in particles per
energy-per-nucleus are plotted vs energy-per-nucleus. The inset shows the H/He
ratio as a function of rigidity [13].

###  2.2 Advantages

In the introduction, we touched briefly on one advantage of approaching the
sun, and here expand on the scope of what it means to go close to the sun. The
most obvious advantage is the previously mentioned inverse square scaling. Due
to the weakly interacting nature of the neutrino, we can expect the flux of
neutrinos to fall off as an inverse square of the distance from which they
were generated.

The dramatically increased flux from the inverse square scaling allows for a
modestly sized detector, on the order of one hundred kilograms of active
volume. For a $3R_{\odot}$ science mission, this would be the flux-equivalent
of a 1 kTon solid scintillating crystal detector, which is comparable to large
earth-based experiments like the KamLAND, a 1 kTon mineral oil scintillator
detector, and Super-K, a 50 kTon water Cherenkov detector [14, 15]. As we
approach the sun, the flux spectrum will change slightly due to the shape of
fusion in the core, but even on the scale of a 3$R_{\odot}$ closest approach
the variation in flux from the near peak of the fusion region to the far peak
is on the order of 1%.

Figure 4: Flux of protons from 250-700 MeV by distance from sun [16]

.

It is worth noting that there does not seem to be much risk of increased of
backgrounds on approach to the sun. The Helios mission measured the proton
flux down to 0.3 AU ($64.5R_{\odot}$), Figure 4, and found that the flux was
unexpectedly flat. This phenomenon has been explained by the modulation of the
high energy cosmic particles by the sun’s magnetic field and the acceleration
of the low energy solar wind as it moves from the sun [17, 18].

Last, it is a straightforward feature of the geometry in orbit that the
resolution of a detector increases with an inverse square scaling. Because of
this, we get the same relative angular resolution scaling that the neutrino
flux sees in Table 1. If our detector is only capable of one tenth the angular
resolving power of detectors like Super Kamiokande, a relatively conservative
mission to 20 solar radii would have significantly improved resolving power.

##  3 Gallium Double Pulsing

In section 2, we introduced the difficulty of measurement using traditional
neutrino detection methods due to high background rates. To counteract this
effect, we are designing a method of looking for electron-type neutrinos via a
double pulse signal. The interaction of gallium with neutrinos has been of
scientific interest since the early 1990’s with the GALLEX experiment and the
SAGE experiment [19, 20]. These experiments used radiochemical methods to
determine the number of neutrino interactions which had taken place. These
experiments were, and our experiment currently is, based on the specific
interaction of a neutrino transmuting gallium into ionized germanium, and
itself into an electron: $\nu_{e}+$ Ga $\to e^{-}+$ Ge${}^{+}.$

It is an important to note that the proposed method is not unique to any
particular gallium-loading method, nor is it strictly necessary to use
gallium. Several other elements could be used for solar neutrino measurements,
such as indium. Our work has focused on gallium because it has the smallest
$Q=235.7$ keV and largest cross section of other double-pulse candidates. Our
current designs focus on the Gadolinium-Aluminum-Gallium Garnet (GAGG)
scintillating crystal, but as we have mentioned, any gallium-loaded material
could be used in this double-pulsing schema. In particular, Gallium III Oxide
is an interesting scintillator in development because of its high gallium mass
fraction in comparison with other crystals.

###  3.1 Gallium-Neutrino Interaction

We propose using a prompt scintillation method to determine when a neutrino
interaction has occurred. The neutrino interaction will often leave the
germanium atom without any excitation energy, but about half of the
interactions will leave the germanium nucleus in an excited state, see Table
2. This motivates a method to look for an initial electron energy deposit
followed by a gamma ray with characteristic timing. This double pulsing allows
us to reject a large fraction of events which bypass our shielding. This
allows the potential for favorable signal-to-background ratios even in high-
background environments like those of space.

The two isotopes of gallium present two different possibilities for neutrino
detection. The first isotope we’ll discuss is gallium 71. Gallium 71 is
transmuted into germanium 71 during interactions with electron type neutrinos.
When the neutrino is sufficiently energetic, this will release an electron
alongside the final germanium nucleus. The mass difference between gallium and
germanium 71 is 235.7(18) keV, and when combined with the mass of the
electron, this gives a bare threshold of 746.7(18) keV for the energy of a
neutrino able to eject an electron at rest from the ground state of germanium
71 [21, 13]. The gallium ground state has spin -3/2, whereas the germanium
ground, first, and second excited states have spins of -1/2, -5/2, and +9/2
respectively. The -5/2 spin state has a half-life of 70 ns, and the metastable
spin +9/2 state has a half life of 20.2 ms. The most likely excited state of
the germanium is the -5/2 state, followed by several higher energy levels. The
+9/2 state should be very unlikely in comparison [22, 23].

Current designs use a highly-segmented detector of small GAGG crystals. The
detector will use silicon photomultipliers (SiPM) to read out the energy
deposited in each of the GAGG cells, and this segmentation allows for
sophisticated particle identification algorithms like have been used in the
NOvA experiment [24]. A highly segmented design has not yet been implemented
in simulation, but the work done in particle identification by the NOvA
experiments should allow our detector to identify particle type and direction
for more effective vetoing. Further studies will determine the efficacy of
such a design, and these studies will determine if a sufficiently powerful
computer or sufficiently high-rate communication device can be included for
this analysis.

