LZ Collaboration

# New constraints on ultraheavy dark matter from the LZ experiment

J. Aalbers  SLAC National Accelerator Laboratory, Menlo Park, CA 94025-7015,
USA  Kavli Institute for Particle Astrophysics and Cosmology, Stanford
University, Stanford, CA 94305-4085 USA  D.S. Akerib  SLAC National
Accelerator Laboratory, Menlo Park, CA 94025-7015, USA  Kavli Institute for
Particle Astrophysics and Cosmology, Stanford University, Stanford, CA
94305-4085 USA  A.K. Al Musalhi  University College London (UCL), Department
of Physics and Astronomy, London WC1E 6BT, UK  F. Alder  University College
London (UCL), Department of Physics and Astronomy, London WC1E 6BT, UK  C.S.
Amarasinghe  University of Michigan, Randall Laboratory of Physics, Ann Arbor,
MI 48109-1040, USA  A. Ames  SLAC National Accelerator Laboratory, Menlo Park,
CA 94025-7015, USA  Kavli Institute for Particle Astrophysics and Cosmology,
Stanford University, Stanford, CA 94305-4085 USA  T.J. Anderson  SLAC National
Accelerator Laboratory, Menlo Park, CA 94025-7015, USA  Kavli Institute for
Particle Astrophysics and Cosmology, Stanford University, Stanford, CA
94305-4085 USA  N. Angelides  Imperial College London, Physics Department,
Blackett Laboratory, London SW7 2AZ, UK  H.M. Araújo  Imperial College London,
Physics Department, Blackett Laboratory, London SW7 2AZ, UK  J.E. Armstrong
University of Maryland, Department of Physics, College Park, MD 20742-4111,
USA  M. Arthurs  SLAC National Accelerator Laboratory, Menlo Park, CA
94025-7015, USA  Kavli Institute for Particle Astrophysics and Cosmology,
Stanford University, Stanford, CA 94305-4085 USA  A. Baker  Imperial College
London, Physics Department, Blackett Laboratory, London SW7 2AZ, UK  S.
Balashov  STFC Rutherford Appleton Laboratory (RAL), Didcot, OX11 0QX, UK  J.
Bang  Brown University, Department of Physics, Providence, RI 02912-9037, USA
J.W. Bargemann  University of California, Santa Barbara, Department of
Physics, Santa Barbara, CA 93106-9530, USA  A. Baxter  University of
Liverpool, Department of Physics, Liverpool L69 7ZE, UK  K. Beattie  Lawrence
Berkeley National Laboratory (LBNL), Berkeley, CA 94720-8099, USA  T. Benson
University of Wisconsin-Madison, Department of Physics, Madison, WI
53706-1390, USA  A. Bhatti  University of Maryland, Department of Physics,
College Park, MD 20742-4111, USA  A. Biekert  Lawrence Berkeley National
Laboratory (LBNL), Berkeley, CA 94720-8099, USA  University of California,
Berkeley, Department of Physics, Berkeley, CA 94720-7300, USA  T.P.
Biesiadzinski  SLAC National Accelerator Laboratory, Menlo Park, CA
94025-7015, USA  Kavli Institute for Particle Astrophysics and Cosmology,
Stanford University, Stanford, CA 94305-4085 USA  H.J. Birch  University of
Michigan, Randall Laboratory of Physics, Ann Arbor, MI 48109-1040, USA  E.
Bishop  University of Edinburgh, SUPA, School of Physics and Astronomy,
Edinburgh EH9 3FD, UK  G.M. Blockinger  University at Albany (SUNY),
Department of Physics, Albany, NY 12222-0100, USA  B. Boxer  University of
California, Davis, Department of Physics, Davis, CA 95616-5270, USA  C.A.J.
Brew  STFC Rutherford Appleton Laboratory (RAL), Didcot, OX11 0QX, UK  P. Brás
Laboratório de Instrumentação e Física Experimental de Partículas (LIP),
University of Coimbra, P-3004 516 Coimbra, Portugal  S. Burdin  University of
Liverpool, Department of Physics, Liverpool L69 7ZE, UK  M. Buuck  SLAC
National Accelerator Laboratory, Menlo Park, CA 94025-7015, USA  Kavli
Institute for Particle Astrophysics and Cosmology, Stanford University,
Stanford, CA 94305-4085 USA  M.C. Carmona-Benitez  Pennsylvania State
University, Department of Physics, University Park, PA 16802-6300, USA  M.
Carter  University of Liverpool, Department of Physics, Liverpool L69 7ZE, UK
A. Chawla  Royal Holloway, University of London, Department of Physics, Egham,
TW20 0EX, UK  H. Chen  Lawrence Berkeley National Laboratory (LBNL), Berkeley,
CA 94720-8099, USA  J.J. Cherwinka  University of Wisconsin-Madison,
Department of Physics, Madison, WI 53706-1390, USA  N.I. Chott  South Dakota
School of Mines and Technology, Rapid City, SD 57701-3901, USA  M.V. Converse
University of Rochester, Department of Physics and Astronomy, Rochester, NY
14627-0171, USA  A. Cottle  University College London (UCL), Department of
Physics and Astronomy, London WC1E 6BT, UK  G. Cox  South Dakota Science and
Technology Authority (SDSTA), Sanford Underground Research Facility, Lead, SD
57754-1700, USA  D. Curran  South Dakota Science and Technology Authority
(SDSTA), Sanford Underground Research Facility, Lead, SD 57754-1700, USA  C.E.
Dahl  Northwestern University, Department of Physics & Astronomy, Evanston, IL
60208-3112, USA  Fermi National Accelerator Laboratory (FNAL), Batavia, IL
60510-5011, USA  A. David  University College London (UCL), Department of
Physics and Astronomy, London WC1E 6BT, UK  J. Delgaudio  South Dakota Science
and Technology Authority (SDSTA), Sanford Underground Research Facility, Lead,
SD 57754-1700, USA  S. Dey  University of Oxford, Department of Physics,
Oxford OX1 3RH, UK  L. de Viveiros  Pennsylvania State University, Department
of Physics, University Park, PA 16802-6300, USA  C. Ding  Brown University,
Department of Physics, Providence, RI 02912-9037, USA  J.E.Y. Dobson  King’s
College London, Department of Physics, London WC2R 2LS, UK  E. Druszkiewicz
University of Rochester, Department of Physics and Astronomy, Rochester, NY
14627-0171, USA  S.R. Eriksen  University of Bristol, H.H. Wills Physics
Laboratory, Bristol, BS8 1TL, UK  A. Fan  SLAC National Accelerator
Laboratory, Menlo Park, CA 94025-7015, USA  Kavli Institute for Particle
Astrophysics and Cosmology, Stanford University, Stanford, CA 94305-4085 USA
N.M. Fearon  University of Oxford, Department of Physics, Oxford OX1 3RH, UK
S. Fiorucci  Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA
94720-8099, USA  H. Flaecher  University of Bristol, H.H. Wills Physics
Laboratory, Bristol, BS8 1TL, UK  E.D. Fraser  University of Liverpool,
Department of Physics, Liverpool L69 7ZE, UK  T.M.A. Fruth  The University of
Sydney, School of Physics, Physics Road, Camperdown, Sydney, NSW 2006,
Australia  R.J. Gaitskell  Brown University, Department of Physics,
Providence, RI 02912-9037, USA  A. Geffre  South Dakota Science and Technology
Authority (SDSTA), Sanford Underground Research Facility, Lead, SD 57754-1700,
USA  J. Genovesi  South Dakota School of Mines and Technology, Rapid City, SD
57701-3901, USA  C. Ghag  University College London (UCL), Department of
Physics and Astronomy, London WC1E 6BT, UK  R. Gibbons  Lawrence Berkeley
National Laboratory (LBNL), Berkeley, CA 94720-8099, USA  University of
California, Berkeley, Department of Physics, Berkeley, CA 94720-7300, USA  S.
Gokhale  Brookhaven National Laboratory (BNL), Upton, NY 11973-5000, USA  J.
Green  University of Oxford, Department of Physics, Oxford OX1 3RH, UK
M.G.D.van der Grinten  STFC Rutherford Appleton Laboratory (RAL), Didcot, OX11
0QX, UK  C.R. Hall  University of Maryland, Department of Physics, College
Park, MD 20742-4111, USA  S. Han  SLAC National Accelerator Laboratory, Menlo
Park, CA 94025-7015, USA  Kavli Institute for Particle Astrophysics and
Cosmology, Stanford University, Stanford, CA 94305-4085 USA  E.
Hartigan-O’Connor  Brown University, Department of Physics, Providence, RI
02912-9037, USA  S.J. Haselschwardt  Lawrence Berkeley National Laboratory