Reaction Products | Energy Threshold | Photon Energy | Half Life
---|---|---|---
Ge${}_{32}^{71E2}+e^{-}$ | 0.408 MeV | 0.175 MeV | 79 ns
Ge${}_{32}^{69M1}+e^{-}$ | 2.313 MeV | 0.086 MeV | 5 $\mu$s
Ge${}_{32}^{69M2}+e^{-}$ | 2.624 MeV | 0.397 MeV | 2.8 $\mu$s
Table 2: Table of the possible reactions of neutrinos with gallium and their
decay products.

###  3.2 Simulations

We have extensively simulated the double pulsing in a variety of scintillator
candidates, and detector configurations. While the exact vetoing rate changes
based on the the detector configuration, the double pulsing has allowed some
configurations to approach vetoing rates of 100% for all particles except
galactic gammas. Galactic gamma rays have been successfully vetoed in simuo at
rates of 75%. Ongoing topological and timing studies are promising to push
this vetoing rate in line with the other particles. These simulations have
focused on the ability of the detector system to identify a neutrino-related
pulse or reject a galactic cosmic ray (GCR) event, and what additional pulses
are generated when these occur.

Long-term, the ability to detect a neutrino double pulse amongst the various
sources of noise is of interest, as is determining the rate of accidental
double pulses due to background events themselves or background events and
neutrino pulses. This will require the construction of a fast Monte Carlo, in
which each step in time is accompanied by a decision to emit a neutrino event
or a background event. This includes both primary particles and any secondary
events like those from activation products.

Before the current design and the updated version of Geant4 were implemented,
an initial fast Monte Carlo program was built and run successfully. A key
component of a previous design was the implementation of a shielding strategy
to try to increase the removal of unwanted pulses. This strategy included
alternating layers of metal and plastic in addition to the outer shell and the
polymer veto. The purpose of said layers was to produce enough charged
particles to better generate a signal in the veto scintillator. The basic
approach was largely successful in reducing the rate from low energy gamma
rays and protons. However, the current design has removed those layers in
order to address other constraints on overall mass and orbit of the spacecraft
around the sun. As the design evolves, inclusion of additional shielding can
be considered.

##  4 Summary

In summary,we propose a near-solar neutrino detector design using the well-
studied transmutation of gallium into germanium. This detector will be able to
take advantage of the inverse square scaling of the neutrino flux to be the
mass-equivalent of a detector on the scale of kilotons while at closest solar
approach. By flying in the space between the earth and the sun, such a
detector will be capable of probing the distance scales between the earth’s
diameter and 1 AU and probing off-axis solar neutrinos, which are impossible
for earth-based experiments.

Such a detector must contend with high-rate cosmic ray backgrounds. We propose
to solve this problem by looking for a double-pulsed gallium signal. This
double pulsing allows for dramatically improved rejection rates compared to
single coincidence rejection. Future work will continue to refine detector
topological rejections. Our rejection rate in-simuo is already at 75% for
gamma rays with little topological or timing cutting, and nearly 100% for
other background particles in similar regimes.

##  5 Acknowledgements

We would like to thank Nasser Barghouty of NASA Headquarters for helping Nick
Solomey put together the initial idea for the $\nu$SOL project during a NASA
summer fellowship.

Funding: This work was supported by the NASA NIAC Program [grant numbers
80NSSC18K0868, 80NSSC19M0971]; MSFC CAN [grant number 80MSFC18M0047]; Wichita
State University MURPA; NASA EPSCoR PDG.

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 LHCb-PUB-2016-019 August 4, 2016

Test of the photon detection system for the LHCb RICH Upgrade in a charged
particle beam

M. K. Baszczyk5,d, M. Benettoni4, R. Calabrese1,a, R.
Cardinale2,b,111Corresponding author, P. Carniti3,c, L. Cassina3,c, G.
Cavallero2,b, L. Cojocariuf, A. Cotta Ramusino1, C. D’Ambrosio7, P. A.
Dorosz5,d, S. Easo9, S. Eisenhardt10, M. Fiorini1,a, C. Frei7, S.
Gambetta2,b,†, V. Gibson8, C. Gotti3,c, N. Harnew13, J. He7,‡, F. Keizer8, W.
Kucewicz5,d, F. Maciuc6, M. Maino3,c, R. Malaguti1, C. Matteuzzi3, M.
McCann12, A. Morris10, F. Muheim10, A. Papanestis9, G. Pessina3, A.
Petrolini2,b, D. Piedigrossi7, A. Pistone2,b, V.M. Placinta6, S. Sigurdsson8,
G. Simi4,e, J. Smith8, P. Spradlin11, L. Tomassetti1,a, S. A. Wotton8.

1Sezione INFN di Ferrara, Ferrara, Italy
2Sezione INFN di Genova, Genova, Italy
3Sezione INFN di Milano Bicocca, Milano, Italy
4Sezione INFN di Padova, Padova, Italy
5Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
6Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
7European Organization for Nuclear Research (CERN), Geneva, Switzerland
8Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
9STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
10School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
11School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
12Imperial College London, London, United Kingdom
13Department of Physics, University of Oxford, Oxford, United Kingdom
aUniversità di Ferrara, Ferrara, Italy
bUniversità di Genova, Genova, Italy
cUniversità di Milano Bicocca, Milano, Italy
dAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
eUniversità di Padova, Padova, Italy
fStefan cel Mare University of Suceava, Romania
$\dagger$ Now at 10
$\ddagger$ Now at University of Chinese Academy of Sciences, Beijing, China

The LHCb detector will be upgraded to make more efficient use of the available
luminosity at the LHC in Run III and extend its potential for discovery. The
Ring Imaging Cherenkov detectors are key components of the LHCb detector for
particle identification. In this paper we describe the setup and the results
of tests in a charged particle beam, carried out to assess prototypes of the
upgraded opto-electronic chain from the Multi-Anode PMT photosensor to the
readout and data acquisition system.

Submitted to JINST

© CERN on behalf of the LHCb collaboration, licence CC-BY-4.0.

###### Contents

  1. 1 Introduction
  2. 2 Experimental setup
    1. 2.1 Optical system
    2. 2.2 Photon detector
    3. 2.3 Trigger and Data Acquisition
      1. 2.3.1 Online Data Monitoring
    4. 2.4 Track Telescope and Readout Synchronisation
      1. 2.4.1 Telescope Description
      2. 2.4.2 Synchronization between the two systems
  3. 3 Simulation
    1. 3.1 Optical simulation
    2. 3.2 Geant4 simulation
  4. 4 Data analysis
    1. 4.1 Threshold scan studies
    2. 4.2 Measurement of dark counts
    3. 4.3 Cross-talk studies
    4. 4.4 Photo-electron yield measurement
      1. 4.4.1 Comparison with simulation
      2. 4.4.2 Analytical estimate of the yield
      3. 4.4.3 Multi-track correlation studies
    5. 4.5 Fit of the ring
    6. 4.6 Cherenkov angle reconstruction
      1. 4.6.1 Results from reconstruction
  5. 5 Conclusions
  6. Acknowledgements

##  1 Introduction

The LHCb experiment [1] performs high-precision measurements of CP violation
and searches for New Physics, taking advantage of the significantly enhanced
production of beauty and charm hadrons at the Large Hadron Collider (LHC) at
CERN. Ring Imaging Cherenkov (RICH) detectors are fundamental to the particle
identification system of the experiment and are essential for most of the
physics results published by LHCb. The two RICH detectors have performed very
successfully during Run 1 of the LHC [2].

In order to expand the potential for discovery and the study of new phenomena
at the LHCb experiment, an upgrade of the detector is planned for Run III. A
principal feature of the upgrade is to read out the detector at every bunch
crossing, a rate of 40 MHz, and apply a more flexible software-based trigger
system to improve the selection of interesting events at a luminosity of
$2\times 10^{33}$cm-2s-1. As a consequence, the current RICH photon detectors
(Hybrid Photon Detectors), with encapsulated front end electronics, will have
to be replaced. Multi-anode Photo-Multiplier Tubes (MaPMT), offering similar
pixel size, are candidates for the replacement. A detailed description of the
RICH upgrade project is given in the Technical Design Report [3].

Tests of the full opto-electronic chain have been performed in a charged
particle beam during Autumn 2014 at the SPS facility at CERN. The performance
of the proposed photon detectors (Hamamatsu R11265 MaPMT [4]) and the
feasibility of the readout and DAQ chain, which includes an external front-end
custom readout chip (CLARO [5]) and the associated data acquisition
electronics (Digital Boards), were assessed.

##  2 Experimental setup

The beam tests were performed in the North Area of the Prevessin site at CERN.
A beam consisting mainly of pions and protons with momentum of 180
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ was obtained from the SPS facility and
guided through a light-tight box containing a glass planoconvex lens, used as
the Cherenkov radiator. The Cherenkov light was detected with MaPMTs housed in
an aluminium structure attached to the box. The box was placed downstream of a
tracking telescope able to record and reconstruct the trajectory of the
incoming beam particles.

###  2.1 Optical system

The optical setup consisted of a planoconvex lens made of borosilicate glass
with two parallel cuts giving a doubly-truncated profile as shown in Figure 1.
The radius of the lens has been measured to be $R=144.6\pm 0.1\,{\rm{mm}}$. It
has a diameter of $151.7\pm 0.1\,{\rm{mm}}$ and a thickness at the centre of
$27.0\pm 0.1\,{\rm{mm}}$. A reflective layer (annulus) $20\,{\rm{mm}}$ wide
was deposited on the spherical surface. The spherical, top and bottom surfaces
of the lens have been blackened in order to absorb scattered photons. The
centre of the lens on the flat surface, out to a radius of $17\,{\rm{mm}}$ has
been blackened to reduce the length of the path where detectable photons are
produced.

Figure 1: The lens used in the testbeam.

Particles enter the lens at the middle of the spherical side producing
Cherenkov photons which are reflected at the flat surface due to total
internal reflection. The photons are reflected again by the thin reflective
layer deposited onto the spherical surface and exit from the lens at the flat
surface. At the focal plane of the lens, the photons form a Cherenkov ring as
shown in Figure 2.

Figure 2: Schematic of the optical setup. Particles traverse the lens
generating Cherenkov light, which is reflected at the flat surface and
reflected and focused on the curved surface of the lens. Most rays converge at
the position of the photon detectors

A view of the system, looking downstream, with the expected position of the
ring on the MaPMTs is shown in Figure 3. The beam passes through the centre of
the image creating a Cherenkov ring with a radius of $\sim 60\,{\rm{mm}}$.
Only four of the available 8 MaPMT sockets are instrumented.

Figure 3: The expected ring position superimposed to the two Elementary Cells,
each with two $8\times 8$ pixel MaPMTs. The beam is entering into the paper.

###  2.2 Photon detector

The photon detectors tested are the Hamamatsu R11265
111http://www.hamamatsu.com/resources/pdf/etd/R11265U_H11934_TPMH1336E.pdf,
which are candidates for the RICH upgrade. The R11265 is an MaPMT capable of
detecting single photons in the wavelength range 200 – 600 nm. It is a
$26.2\,{\rm{mm}}$ square device, with $64$ $(8\times 8$) pixels, and an active
area of $23\times 23\,{\rm{mm^{2}}}$ such that the geometrical acceptance is
$77\%$. The pixel size is approximately $2.9\times 2.9\,{\rm{mm^{2}}}$. The
typical average gain with a standard voltage divider provided by the
manufacturer is $10^{6}$ at $1\,{\rm{kV}}$. The maximum pixel-to-pixel gain
variation is a factor 3.