(LBNL), Berkeley, CA 94720-8099, USA  S.A. Hertel  University of
Massachusetts, Department of Physics, Amherst, MA 01003-9337, USA  G.
Heuermann  University of Michigan, Randall Laboratory of Physics, Ann Arbor,
MI 48109-1040, USA  G.J. Homenides  University of Alabama, Department of
Physics & Astronomy, Tuscaloosa, AL 34587-0324, USA  M. Horn  South Dakota
Science and Technology Authority (SDSTA), Sanford Underground Research
Facility, Lead, SD 57754-1700, USA  D.Q. Huang  University of Michigan,
Randall Laboratory of Physics, Ann Arbor, MI 48109-1040, USA  D. Hunt
University of Oxford, Department of Physics, Oxford OX1 3RH, UK  C.M. Ignarra
SLAC National Accelerator Laboratory, Menlo Park, CA 94025-7015, USA  Kavli
Institute for Particle Astrophysics and Cosmology, Stanford University,
Stanford, CA 94305-4085 USA  E. Jacquet  Imperial College London, Physics
Department, Blackett Laboratory, London SW7 2AZ, UK  R.S. James  University
College London (UCL), Department of Physics and Astronomy, London WC1E 6BT, UK
J. Johnson  University of California, Davis, Department of Physics, Davis, CA
95616-5270, USA  A.C. Kaboth  Royal Holloway, University of London, Department
of Physics, Egham, TW20 0EX, UK  A.C. Kamaha  University of Califonia, Los
Angeles, Department of Physics & Astronomy, Los Angeles, CA 90095-1547  D.
Khaitan  University of Rochester, Department of Physics and Astronomy,
Rochester, NY 14627-0171, USA  A. Khazov  STFC Rutherford Appleton Laboratory
(RAL), Didcot, OX11 0QX, UK  I. Khurana  University College London (UCL),
Department of Physics and Astronomy, London WC1E 6BT, UK  J. Kim  University
of California, Santa Barbara, Department of Physics, Santa Barbara, CA
93106-9530, USA  J. Kingston  University of California, Davis, Department of
Physics, Davis, CA 95616-5270, USA  R. Kirk  Brown University, Department of
Physics, Providence, RI 02912-9037, USA  D. Kodroff  Pennsylvania State
University, Department of Physics, University Park, PA 16802-6300, USA  L.
Korley  University of Michigan, Randall Laboratory of Physics, Ann Arbor, MI
48109-1040, USA  E.V. Korolkova  University of Sheffield, Department of
Physics and Astronomy, Sheffield S3 7RH, UK  H. Kraus  University of Oxford,
Department of Physics, Oxford OX1 3RH, UK  S. Kravitz  Lawrence Berkeley
National Laboratory (LBNL), Berkeley, CA 94720-8099, USA  University of Texas
at Austin, Department of Physics, Austin, TX 78712-1192, USA  L. Kreczko
University of Bristol, H.H. Wills Physics Laboratory, Bristol, BS8 1TL, UK  B.
Krikler  University of Bristol, H.H. Wills Physics Laboratory, Bristol, BS8
1TL, UK  V.A. Kudryavtsev  University of Sheffield, Department of Physics and
Astronomy, Sheffield S3 7RH, UK  J. Lee  IBS Center for Underground Physics
(CUP), Yuseong-gu, Daejeon, Korea  D.S. Leonard  IBS Center for Underground
Physics (CUP), Yuseong-gu, Daejeon, Korea  K.T. Lesko  Lawrence Berkeley
National Laboratory (LBNL), Berkeley, CA 94720-8099, USA  C. Levy  University
at Albany (SUNY), Department of Physics, Albany, NY 12222-0100, USA  J. Lin
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA 94720-8099, USA
University of California, Berkeley, Department of Physics, Berkeley, CA
94720-7300, USA  A. Lindote  Laboratório de Instrumentação e Física
Experimental de Partículas (LIP), University of Coimbra, P-3004 516 Coimbra,
Portugal  R. Linehan  SLAC National Accelerator Laboratory, Menlo Park, CA
94025-7015, USA  Kavli Institute for Particle Astrophysics and Cosmology,
Stanford University, Stanford, CA 94305-4085 USA  W.H. Lippincott  University
of California, Santa Barbara, Department of Physics, Santa Barbara, CA
93106-9530, USA  M.I. Lopes  Laboratório de Instrumentação e Física
Experimental de Partículas (LIP), University of Coimbra, P-3004 516 Coimbra,
Portugal  E. Lopez Asamar  Laboratório de Instrumentação e Física Experimental
de Partículas (LIP), University of Coimbra, P-3004 516 Coimbra, Portugal  W.
Lorenzon  University of Michigan, Randall Laboratory of Physics, Ann Arbor, MI
48109-1040, USA  C. Lu  Brown University, Department of Physics, Providence,
RI 02912-9037, USA  S. Luitz  SLAC National Accelerator Laboratory, Menlo
Park, CA 94025-7015, USA  P.A. Majewski  STFC Rutherford Appleton Laboratory
(RAL), Didcot, OX11 0QX, UK  A. Manalaysay  Lawrence Berkeley National
Laboratory (LBNL), Berkeley, CA 94720-8099, USA  R.L. Mannino  Lawrence
Livermore National Laboratory (LLNL), Livermore, CA 94550-9698, USA  C. Maupin
South Dakota Science and Technology Authority (SDSTA), Sanford Underground
Research Facility, Lead, SD 57754-1700, USA  M.E. McCarthy  University of
Rochester, Department of Physics and Astronomy, Rochester, NY 14627-0171, USA
G. McDowell  University of Michigan, Randall Laboratory of Physics, Ann Arbor,
MI 48109-1040, USA  D.N. McKinsey  Lawrence Berkeley National Laboratory
(LBNL), Berkeley, CA 94720-8099, USA  University of California, Berkeley,
Department of Physics, Berkeley, CA 94720-7300, USA  J. McLaughlin
Northwestern University, Department of Physics & Astronomy, Evanston, IL
60208-3112, USA  R. McMonigle  University at Albany (SUNY), Department of
Physics, Albany, NY 12222-0100, USA  E.H. Miller  SLAC National Accelerator
Laboratory, Menlo Park, CA 94025-7015, USA  Kavli Institute for Particle
Astrophysics and Cosmology, Stanford University, Stanford, CA 94305-4085 USA
E. Mizrachi  University of Maryland, Department of Physics, College Park, MD
20742-4111, USA  Lawrence Livermore National Laboratory (LLNL), Livermore, CA
94550-9698, USA  A. Monte  University of California, Santa Barbara, Department
of Physics, Santa Barbara, CA 93106-9530, USA  M.E. Monzani  SLAC National
Accelerator Laboratory, Menlo Park, CA 94025-7015, USA  Kavli Institute for
Particle Astrophysics and Cosmology, Stanford University, Stanford, CA
94305-4085 USA  Vatican Observatory, Castel Gandolfo, V-00120, Vatican City
State  J.D. Morales Mendoza  SLAC National Accelerator Laboratory, Menlo Park,
CA 94025-7015, USA  Kavli Institute for Particle Astrophysics and Cosmology,
Stanford University, Stanford, CA 94305-4085 USA  E. Morrison  South Dakota
School of Mines and Technology, Rapid City, SD 57701-3901, USA  B.J. Mount
Black Hills State University, School of Natural Sciences, Spearfish, SD
57799-0002, USA  M. Murdy  University of Massachusetts, Department of Physics,
Amherst, MA 01003-9337, USA  A.St.J. Murphy  University of Edinburgh, SUPA,
School of Physics and Astronomy, Edinburgh EH9 3FD, UK  A. Naylor  University
of Sheffield, Department of Physics and Astronomy, Sheffield S3 7RH, UK  C.
Nedlik  University of Massachusetts, Department of Physics, Amherst, MA
01003-9337, USA  H.N. Nelson  University of California, Santa Barbara,
Department of Physics, Santa Barbara, CA 93106-9530, USA  F. Neves
Laboratório de Instrumentação e Física Experimental de Partículas (LIP),
University of Coimbra, P-3004 516 Coimbra, Portugal  A. Nguyen  University of
Edinburgh, SUPA, School of Physics and Astronomy, Edinburgh EH9 3FD, UK  J.A.
Nikoleyczik  University of Wisconsin-Madison, Department of Physics, Madison,
WI 53706-1390, USA  I. Olcina<EMAIL_ADDRESS>Lawrence Berkeley National
Laboratory (LBNL), Berkeley, CA 94720-8099, USA  University of California,
Berkeley, Department of Physics, Berkeley, CA 94720-7300, USA  K.C. Oliver-
Mallory  Imperial College London, Physics Department, Blackett Laboratory,
London SW7 2AZ, UK  J. Orpwood  University of Sheffield, Department of Physics