A dedicated radiation tolerant ASIC, the CLARO, was used to read out the
photon detectors. The CLARO is an 8-channel chip containing an analogue pulse
shaping amplifier and a binary discriminator allowing the detection of single
photons. Each channel has an individual threshold, programmed through a 6 bits
register, resulting in 64 threshold values. The baseline of the amplifier is
recovered within 25 ns, in order to suppress signal spill-over, and it has low
power consumption at $\sim 1\,{\rm{mW}}$ per channel.

The photon detector assembly, housing MaPMTs, readout electronics and
ancillary systems, is conceived as a modular structure based on independent
functional units. The basic unit is the Elementary Cell (EC) designed to be
common to both RICH detectors of LHCb. Each EC houses 4 MaPMTs and front-end
electronics and consists of:

  * •

The baseboard (BB) with custom sockets to house 4 MaPMTs. It provides power,
common High Voltage (HV) to the photocathodes of the MaPMTs, four resistor
divider chains which supply potentials to the dynodes and connect the MaPMT
anodes to the CLARO inputs.

  * •

Four Front-End Boards (FEB), each equipped with eight CLARO chips.

  * •

The backboard (BkB), which interfaces the FEBs to the Digital Board(DB) for
configuration and read out.

All the components are assembled within an aluminium case serving as
mechanical support structure and providing heat dissipation and ground
connection. An exploded view of the EC is shown in Figure 4.

Figure 4: An exploded view of the Elementary Cell. Showing from left to right,
the BkB, 4 FEBs with aluminium shell, BB and MaPMTs.

Two EC have been installed at the focal plane of the lens on either side of
the beam. Only half of each EC was instrumented and read out by two FEBs. The
setup was installed on a remotely controllable translation table in order to
align it in the plane perpendicular to the beam.

Figure 5 shows the light-tight box installed in the experimental area, where
the two EC are visible.

Figure 5: The box installed in the testbeam experimental area with two half
ECs, equipped with 2 FEBs able to read 128 channels (2 MaPMTs each).

A view of the inside of the box is shown in Figure 6.

Figure 6: A view of the inside of the box. The borosilicate-glass lens and the
entrance windows of the two ECs are visible.

###  2.3 Trigger and Data Acquisition

The digital signal outputs of the CLARO are connected to an FPGA on the
Digital Board, collecting events in response to triggers. The DB formats the
data into multi-event packets (MEP) and transmits them via Gbit Ethernet to a
PC where they are saved. The Gbit Ethernet links are also used to configure
the FPGA on the DB and the CLARO chips. The control of the data aquisition
(DAQ) system is achieved using a Graphical User Interface (GUI). The GUI
manages configuration parameters for the EC (such as the CLARO chip
thresholds) and provides run control functions. Triggers can be generated
externally by beam particles or by an internal pulser. Particles traversing
two scintillator planes placed up and downstream the beam telescope generate a
coincidence that can be used as an external trigger. This trigger signal is
received by the trigger board, where it is conditioned and fanned out to the
DBs. Alternatively the trigger board can generate its own triggers. The logic
on the trigger board also receives a gate signal from each connected DB
indicating that it is ready to accept a trigger. Triggers are only sent when
the gate signals of all connected DBs are asserted in order to prevent buffer
overflow at high trigger rate. One of the trigger outputs is sent to the beam
telescope trigger board to provide synchronisation between the two systems.

####  2.3.1 Online Data Monitoring

A quasi-online data monitor has been developed in order to validate the data
during acquisition. A decoding program is able to read the data before the end
of the run and to display monitoring histograms. A map of the accumulated hits
on the four MaPMTs is shown in Figure 7. Other histograms, such as
distributions of the hit multiplicity, are also available to monitor the
performance of the system.

Figure 7: A typical map of accumulated hits in a run on the four read out
MaPMTs. Each MaPMT clearly shows a section of the Cherenkov ring. The
horizontal distance between the two pairs of MaPMT is not to scale.

###  2.4 Track Telescope and Readout Synchronisation

####  2.4.1 Telescope Description

The beam can be tracked in space with a dedicated track telescope, comprising
8 planes of silicon pixel detectors read out with the TimePix3 (TP3) chip.
Each plane has a size of about $14~{}\mathrm{mm}\times 14~{}\mathrm{mm}$ and
is subdivided in pixels of $55~{}\mu\mathrm{m}\times 55~{}\mu\mathrm{m}$. At a
typical particle momentum of 180${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, the
reconstructed tracks provide excellent position resolution of order a few
$\mu$m at the lens. The telescope has a triggerless readout: hits are recorded
continuously once a run is started. Each hit pixel records the position of a
particle and a timestamp with a precision of 1 ns. The data are then analysed
offline and tracks are formed from hits in each plane that have consistent
times. The telescope also writes 64-bit trigger timestamps, which are saved
every time an external trigger is sent to the TP3.

The tracking information for the particles passing through the lens radiator
is essential in order to reconstruct the Cherenkov angle and to improve the
simulation by providing it with the correct beam profile. Moreover, the
tracking data can identify events with multiple beam particles within the
trigger gate of the MaPMT acquisition and help correctly estimate the number
of expected photons per event.