and Astronomy, Sheffield S3 7RH, UK  K.J. Palladino  University of Oxford,
Department of Physics, Oxford OX1 3RH, UK  J. Palmer  Royal Holloway,
University of London, Department of Physics, Egham, TW20 0EX, UK  N.J.
Pannifer  University of Bristol, H.H. Wills Physics Laboratory, Bristol, BS8
1TL, UK  N. Parveen  University at Albany (SUNY), Department of Physics,
Albany, NY 12222-0100, USA  S.J. Patton  Lawrence Berkeley National Laboratory
(LBNL), Berkeley, CA 94720-8099, USA  B. Penning  University of Michigan,
Randall Laboratory of Physics, Ann Arbor, MI 48109-1040, USA  G. Pereira
Laboratório de Instrumentação e Física Experimental de Partículas (LIP),
University of Coimbra, P-3004 516 Coimbra, Portugal  E. Perry  University
College London (UCL), Department of Physics and Astronomy, London WC1E 6BT, UK
T. Pershing  Lawrence Livermore National Laboratory (LLNL), Livermore, CA
94550-9698, USA  A. Piepke  University of Alabama, Department of Physics &
Astronomy, Tuscaloosa, AL 34587-0324, USA  Y. Qie  University of Rochester,
Department of Physics and Astronomy, Rochester, NY 14627-0171, USA  J.
Reichenbacher  South Dakota School of Mines and Technology, Rapid City, SD
57701-3901, USA  C.A. Rhyne  Brown University, Department of Physics,
Providence, RI 02912-9037, USA  Q. Riffard  Lawrence Berkeley National
Laboratory (LBNL), Berkeley, CA 94720-8099, USA  G.R.C. Rischbieter
University of Michigan, Randall Laboratory of Physics, Ann Arbor, MI
48109-1040, USA  H.S. Riyat  University of Edinburgh, SUPA, School of Physics
and Astronomy, Edinburgh EH9 3FD, UK  R. Rosero  Brookhaven National
Laboratory (BNL), Upton, NY 11973-5000, USA  T. Rushton  University of
Sheffield, Department of Physics and Astronomy, Sheffield S3 7RH, UK  D.
Rynders  South Dakota Science and Technology Authority (SDSTA), Sanford
Underground Research Facility, Lead, SD 57754-1700, USA  D. Santone  Royal
Holloway, University of London, Department of Physics, Egham, TW20 0EX, UK
A.B.M.R. Sazzad  University of Alabama, Department of Physics & Astronomy,
Tuscaloosa, AL 34587-0324, USA  R.W. Schnee  South Dakota School of Mines and
Technology, Rapid City, SD 57701-3901, USA  S. Shaw  University of Edinburgh,
SUPA, School of Physics and Astronomy, Edinburgh EH9 3FD, UK  T. Shutt  SLAC
National Accelerator Laboratory, Menlo Park, CA 94025-7015, USA  Kavli
Institute for Particle Astrophysics and Cosmology, Stanford University,
Stanford, CA 94305-4085 USA  J.J. Silk  University of Maryland, Department of
Physics, College Park, MD 20742-4111, USA  C. Silva  Laboratório de
Instrumentação e Física Experimental de Partículas (LIP), University of
Coimbra, P-3004 516 Coimbra, Portugal  G. Sinev  South Dakota School of Mines
and Technology, Rapid City, SD 57701-3901, USA  R. Smith
<EMAIL_ADDRESS>Lawrence Berkeley National Laboratory (LBNL),
Berkeley, CA 94720-8099, USA  University of California, Berkeley, Department
of Physics, Berkeley, CA 94720-7300, USA  V.N. Solovov  Laboratório de
Instrumentação e Física Experimental de Partículas (LIP), University of
Coimbra, P-3004 516 Coimbra, Portugal  P. Sorensen  Lawrence Berkeley National
Laboratory (LBNL), Berkeley, CA 94720-8099, USA  J. Soria  Lawrence Berkeley
National Laboratory (LBNL), Berkeley, CA 94720-8099, USA  University of
California, Berkeley, Department of Physics, Berkeley, CA 94720-7300, USA  I.
Stancu  University of Alabama, Department of Physics & Astronomy, Tuscaloosa,
AL 34587-0324, USA  A. Stevens  University College London (UCL), Department of
Physics and Astronomy, London WC1E 6BT, UK  Imperial College London, Physics
Department, Blackett Laboratory, London SW7 2AZ, UK  K. Stifter  Fermi
National Accelerator Laboratory (FNAL), Batavia, IL 60510-5011, USA  B. Suerfu
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA 94720-8099, USA
University of California, Berkeley, Department of Physics, Berkeley, CA
94720-7300, USA  T.J. Sumner  Imperial College London, Physics Department,
Blackett Laboratory, London SW7 2AZ, UK  M. Szydagis  University at Albany
(SUNY), Department of Physics, Albany, NY 12222-0100, USA  W.C. Taylor  Brown
University, Department of Physics, Providence, RI 02912-9037, USA  D.R. Tiedt
South Dakota Science and Technology Authority (SDSTA), Sanford Underground
Research Facility, Lead, SD 57754-1700, USA  M. Timalsina  Lawrence Berkeley
National Laboratory (LBNL), Berkeley, CA 94720-8099, USA  South Dakota School
of Mines and Technology, Rapid City, SD 57701-3901, USA  Z. Tong  Imperial
College London, Physics Department, Blackett Laboratory, London SW7 2AZ, UK
D.R. Tovey  University of Sheffield, Department of Physics and Astronomy,
Sheffield S3 7RH, UK  J. Tranter  University of Sheffield, Department of
Physics and Astronomy, Sheffield S3 7RH, UK  M. Trask  University of
California, Santa Barbara, Department of Physics, Santa Barbara, CA
93106-9530, USA  M. Tripathi  University of California, Davis, Department of
Physics, Davis, CA 95616-5270, USA  D.R. Tronstad  South Dakota School of
Mines and Technology, Rapid City, SD 57701-3901, USA  W. Turner  University of
Liverpool, Department of Physics, Liverpool L69 7ZE, UK  A. Vacheret  Imperial
College London, Physics Department, Blackett Laboratory, London SW7 2AZ, UK
A.C. Vaitkus  Brown University, Department of Physics, Providence, RI
02912-9037, USA  V. Velan  Lawrence Berkeley National Laboratory (LBNL),
Berkeley, CA 94720-8099, USA  A. Wang  SLAC National Accelerator Laboratory,
Menlo Park, CA 94025-7015, USA  Kavli Institute for Particle Astrophysics and
Cosmology, Stanford University, Stanford, CA 94305-4085 USA  J.J. Wang
University of Alabama, Department of Physics & Astronomy, Tuscaloosa, AL
34587-0324, USA  Y. Wang  Lawrence Berkeley National Laboratory (LBNL),
Berkeley, CA 94720-8099, USA  University of California, Berkeley, Department
of Physics, Berkeley, CA 94720-7300, USA  J.R. Watson  Lawrence Berkeley
National Laboratory (LBNL), Berkeley, CA 94720-8099, USA  University of
California, Berkeley, Department of Physics, Berkeley, CA 94720-7300, USA
R.C. Webb  Texas A&M University, Department of Physics and Astronomy, College
Station, TX 77843-4242, USA  L. Weeldreyer  University of Alabama, Department
of Physics & Astronomy, Tuscaloosa, AL 34587-0324, USA  T.J. Whitis
University of California, Santa Barbara, Department of Physics, Santa Barbara,
CA 93106-9530, USA  M. Williams  University of Michigan, Randall Laboratory of
Physics, Ann Arbor, MI 48109-1040, USA  W.J. Wisniewski  SLAC National
Accelerator Laboratory, Menlo Park, CA 94025-7015, USA  F.L.H. Wolfs
University of Rochester, Department of Physics and Astronomy, Rochester, NY
14627-0171, USA  S. Woodford  University of Liverpool, Department of Physics,
Liverpool L69 7ZE, UK  D. Woodward  Lawrence Berkeley National Laboratory
(LBNL), Berkeley, CA 94720-8099, USA  Pennsylvania State University,
Department of Physics, University Park, PA 16802-6300, USA  C.J. Wright
University of Bristol, H.H. Wills Physics Laboratory, Bristol, BS8 1TL, UK  Q.
Xia  Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA 94720-8099,
USA  X. Xiang  Brown University, Department of Physics, Providence, RI
02912-9037, USA  Brookhaven National Laboratory (BNL), Upton, NY 11973-5000,
USA  J. Xu  Lawrence Livermore National Laboratory (LLNL), Livermore, CA
94550-9698, USA  M. Yeh  Brookhaven National Laboratory (BNL), Upton, NY
11973-5000, USA  E.A. Zweig  University of Califonia, Los Angeles, Department
of Physics & Astronomy, Los Angeles, CA 90095-1547

(Received: date / Accepted: date)

###### Abstract

Searches for dark matter with liquid xenon time projection chamber experiments
have traditionally focused on the region of the parameter space that is
characteristic of weakly interacting massive particles, ranging from a few
$\text{\,}\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}\mathrm{c}^{2}$ to a few
$\text{\,}\mathrm{T}\mathrm{e}\mathrm{V}\mathrm{/}\mathrm{c}^{2}$. Models of
dark matter with a mass much heavier than this are well motivated by early
production mechanisms different from the standard thermal freeze-out, but they
have generally been less explored experimentally. In this work, we present a
re-analysis of the first science run (SR1) of the LZ experiment, with an
exposure of $0.9$ tonne$\times$year, to search for ultraheavy particle dark
matter. The signal topology consists of multiple energy deposits in the active
region of the detector forming a straight line, from which the velocity of the
incoming particle can be reconstructed on an event-by-event basis. Zero events
with this topology were observed after applying the data selection calibrated
on a simulated sample of signal-like events. New experimental constraints are
derived, which rule out previously unexplored regions of the dark matter
parameter space of spin-independent interactions beyond a mass of
$10^{17}\text{\,}\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}\mathrm{c}^{2}$.

##  I Introduction

The astrophysical evidence for the existence of dark matter (DM) is widespread
[1, 2, 3]. Despite the abundance of indirect evidence manifested through the
gravitational effects of dark matter on luminous matter, its nature remains
elusive [4, 5]. New particles have been invoked to explain this puzzle, with
the weakly interacting massive particle (WIMP) and the QCD axion being two of
the most popular candidates [6, 7]. However, searches for these two particles
have so far come back empty-handed [8, 9].

The LZ experiment recently set the most stringent limit on the spin-
independent DM-nucleon cross section in its first WIMP search run [10]. The LZ
experiment is located in the Davis Campus at the Sanford Underground Research
Facility (SURF) in Lead, South Dakota (USA). It employs a large, dual-phase
time projection chamber (TPC) of approximately $1.5\text{\,}\mathrm{m}$ in
diameter and height, containing 7 active tonnes of liquid xenon (LXe). It
features two additional detectors: an instrumented “Skin” of LXe used to veto
gamma-ray and neutron interactions around the active region, and an Outer
Detector (OD) surrounding the TPC that is highly efficient at tagging neutrons
and gamma-rays escaping the TPC. A full description of the LZ experiment can
be found in Ref. [11].