####  2.4.2 Synchronization between the two systems

The association between the hits collected with the RICH acquisition system
and the tracks from the telescope is made using timestamps. Every time a RICH
event is acquired a signal is sent to the telescope, where it is registered
and time stamped. There is a time delay of about 330 ns between the RICH
signal and the tracks, as shown in Figure 8. The search time window was a few
hundred ns. The time distribution of the tracks is very sharp, with an RMS of
2 ns showing good communication between the two systems. Figure 8 shows the
number of tracks that can be found within a 50 ns window centred at -330 ns.
More than 97% of the RICH events have at least one telescope track associated
with the event, while around 1% of the events have more than one associated
track. The missing track information, in less than 3% events, is due to the
inefficiency of the tracking system.

Figure 8: Left: Distribution of the delay between RICH triggers and tracks
recorded by the telescope. Right: Distribution of the number of tracks
associated to about $6\times 10^{5}$ events. Less than $3\%$ of the events
have no tracks associated, while about $1\%$ of the events have more than one
track associated.

##  3 Simulation

A simulation was used in order to understand and optimise the experimental
setup. Two different methods have been used to allow quick development and to
cross check the results. A ray-tracing simulation using a fast and flexible
optical CAD software package222Optica 3, http://www.opticasoftware.com and
Wolfram Mathematica 9, http://www.wolfram.com/mathematica has been used to
optimise the optical system and make an initial estimate of its performance.
In addition to this, a more detailed simulation of the testbeam setup using
the Geant4 [6] software toolkit was performed for a complete evaluation of the
system performance, including the reconstructed Cherenkov angle resolution.

###  3.1 Optical simulation

In preparation for the beam test the optical CAD software has been used to
assess different setup configurations. The goal was to find a configuration
able to focus the Cherenkov photons on a focal plane which is sufficiently
displaced from the beam axis to avoid direct exposure of the MaPMTs to the
particles of the beam. The measured transmission properties of the used lens
were inputs for the simulation.

Figure 9: The Cherenkov photon tracing (seen from the top) obtained using the
optical CAD. The different colours represent Cherenkov photons with different
energy.

Figure 9 shows ray-traced photons that correspond to the geometrical setup
shown in Figure 2. Figure 10 shows the Cherenkov ring, which is incomplete as
the lens is cropped and does not cover a full circle. The thickness of the
ring is of the order of one MaPMT pixel, less than 3 mm. The best focal
distance is determined by simulations and located at $25\,{\rm{mm}}$ from the
flat side of the lens. The focused ring has an expected radius with a mean
value of $R_{\rm ring}=59.8\,{\rm{mm}}$ and an RMS of $0.6\,{\rm{mm}}$.
(Figure 10, right).

The thickness of the ring was minimised by studying the effects of the
emission point of Cherenkov photons in the radiator and the chromatic
dispersion. In order to take into account the chromatic dispersion, the full
Cherenkov spectrum was generated and then convoluted with the quantum
efficiency of the MaPMTs shown in Figure 11. Including both effects in the
simulation and collecting photons from the full length of the particle path
inside the glass, the RMS of the photon distribution (ring thickness) was 1.9
mm. In order to reduce it, black tape was used to allow only photons emitted
in the first 13 mm of the glass to reach the photon detectors. In this way the
RMS was reduced to 0.63 mm. Reducing the number of photons also lowered the
probability of double hits on the same pixel that could bias the photon yield
estimate.

The contribution of the chromatic dispersion was evaluated by fixing the
emission point, giving a contribution to the RMS of 0.6 mm. Similarly, fixing
the wavelength of the emitted Cherenkov photons, the emission point error
contribution is evaluated to be $0.12\,{\rm{mm}}$.

Simulating a beam with a Gaussian spread of about 10 mm in both directions had
negligible difference compared with a beam with zero spatial extent. Finally,
the biggest contribution to the width of the ring is the pixel size of the
MaPMTs which at 3 mm gives an RMS of $\sim\frac{3\,{\rm{mm}}}{\sqrt{12}}=(\sim
0.9\,{\rm{mm}})$.

Figure 10: Expected ring of Cherenkov photons at the photodetector plane on
the left. On the right, the radius distribution with an RMS of
$0.6\,{\rm{mm}}$. Since the lens is cut at the top and bottom, the expected
ring is cut at $\pm 40\,{\rm{mm}}$ in the vertical direction.

Figure 11: The typical Super Bi-alkali photocathode quantum efficiencies from
the tube manufacturer for borosilicate (BS) glass (dashed) and UV glass
(continuous) on the left. On the right, the measured quantum efficiencies for
the four MaPMTs used in these tests.

###  3.2 Geant4 simulation

The simulation and reconstruction of the testbeam data use a common software
framework so that the same detector description is used for both. It is
configured within the LHCb software framework and uses the Geant4 toolkit for
the detector simulation. The information relating to the geometry, material
and optical properties of the various components of the testbeam setup is read
from a database which includes the size and shape of the radiator, the
geometry of the MaPMTs and the pixel size. The Geant4 toolkit simulates the
physics processes of the charged particle interactions with the detector, the
production and transport of Cherenkov photons, the reflection and refraction
at the optical boundaries and the production of photo-electrons. The measured
quantum efficiencies of the MaPMTs as a function of the photon wavelength are
also included (Figure 11) together with the optical properties of the glass
radiator. The refractive index is then scaled using the mean Cherenkov angle
reconstructed from the data, as described in the following section. The beam
divergence is obtained from the measurement of the beam direction using the
tracking telescope described in Section 2.4.1. The detection efficiency of
each of the pixels in the MaPMTs, due to the readout threshold applied, is
obtained from the measurements taken during the testbeam. The number of
detected photons per charged track obtained from the simulation is compared
with that from data in Section 4.4.

##  4 Data analysis

###  4.1 Threshold scan studies

Several threshold scan runs were performed throughout the test period, at
various MaPMT bias voltages, all with 1 million events per threshold setting.
The threshold settings spanned from threshold 7 to threshold 63 in steps of 2
units, where each unit is about $35\times 10^{3}\,e^{-}$. Threshold scans were
performed using Cherenkov photons and this implies that off-ring pixels were
illuminated only by stray photons and their event rate is much lower than that
for pixels on the Cherenkov ring. Nevertheless the spectra of off-ring pixels
could be reconstructed adequately despite the lower statistics. The integral
spectra obtained from these runs were then differentiated and the resulting
pulse-height spectra for each pixel were fitted with three Gaussian functions
(noise pedestal, single photon peak and double photon peak). Two typical
spectra, with the fit superimposed, for a pixel on the ring (blue) and off the
ring (red) in the default working condition (MaPMT biased at 1000 V) are shown
in Figure 12.

Figure 12: Single photon spectrum for a pixel on the ring (pixel 26 MaPMT C)
in blue (upper curve) and for a pixel off the ring (Pixel 50 MaPMT D) in red
(lower curve). The dashed lines indicate the chosen value of the threshold for
each pixel (17 for pixel C26 and 15 for pixel D50).

The spectra were used to determine the best value of the threshold for each
pixel, defined as the minimum between the noise pedestal and the single photon
peak. By selecting this threshold value, it is possible to reject most of the
noise while maintaining an adequate photon detection efficiency. Figure 13
shows a plot of the photon detection efficiency and the pedestal noise
rejection with respect to the threshold settings for one of the pixels of
Figure 12. The efficiency is calculated as the ratio of the integral above
threshold to the integral of the complete single photon peak, while noise
rejection is calculated as the ratio of the integrated noise pedestal below
the chosen threshold to the integral of the pedestal above the lowest
available threshold.

Figure 13: Single photon peak detection efficiency and noise rejection vs
threshold setting for pixel 26 on MaPMT C. The red line and the data-tips
indicate their value at the chosen threshold setting.

###  4.2 Measurement of dark counts

Several runs were taken without beam using the internal trigger described in
Section 2.3. The number of hits recorded by each anode without beam is
referred to as the dark count. Around 10 million events were recorded for each
run at different values of high voltage from 960 V to 1080 V in steps of 20 V.
The threshold was set to be uniform across all channels, without using the
individual setting, therefore the high voltage dependence cannot be properly
characterised. In order to estimate the dark count rate, the number of
recorded hits at each anode is divided by the number of triggers and the
length of time that the device is actively recording photons after each
trigger, which was set to $62.5$ ns. The dark count rate is calculated for all
anodes, and the mean value for each MaPMT is plotted as a function of high
voltage in Figure 14. It should be noted that the dark count rate is
negligible compared to the hit rate for runs taken with beam.

The manufacturer provides measurements of the dark current and average gain
for each MaPMT, which can be used to calculate the average dark count rate
across all anodes in the device. As the dark current and dark count
measurements are made in a very different way, it is only possible to make a
qualitative comparison. The measurements are compatible to within an order of
magnitude, i.e. tens of Hz. The MaPMTs with the highest and lowest dark
currents given by the manufacturer, also have the highest and lowest dark
count rates as measured in our testbeam setup.

Figure 14: A plot of average dark count rate for each MaPMT as a function of
high voltage.

###  4.3 Cross-talk studies

From the acquired data it is possible to estimate the cross-talk of the entire
opto-electronic chain. This can be done by looking at pairs or clusters of
neighbouring active pixels during the same event in a region of the MaPMT far
from the Cherenkov ring. On the ring the rate of Cherenkov photons is quite
high (about 4 photons per event per MaPMT are expected) so there would be a
non negligible probability of two real photons hitting neighbouring pixels,
resulting in a false cross-talk count. For this reason all the pixels on the
ring and the nearest neighbours are masked out in this analysis. Furthermore,
since the illumination rate of pixels off-ring is less than 1% of the total
events, the probability of accidental coincidence between two neighbouring
pixels can be neglected. Also the dark counts are low enough to be ignored.
For these reasons, the coincidences are attributed to cross-talk.

Using the binary data from the read out system it is not possible to
distinguish which of the two neighbouring pixels induced cross-talk on the
other, thus the number of cross-talk events was evenly split between the two
pixels. Based on these considerations the cross-talk probability is calculated
as:

${\rm\operatorname{Cross-talk}}\left(i\rightarrow
j\right)=\frac{N_{ij}/2}{N_{i}}$ (1)

where $N_{ij}$ is the number of events where both pixels are on and $N_{i}$ is
the number of events where at least pixel $i$ is on. The same calculation is
done exchanging pixel $j$ with pixel $i$ and the final cross-talk value
between the pair is the mean of the two values.

The histogram of the computed values for the runs with thresholds set for each
channel, is plotted in Figure 15. The mean value across the two MaPMT
considered (C and D) is 1.48%. These results are obtained in real working
conditions and include the contributions from the whole opto-electronic chain.
This low cross-talk was possible thanks to the careful design of the entire
system, including the good quality of the MaPMT selected, the layout of the
front-end board and the CLARO preamplifier design [5]. This result is in good
agreement with previous test-bench measurements.

Figure 15: Histogram of the cross-talk probability. The mean value is 1.48%.