In the present work, we consider the search for ultraheavy dark matter
particles with the LZ experiment using the same dataset that was used to
search for WIMPs in Science Run 1 (SR1) [10] with an overall exposure of $0.9$
tonne$\times$year. Several mechanisms to create such heavy particles in the
early universe have been proposed [12, 13]. For example, the unitary limit
imposed on particles produced by thermal freeze-out can be circumvented with
composite dark matter models in which light constituents fused together
relatively late in the history of the Universe [14, 15, 16, 17, 18, 19].
Astrophysical constraints on high mass dark matter interactions with nuclei
exist, but they are rather weak, arising mainly from observations of gas
clouds [20], cosmic rays [21, 22], white dwarf explosions [23], and ancient
mica [24].

As opposed to WIMPs, particles in the high mass region of the parameter space
lose only a small fraction of their energy with each scattering interaction
with Standard Model (SM) particles. In addition, they are likely to scatter
several times inside a detector, creating a track-like event. These particles
are commonly known as multiply interacting massive particles (MIMPs) [25]. At
the astrophysical level MIMPs are expected to act as collisionless, point-like
particles, likewise WIMPs [26]. A few experimental searches for MIMPs already
exist [27, 28, 29, 30], but they are noticeably small in number compared to
WIMP searches.

The paper is organized as follows: in Section II we describe the main features
of a MIMP interaction in the LZ experiment. We present the data selection in
Section III, discuss the main findings in Section IV, and conclude in Section
V.

##  II Signal topology

A single scatter (SS) in the active region of the TPC results in a prompt
scintillation signal in the liquid phase (S1) and a secondary proportional
scintillation signal in the gaseous phase (S2). The second light signal is
created via electroluminescence from ionisation electrons that are drifted
through the liquid by an applied electric field and subsequently extracted to
the gaseous phase. These light signals are observed by two arrays of
photomultiplier tubes (PMT) located at the top and bottom of the TPC. The
location of an energy deposit in the TPC is reconstructed from the time
difference between the S1 and S2 signals (z coordinate) and the spatial
distribution of the S2 signal in the top PMT array (x and y coordinates).

In the region of the DM parameter space explored in the search for WIMPs by LZ
in Ref. [10], with masses around
$100\text{\,}\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}\mathrm{c}^{2}$ and WIMP-
nucleon interaction cross sections of the order of
$10^{-47}\text{\,}\mathrm{c}\mathrm{m}^{2}$, the flux of transits of dark
matter across the detector is relatively high, but the probability that any
given transit results in a single scatter is very low. By contrast, in the
region of high mass ($>$
$10^{4}\text{\,}\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}\mathrm{c}^{2}$) and
high cross section ($>$ $10^{-31}\text{\,}\mathrm{c}\mathrm{m}^{2}$) of the
dark matter parameter space, the expected flux of dark matter transits is
heavily reduced due to the low DM number density, but each of them is expected
undergo multiple scatters (MS) inside the detector [25]. Consequently, a
dedicated analysis looking for multiple-scatter events is required to search
for MIMPs. It is important to note that scatters from a transiting MIMP would
form a straight line given that the angular deflection in each interaction is
vanishingly small for dark matter masses much heavier than the xenon nucleus
[31].

A cartoon of this signal topology is shown in Figure 1. Multiple S1 pulses
occur in a short period of time (typically a few $\text{\,}\mu\mathrm{s}$) and
are followed by multiple S2 pulses occurring over the following few hundreds
of $\text{\,}\mu\mathrm{s}$. The time separation between the S1 pulses is
determined by the arrival times of each scatter, while the time between S2
pulses is determined by the scatter depths [32, 33]. Importantly, the
positions measured from the S2 pulses and the times measured by the S1 pulses
can be used to reconstruct both the magnitude and direction of the velocity
vector on an event-by-event basis.

The experimental signature of multiple S1s and multiple S2s forming a track is
rather extraordinary. There are only a limited number of processes that could
mimic this signature. First, muons can create events with multiple S2s.
However, muons deposit large amounts of energy in the detector, of order of
hundreds of MeV, and they can be easily tagged by the external veto detectors.
Second, the correlated radiogenic emission of 214Bi-214Po and 212Bi-212Po
decays, originated in the 238U and 232Th decay chains, respectively. The
product of the first decay has a half-life short enough for its decay to be
likely to occur within the same event window, but long enough for the S1
pulses to be resolvable. However, the energy deposited by the emitted
particles is an order of magnitude larger than that of a recoil energy
produced by a MIMP and they are expected to occur in the same physical
location; hence, they do not constitute a relevant background. Third, gamma-
rays and neutrons may scatter at multiple resolvable positions in the
detector, producing multiple S2s. However, gamma-ray or MeV neutrons move too
quickly (covering the full 1.5 m dimensions of LZ in under 5 ns) for the
multiple scatters they may deposit to produce separate S1s. Slower neutrons
moving at velocities consistent with a MIMP signal have insufficient kinetic
energy to produce above-threshold nuclear recoil signals. Moreover, neutrons
scatter by forming an erratic pattern rather than a straight line due to the
low mass of a neutron with respect to the xenon nucleus, which makes them easy
to reject. Overall, the expected sources of background for the MIMP search are
limited to rare cases of pulse pileup from accidental coincidences [34]. We
estimate that the pileup of single-scatter events in the SR1 exposure yields
less than 0.17 events, rendering the total background rate negligible.

Figure 1: Illustration of a MIMP crossing the TPC of the LZ experiment and
creating three distinct scatters in the active region. Each of these energy
depositions is observed as a pair of S1 and S2 light signals in the liquid and
gas regions, respectively.

Prior to searching for MIMPs in the LZ SR1 data, we studied the signal
topology in detail with a simulated sample of track-like events traversing the
detector. We used an LZ-specific software package to simulate DM transits
across the TPC. Velocities and incident angles were sampled randomly from the
Standard Halo Model (SHM) velocity distribution [35] and propagated through to
the detector assuming the same parametric model of the LZ detector used for
the WIMP search [10]. Since the DM energy spectrum is independent of mass in
the high-mass limit, we assumed a fixed dark matter mass of
$10^{17}\text{\,}\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}\mathrm{c}^{2}$ and
varied the DM-nucleon cross section.

Pulses which arrive closely spaced in time relative to the pulse width may not
be resolved by the LZ pulse finder algorithm, and therefore, it is especially
important to the MIMP search that the simulations account for this pulse
merging effect. LZ’s parametric simulation model determines pulses to be
merged based on their separation in time, width, and relative pulse area [36,
37]. Generally, pulses merge when their separation in arrival time is below
approximately $200\text{\,}\mathrm{n}\mathrm{s}$ for S1s and
$2\text{\,}\mu\mathrm{s}$ for S2s. The effects of pulse merging are
illustrated in Figure 2, which shows the average number of true scatters,
reconstructed S1 pulses, and reconstructed S2 pulses as a function of the
spin-independent DM-nucleon cross section. Above a cross section of
$10^{-30}\text{\,}\mathrm{c}\mathrm{m}^{2}$, the average number of
reconstructed S1 pulses in a simulated MIMP event starts to decrease due to
pulse merging. Generally, S2 pulses are more easily resolved than S1 pulses
due to their larger separation in time. The maximum cross section probed in
this analysis is $10^{-29}\text{\,}\mathrm{c}\mathrm{m}^{2}$, above which the
S1 and S2 pulses in a MIMP event are exceedingly unlikely to be reconstructed
as individual pulses.

Given the relatively high cross sections probed in this search, it is also
important to consider the significance of Earth’s shielding, referred to as
the overburden. To determine the overburden boundary, we performed simulations
of the MIMP flux from every direction for different mass and cross section
values in the dark matter parameter space. We set the overburden boundary
along those points in the parameter space where less than 1 in $10^{5}$ dark
matter particles propagated through the Earth maintain a sufficiently large
velocity to cause a deposit in the LZ experiment with an energy above 1 keV.
For cross sections below our maximum search value of
$10^{-29}\text{\,}\mathrm{c}\mathrm{m}^{2}$, we find that the overburden
boundary is only relevant for masses below approximately 105 GeV/c2. Note that
at that mass regime the expected number of dark matter transits in LZ without
considering the overburden is much greater than 105. However, we decided to
choose the conservative value of 105 trials to optimize the use of limited
computational resources. For more details on the simulation procedure, please
see Ref. [38].

Figure 2: Average number of reconstructed S1 (green), S2 (blue), and true
scatters (black) in simulated events as a function of the spin-independent DM-
nucleon cross section assuming a DM mass of
$10^{17}\text{\,}\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}\mathrm{c}^{2}$. The
simulated events are required to have at least one true scatter. However, note
that not all simulated scatters will produce both an S1 and an S2 pulse. The
LZ pulse reconstruction software starts merging S1 pulses at lower cross
sections than S2 pulses.

##  III Methodology

The SR1 dataset was acquired during a period of 116 calendar days. Of that
period, approximately 89 livedays were dedicated to acquiring WIMP search
data. That period is reduced down to 60 livedays after applying data quality
cuts designed to exclude periods in which the detector environment was
unsuitable for conducting a physics search [10]. Most notably, hold-off times
of tens of milliseconds were excluded after large S2s, which are known to be
typically followed by elevated photon and electron emission rates [39].
Moreover, periods of time immediately after a muon was tagged by LZ’s veto
system were removed. The strategy employed in Ref. [10] to search for WIMPs
was to look for single-scatter events uniformly distributed in the TPC with no
accompanying signals in either of the veto detectors (Skin or OD). A strict
data selection in the region-of-interest (ROI) of 3–80 phd in corrected S1
area, $>600$ phd in uncorrected S2 area (equivalent to 10 extracted electrons)
and $<10^{5}$ phd in corrected S2 area was applied. Moreover, a profile
likelihood ratio (PLR) analysis was conducted to evaluate the compatibility of
the surviving single-scatter events with LZ’s WIMP search background model,
described in Ref. [34]. By contrast, in the MIMP search we look for multiple-
scatter events of the kind described in Section II and design data quality
cuts that are as loose as possible to minimize the reduction of the signal
detection efficiency. We start with the same 60 live day dataset, referred to
as the initial selection, and introduce new data selection criteria specific
to the MIMP search. To mitigate experimenter bias, we calibrated the data
selection on a simulated dataset before applying it to the observed dataset.
Furthermore, and given the remarkable topology of the sought-after signal, we
set deliberately loose cut boundaries.

The first MIMP-specific cut we apply to the data is the multiplicity cut,
which ensures that more than 1 S1 and more than 1 S2 pulses are registered in
the event. Then, the good S1 cut is applied to select S1 pulses of a certain
quality according to two criteria: first, we only accept S1 pulses in which
the observed light is not overly concentrated in one PMT; second, we veto
events that have a nearly coincident signal with the Outer Detector within a
few hundred nanoseconds around the S1 arrival time (following the same
strategy that was devised for the SR1 WIMP search [10]). It is important to
note that we do not consider possible MIMP interactions in either the Skin or
the OD.

A fiducial cut is applied to take advantage of the reduced radioactivity of
the inner volume of the detector due to self-shielding. Events are required to
have at least two S2 pulses reconstructed within the fiducial volume. This
volume is defined by a cylinder approximating the WIMP search fiducial volume
[10], albeit slightly expanded—the extraordinary signature of a MIMP signal
compared to a WIMP affords some extra lenience in the fiducialization.
Elevated rates outside the fiducial volume make pileup of those events more
likely. Additionally, the cut at the top of the detector mitigates a prominent
background source of event misreconstruction due to interactions that occur in
the gas phase. The fiducial region is defined by a radius of
$70\text{\,}\mathrm{c}\mathrm{m}$ from the center and a bottom and a top that
are $2\text{\,}\mathrm{c}\mathrm{m}$ and $135\text{\,}\mathrm{c}\mathrm{m}$
above the cathode, respectively.

MIMPs are not expected to be noticeably deflected by xenon atoms as they
transit LZ. We exploit this feature by introducing a colinearity cut. The
colinearity of the scatter positions reconstructed from each S2 in a candidate
MIMP track is evaluated in two steps. First, a weighted orthogonal distance
regression of the $xy$ coordinates of each S2 is performed. We adopt the same
S2 position resolution model described in Ref. [34]. The $xy$ colinearity cut
is placed on the corresponding reduced $\chi^{2}$ value. We apply an upper
boundary of reduced $\chi^{2}$ equal to 2, informed by the reduced $\chi^{2}$
distribution of simulated MIMP-like events at a DM-nucleon cross section of
$10^{-30}$ cm2 (which is near the peak S2 pulse multiplicity, see Figure 2).
Second, we check that the ordering of S2 pulses along the length of the track
is monotonic. Events with exactly two S2s pass the colinearity cut trivially.

If an event passes the colinearity cut, a three-dimensional best fit track is
calculated, along with regressed positions $\mathbf{s}_{i}$ of each scatter
along this track. Here $i$ ranges from 1 to the total number $N$ of S2 pulses
in the event, with the ordering determined by the distance along the track. A
test of the uniformity of the scatters along the track is performed in this
one-dimensional position space. An estimate of the mean free path ($\lambda$)
is provided by the distance between the furthest apart scatters divided by the
number of gaps between scatters,

$\lambda=\frac{|\mathbf{s}_{N}-\mathbf{s}_{1}|}{N-1}.$ (1)

Then, the distance between scatters, along with the distance between the
endpoint scatters and the extrapolated intersections with the TPC boundary,
are compared to $\lambda$. The event is rejected if the largest gap exceeds a
distance of $20\lambda$ or the smallest gap is lower than $0.01\lambda$.

Additionally, we use a velocity cut to compare the reconstructed velocity of
the candidate MIMP event to the expected dark matter velocity distribution in
the galactic halo. The regressed positions $\mathbf{s}_{i}$ are used to
estimate the magnitude of the velocity vector of the MIMP particle,

$v=\frac{|\mathbf{s}_{N}-\mathbf{s}_{1}|}{t_{N}-t_{1}},$ (2)

where the times $t_{1}$ and $t_{N}$ are the arrival times of the first and
last S1 pulses, respectively. This reconstructed velocity metric is subject to
some deviation from the true one. For instance, two nearby scatters can cause
merged pulses, and some scatters may not produce both an S1 and S2 pulse above
threshold. Both effects are more likely to result in the loss of S1s than S2s,
which causes the velocity to be overestimated due to the reduction in time
between the reconstructed S1 pulses. The velocity cut is based on the
distribution of simulated reconstructed velocities, which is generally broader
than the true incident velocity distribution. Figure 3 shows the reconstructed
velocity distribution of MIMP-like events for four different spin-independent
DM-nucleon cross sections. Reconstructed velocities below
$50\text{\,}\mathrm{k}\mathrm{m}\mathrm{/}\mathrm{s}$ and above
$1200\text{\,}\mathrm{k}\mathrm{m}\mathrm{/}\mathrm{s}$ are considered invalid
MIMP candidates. These values are based on the tails of the reconstructed
velocity distribution (0.4th and 96.6th percentiles), for the reference cross
section of $10^{-30}\text{\,}\mathrm{c}\mathrm{m}^{2}$ (above this cross
section, S1 pulses are likely to start merging, as shown in Figure 2). Note
that the blue histogram representing the lower cross section of 3$\cdot$10-32
cm2 peaks at a lower velocity than the SHM (shown in red) because of the
$v^{-2}$ dependence of the differential DM-nucleus cross section [40, 41, 42],
favoring the detection of slower MIMPs.