###  4.4 Photo-electron yield measurement

The distribution of the number of recorded hits has been studied with data in
order to calculate the number of detected Cherenkov photons. A loose selection
has been applied in order to reject possible noisy events. In particular
events with more than 10 hits in any one MaPMT or more than 30 hits in the
four MaPMTs have been rejected. The distribution of the number of hit pixels
per event for each MaPMT and in total is shown in Figure 16. These are
compared with the results from the Geant4 simulation and are also cross-
checked using an analytical estimate.

Figure 16: Multiplicity distribution for each of the four MaPMTs (top).
Distribution of the total number of hits in data with the expected
distribution obtained from the Geant4 simulation superimposed (bottom).

####  4.4.1 Comparison with simulation

The distributions of the number of hits per track in each MaPMT are shown in
the upper plots of Figure 16. The lower plot compares the total number
observed in data with that from the simulation as described in Section 3. The
mean number of hits per track, in data and in simulation, are given in Table 1
and agree within uncertainties. The uncertainties mainly come from the
determination of the inefficiencies in the readout and the knowledge of the
refractive index of the radiator.

####  4.4.2 Analytical estimate of the yield

The expected number of detected photo-electrons per unit length and per unit
of wavelength from a saturated track is given by:

$\frac{d^{2}N}{d\lambda
dx}=\frac{2\pi\alpha}{\lambda^{2}}(1-\frac{1}{n^{2}(\lambda)})\cdot{\rm
QE_{\rm MaPMT}(\lambda)}\cdot\hat{T}_{\rm lens}(\lambda)\\\
\times\epsilon_{\rm geo}\cdot\epsilon_{\rm Mirror-
refl}(\lambda)\cdot\epsilon_{\rm interface}(\lambda)\cdot\epsilon_{\rm
threshold}\cdot\epsilon_{\rm pixel}$ (2)

where $\alpha\simeq\frac{1}{137}$ is the fine structure constant, $n$ is the
refractive index of the lens and

  * •

${\rm QE_{\rm MaPMT}(\lambda)}$: quantum efficiency of the MaPMTs measured in
the laboratory (see Figure 11).

  * •

$\hat{T}_{\rm lens}(\lambda)$: average transmission of the borosilicate lens
measured in the laboratory and evaluated for the average photon path length.

  * •

$\epsilon_{geo}$: geometrical acceptance of the MaPMT with respect to the full
ring, given by optical simulations.

  * •

$\epsilon_{\rm Mirror-refl}=0.9$: assumed coefficient of the reflective layer
on the back surface of the lens. In first approximation it is considered
independent of the wavelength.

  * •

$\epsilon_{\rm interface}$: transmission coefficient at the plane surface of
the lens $\sim 96\%$, assumed independent of the wavelength

  * •

$\epsilon_{\rm threshold}$: average of the digital read out efficiency (see
4.1)

  * •

$\epsilon_{\rm pixel}$: dead area around each pixel (13%).

Integrating over the wavelength spectrum and the radiator length (13 mm) we
obtain the expected number of photo-electrons. These are shown in Table 1.
There is a reasonable agreement between the number of hits and the number
expected.

| Data | Simulation | Analytical estimate
---|---|---|---
| mean | RMS | mean | RMS | mean
Total | 13.4 | 3.8 | 13.1 | 2.9 | -
PMT A | 3.6 | 1.7 | 3.1 | 1.5 | 3.8
PMT B | 3.3 | 1.6 | 3.1 | 1.5 | 4.1
PMT C | 4.4 | 1.9 | 3.3 | 1.5 | 3.9
PMT D | 4.2 | 1.8 | 3.3 | 1.5 | 4.1
Table 1: Comparison of average yield in each MaPMT from data, simulation and
analytical estimate. For the analytical estimate the uncertainty on the
transmission curve gives an error of $\pm 0.01$ photo-electrons on the yields.
Other sources of error are negligible.

####  4.4.3 Multi-track correlation studies

A study of the correlation between multi-track events and number of photo-
electron hits on the MaPMTs has been performed. Figure 17 shows the
distribution of the number of hits for each MaPMT for events that contained
one, two and three beam particle tracks. Table 2 shows the parameters of these
distributions. It is clear that as the number of tracks in the event increases
so does the number of hits, as expected. The number of photons is not
proportional to the number of tracks as each pixel is read out in binary mode
and the probability that two photons will hit the same pixel increases with
the number of tracks. The correlation is in good agreement with the simulation
when the binary readout effect is included.

Figure 17: Distributions of the number of hits in each MaPMT for events with one, two and three tracks associated. | N${}_{\text{hits, 1 track}}$ | N${}_{\text{hits, 2 tracks}}$ | N${}_{\text{hits, 3 tracks}}$
---|---|---|---
PMT | Mean | RMS | Mean | RMS | Mean | RMS
PMT A | 3.93 | 3.31 | 6.78 | 4.17 | 8.71 | 3.90
PMT B | 3.58 | 3.20 | 6.31 | 4.06 | 8.17 | 4.53
PMT C | 4.70 | 3.68 | 7.35 | 4.29 | 8.34 | 2.80
PMT D | 4.50 | 3.89 | 7.26 | 4.70 | 8.47 | 3.98
Table 2: Parameters of the distributions of the number of hits for events with
one, two and three tracks associated.

###  4.5 Fit of the ring

A ring fit procedure has been developed in order to obtain a robust value for
the Cherenkov ring radius, centre and resolution and to compare the data with
the values expected from simulations. Two different procedures have been
developed. The first one uses the integrated events. For each run, a
minimization of the circle-to-data distance weighted by the number of hits per
pixel is performed on the accumulated number of hits per pixel assuming a
uniform distribution inside the pixel. The fitted ring superimposed to the
real data is shown in Figure 18 for two different runs. A radius of
$R=60.5\,{\rm{mm}}$ and an RMS of 0.5 mm, compatible with the values expected
from simulations, are obtained.