Lastly, we apply an ROI cut that restricts the search space of total S1 and S2
areas. This cut is set conservatively based on the expected distribution of
simulated MIMP events in the space of total S1 area and total S2 area, shown
in Figure 4. The events surviving the previously described data analysis cuts
are shown as black points. All events are distributed in the excluded region
of small summed S1 sizes and large ($>10^{5}$ phd) summed S2 sizes. This is
characteristic of pileup backgrounds, rather than MIMP-like events. As an
example, we show the S1 and S2 waveforms of the event labelled “Event A” in
Figure 5. The narrow, flat-top shape of the S2 pulses reveals that this is an
event that originated near the liquid surface, where electron diffusion is
limited due to the short drift length. The true S1 pulse can actually be seen
on the left of the first S2 pulse. However, it was merged into the S2 by the
pulse reconstruction algorithm. Given that the true drift length of the energy
deposit that created the S2 pulses is of the order of a few
$\text{\,}\mu\mathrm{s}$, the reconstructed S1 pulses happening hundreds of
$\text{\,}\mu\mathrm{s}$ apart cannot have originated from the same energy
deposit.

The total signal acceptance, shown in Figure 6, was evaluated from the sample
of simulated MIMP events. The fiducial, uniformity, and velocity cuts have the
largest impact on the total signal acceptance, with a more pronounced effect
for increasing cross sections. At cross sections above
$10^{-30}{cm^{2}}\text{\,}\mathrm{t}$he acceptance drops significantly, mostly
due to the velocity cut. This is due to a noticeable increase in pulse
merging, as was shown in Figure 2, causing the reconstructed velocity to be
outside the cut boundaries.

Figure 3: Reconstructed velocities for simulated MIMP events with DM-nucleon
cross sections 3$\times$10-32 cm2 (blue), 3$\times$10-31 cm2 (gold), 10-30 cm2
(black), 3$\times$10-30 cm2 (green) for a DM mass of
$10^{17}\text{\,}\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}\mathrm{c}^{2}$. The
Standard Halo Model velocity distribution is shown as the shaded red region
for reference. The exclusion regions imposed by the velocity cut are indicated
by the shaded grey areas. Figure 4: Cut boundaries for the ROI cut in the
space of total S1 area and total S2 area. The excluded regions are indicated
by the gray areas. The 68% and 95% contours of the population of simulated
MIMPs with a cross section of 10-30 cm2 are shown in light and dark blue,
respectively. Events passing all the data analysis cuts before this one are
shown as black points. The S1 and S2 pulses of one of the points (Event A) are
displayed in Figure 5. Figure 5: S1 and S2 waveforms for Event A highlighted
in Figure 4. A total of two S1 and two S2 pulses were reconstructed in this
event, respectively. The narrow, flat-top shape of the S2 pulses is
characteristic of an energy deposit occurring near the liquid surface. The two
S1 pulses shown on the left cannot originate from the same energy deposit that
created the S2 pulses given their time separation. This event is removed by
the ROI cut. Figure 6: Acceptance of the cuts listed in Table 1 as a function
of the DM-nucleon scattering cross section evaluated on a simulated dataset of
MIMP-like events of mass
$10^{17}\text{\,}\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}\mathrm{c}^{2}$. Each
colored line shows the acceptance conditional on applying the previous listed
cuts. By contrast, the black line shows the total acceptance with respect to
the initial selection. A 1$\sigma$ binomial uncertainty band is indicated in
grey. The acceptance is generally high except for cross sections larger than
$10^{-30}\text{\,}\mathrm{c}\mathrm{m}^{2}$, when most events start failing
the velocity cut (pink).

##  IV Results and discussion

The effect of each analysis cut on the SR1 dataset is shown in Table 1. The
last column shows the number of events surviving each cut, reaching a total
count of 0 after we apply all data selection cuts. Dark matter models for
which the expected number of signal events exceeds 2.44 (after accounting for
the signal acceptance shown in Figure 6) are excluded at 90% confidence level,
which follows the Feldman & Cousins convention for an observation of 0 events
and a mean background of 0 events [43]. We show these limits in Figure 7,
labelled “LZ SR1 MS”, alongside previous limits derived from similar multi
scatter searches conducted by other experiments [27, 28, 29, 30].

In addition to the limits obtained from this multiple-scatter analysis, we
extend limits based on the LZ SR1 WIMP search presented in Ref. [10] to high
masses and cross sections, labelled in Figure 7 as “LZ SR1 SS”. In that
publication, limits are displayed up to a mass of 10 TeV/c2; at this mass, a
WIMP model on the limit curve would yield 4.4 expected signal events based on
the results from the corresponding PLR analysis. This result is extrapolated
to high masses along a contour with an equal expected number of signal events.
This extrapolation is justified by the fact that the expected recoil rate
spectrum is independent of mass for dark matter masses much greater than the
xenon atomic mass [40, 41, 42]. Note that this limit cannot be extrapolated
indefinitely since only a negligible amount of dark matter transits at high
cross sections will produce one scatter (those transits that result in more
than one scatter are removed by the single-scatter requirement [10]). This
effect sets a ceiling on the SS limit, as shown in Figure 7. In addition, the
fact that the number of single scatters decreases while the number of multiple
scatters increases for increasing cross section values explains why the “LZ
SR1 MS” limits have higher reach. The MS analysis has superior signal
acceptance at high cross sections and can yield exclusion limits that reach
larger masses compared to the SS analysis.