Figure 18: The fitted ring superimposed to the integrated events. The figure
shows the superimposition of two different runs taken with the ECs shifted in
the vertical direction in order to illuminate different pixels of the MaPMTs.

The second procedure is based on fits to single events: each event is fitted
independently. The ring centre coordinates $(x,y)$ and the radius are the free
parameters of the fit. The hit position is taken as the centre of the pixel
with an error given by the pixel size. For each event the distance between
pixel centre and ring is minimised. A fit for a single event is shown in
Figure 19.

Figure 19: Plot of the hits of a single event with the fitted ring
superimposed.

Distributions of the centre coordinates and of the radius extracted from the
single event fits are reported in Figure 20.

Figure 20: Centre coordinates $(x,y)$ and radius distributions of
reconstructed Cherenkov rings.

The mean value of the radius of $60.3\,{\rm{mm}}$ and the sigma of the
distribution $\sigma_{\rm R}=0.5\,{\rm{mm}}$ are in good agreement with the
values calculated with the first method and with the values expected from the
simulation.

###  4.6 Cherenkov angle reconstruction

The reconstruction of the Cherenkov angle is performed using the algorithm
described in [7], which requires as inputs the hit detection point, the photon
emission point, the centre of curvature of the mirror and the direction of the
charged track. In this case the ‘mirror’ is the curved surface of the lens
where there is a reflective coating and its radius of curvature is the same as
that of the lens. The algorithm makes use of the fact that one can define a
plane of reflection for the photons reflected at the mirror using the three
input coordinates and that the mirror reflection point is also in this plane
defined by these three coordinates.

The photon emission point is taken to be the mid-point of the track segment
radiating detectable photons. To simplify the geometry in the reconstruction,
the photon’s reflection on the flat surface of the lens is accounted for by
using an (optically equivalent) virtual emission point outside of the lens.
The virtual emission point is the reflection of the emission point in the flat
surface of the lens. The photons undergo a refraction when exiting the
radiator towards the MaPMT plane. An “image plane” is considered where the
photons would have traveled the same optical path length, without this
refraction. Using simulated data, every pixel centre on the MaPMT plane is
mapped to this “image plane”. The hits mapped on to this plane are used as the
detection point for the reconstruction algorithm. These transformations for
the emission point and detection point ensure that the three input coordinates
are in the plane as required by the algorithm described in [7].

####  4.6.1 Results from reconstruction

In Figure 21 the distribution of the reconstructed Cherenkov angle is shown
for data and in Figure 22 the same quantity is shown for the simulated data.
The two distributions have been fitted in the range 0.84 – 0.91 mrad with a
Gaussian function. The values of the fitted mean and width are quoted in the
corresponding captions. From these figures it can be seen that resolution in
data is compatible with that from simulation. The components of the resolution
from simulated data are shown in Table 3, which indicate that the resolution
is dominated by the pixel size. The chromatic error comes from the variation
of refractive index of the radiator with wavelength. The pixel size effect
also results in the small structures seen in the tail background regions in
Figure 21 and Figure 22.

Figure 21: Reconstructed Cherenkov angle from real data. This plot contains the data from all four MaPMTs. A Gaussian fit to the main peak has a mean of 875 mrad and a width of 17 mrad.  Figure 22: Reconstructed Cherenkov angle from full simulation. This plot contains the data from all four MaPMTs. A Gaussian fit to the main peak has a mean of 875 mrad and a width of 17 mrad.  | Resolution
---|---
| mrad
Chromatic | 4.5
Emission point | 7.4
Pixel size | 15.8
Total simulation | 17.0 $\pm$ 1.3
Data | 17.0 $\pm$ 0.8
Table 3: Cherenkov angle resolutions from data and simulations. The components
contributing to the resolution are also listed. The overall resolution and its
uncertainty are dominated by the pixel size contribution.

##  5 Conclusions

The results of the beam tests at the CERN SPS using the baseline photon
detectors and electronics for the LHCb RICH Upgrade have been presented. Using
a lens as a solid Cherenkov radiator at the same time as a focusing element,
Cherenkov rings have been observed. The setup has been used to test the main
concept for the integration of the electronics and photon detectors in a
complete readout system able to take data at a readout rate of 40 MHz,
including the compact design of four MaPMTs into an Elementary Cell. The opto-
electronics chain was similar to that proposed for the photon detector array
of the RICH upgrade. Results show the capability to detect single photons,
with a low dark current. The measured cross-talk level is low and compatible
with the RICH upgrade requirements. The spatial resolution obtained from the
reconstruction of the Cherenkov ring showed a good agreement with simulations.
Further characterisation of new prototypes will be carried out in future beam
tests, progressively integrating more modular units and with improved Data
Acquision and Detector Control Systems.

## Acknowledgements

The authors would like to thank all the LHCb technical staff in the
universities and institutes and especially at CERN who contributed to the RICH
test-beam activity. We gratefully acknowledge the CERN SPS machine operators
for the delivery of stable and reliable beams. The Science Technology and
Facilities Council (STFC) and Istituto Nazionale di Fisica Nucleare (INFN) are
also acknowledged for funding this work.
We also thank T. Gys, K. Wyllie, H. Schindler, M. van Beuzelkom, T. Schneider,
C. David and F. Fontanelli.
This project has also received funding from the European Union’s Horizon 2020
Research and Innovation programme under Grant Agreement no. 654168.

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