Table 1: List of data analysis cuts applied to the SR1 dataset to search for MIMPs. The number of surviving events after each cut is indicated in the last column. Cut ID | Name | Description | Events
---|---|---|---
0 | Initial selection | See Section III | 10137
1 | Multiplicity |  $>$1 S1s; $>$1 S2s | 1538
2 | Good S1 | No S1s are overly concentrated in one PMT or have a coincident signal in the OD | 1400
3 | Fiducial |  $\geq 2$ S2s with z $\in$ (2, 135) cm and $r<$ 70 cm | 269
4 | Colinearity | Reduced $\chi^{2}<2$; scatters are causally ordered along the track | 237
5 | Uniformity | Scatters are distributed along the track uniformly | 67
6 | Velocity | Reconstructed $v$ $\in$ (50, 1200) km/s | 11
7 | ROI | Total S1 and total S2 area is within signal region | 0

We assume two different dark matter models for the limits shown in Figure 7.
Instead of carrying out a comprehensive study of theoretical models, we focus
our attention to showing the results of this search under two contrasting
models. First, the upper panel of Figure 7 shows the exclusion limits assuming
the cross section model that is typically adopted in direct detection
searches. This assumes a spin-independent DM-nuclear scattering in which the
total DM-nucleus cross section ($\sigma_{\chi N}$) is coherently enhanced with
respect to the DM-nucleon cross section ($\sigma_{\chi n}$). In this case, the
differential cross section for the DM-nucleus elastic scattering takes the
form [44, 42]

$\frac{d\sigma_{\chi N}}{dE_{R}}=\frac{d\sigma_{\chi
n}}{dE_{R}}\left(\frac{\mu_{\chi N}}{\mu_{\chi
n}}\right)^{2}A^{2}|F_{N}(q)|^{2},$ (3)

where $E_{R}$ is the recoil energy of the nucleus, $\mu_{\chi N}$ and
$\mu_{\chi n}$ are the reduced masses of the DM-nucleus and DM-nucleon cross
sections, respectively, $A$ is the number of nucleons in the nucleus, and
$F_{N}(q)$ is the nuclear form factor, for which we consider the Helm form
factor [45]. In the heavy dark matter limit, a factor of $A^{2}$ arises from
the ratio of the two reduced masses, resulting in the expression

$\frac{d\sigma_{\chi N}}{dE_{R}}=\frac{d\sigma_{\chi
n}}{dE_{R}}A^{4}|F_{N}(q)|^{2}.$ (4)

Note that the derivation of this relationship assumes a regime of low
interaction strength, so the $A^{4}$ scaling may not be a reasonable
assumption for high DM-nucleon cross sections [46]. Precise scaling between
the DM-nucleon and DM-nucleus cross sections is dependent on the choice of the
interaction potential. Additionally, at high masses where composite dark
matter models are especially relevant, it may be required to consider a form
factor term not only for the nucleus but also for the dark matter particle
[18]. We leave a more comprehensive study of alternative dark matter models to
future publications.

Second, we consider a contact interaction model with no coherent enhancement
of the per-nucleon cross section, taking the form

$\frac{d\sigma_{\chi N}}{dE_{R}}=\frac{d\sigma_{\chi
n}}{dE_{R}}|F_{N}(q)|^{2}.$ (5)

This model has also been selected as an additional benchmark for the
sensitivity of high cross section dark matter searches in other studies [47,
48, 27]. Without the $A^{4}$ enhancement, the heavier xenon nucleus loses some
advantage in probing dark matter at low cross sections. This is apparent in
the lower panel of Figure 7, which shows an increased overlap between the LZ
MS limit and previous constraints using other target elements [28, 29, 30].

Figure 7: The 90% confidence level upper limit on the DM scattering cross
section as a function of DM mass assuming two contrasting models of scattering
with the nucleus. First, a coherent, spin-independent scattering (top);
second, a non-coherent scattering between a dark matter particle and the
nucleus (bottom). An $A^{4}$ scaling arises in the first case due to the
coherent and kinematic enhancements of the signal rate (see text). The results
from the MIMP search analysis are shown as solid lines, while the extrapolated
limits from the WIMP search analysis in Ref. [10] are shown as dashed lines.
Constraints from other experiments are also shown: XENON1T [27], DEAP [28],
DAMA [29], and Chicago [30]. The extrapolation of the constraint set by
XENON1T to lower masses is shown with a dash-dotted grey line.

With the results from this analysis, we are able to probe an intermediate
parameter space between the LZ SR1 SS limit and MS limits set by other
experiments [27, 28, 29, 30]. In the LZ SR1 MS analysis, MIMP signals must
include well-separated S1s and S2s. At high cross sections, the LZ SR1 MS
analysis loses sensitivity when multiple pulses are no longer resolvable,
causing the “turnaround” at high masses. By contrast, similar searches by
DEAP-3600 [48] and XENON1T [27] seek a MIMP signal topology consisting of
single pulses with anomalous shape caused by the merging of many closely-
spaced signals. Consequently, the limits from those searches can extend to
higher cross section, but their sensitivity to dark matter models resulting in
a low multiplicity of scatters (i.e. low cross section) is heavily
constrained.

##  V Conclusions

By considering transiting dark matter that has a high probability of
interacting within its path length across the LZ TPC detector, such that
multiple scatters become likely, we demonstrated that LZ can extend its
sensitivity to dark matter models of high masses and high cross sections. The
low energy threshold and large surface area of LZ makes this kind of search
favorable. After data selection, we did not observe any event that was
consistent with a transiting MIMP in the SR1 dataset. Based on this result, we
set competitive per-nucleus limits and world-leading per-nucleon limits for
dark matter at high mass. The maximum mass probed by LZ is extended to
3.9$\times$1017
$\text{\,}\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}\mathrm{c}^{2}$ compared to
an extrapolation of the WIMP search exclusion limit from Ref. [10]. In the
full exposure of 1000 day live days, and assuming a similar total acceptance
as the one shown in Figure 6, we predict LZ will probe dark matter masses up
to 6.5$\times$1018
$\text{\,}\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}\mathrm{c}^{2}$.

Additionally, the rich information in MIMP events, especially full
reconstruction of the velocity vector, will be valuable for confirming the
dark matter origin as well as reconstructing dark matter properties in the
event of the observation of this type of signal. For some models, the single-
scatter and multiple-scatter channels can provide complementary information
that will be essential to investigate any excess observed in the data.

###### Acknowledgements.

The research supporting this work took place in part at SURF in Lead, South
Dakota. Funding for this work is supported by the U.S. Department of Energy,
Office of Science, Office of High Energy Physics under Contract Numbers DE-
AC02-05CH11231, DE-SC0020216, DE-SC0012704, DE-SC0010010, DE-AC02-07CH11359,
DE-SC0012161, DE-SC0015910, DE-SC0014223, DE-SC0010813, DE-SC0009999, DE-
NA0003180, DE-SC0011702, DE-SC0010072, DE-SC0015708, DE-SC0006605, DE-
SC0008475, DE-SC0019193, DE-FG02-10ER46709, UW PRJ82AJ, DE-SC0013542, DE-
AC02-76SF00515, DE-SC0018982, DE-SC0019066, DE-SC0015535, DE-SC0019319, DE-
AC52-07NA27344, & DOE-SC0012447, & DE-SC0024225. This research was also
supported by U.S. National Science Foundation (NSF); the UKRI’s Science &
Technology Facilities Council under award numbers ST/M003744/1, ST/M003655/1,
ST/M003639/1, ST/M003604/1, ST/M003779/1, ST/M003469/1, ST/M003981/1,
ST/N000250/1, ST/N000269/1, ST/N000242/1, ST/N000331/1, ST/N000447/1,
ST/N000277/1, ST/N000285/1, ST/S000801/1, ST/S000828/1, ST/S000739/1,
ST/S000879/1, ST/S000933/1, ST/S000844/1, ST/S000747/1, ST/S000666/1,
ST/R003181/1; Portuguese Foundation for Science and Technology (FCT) under
award numbers PTDC/FIS-PAR/2831/2020; the Institute for Basic Science, Korea
(budget number IBS-R016-D1). We acknowledge additional support from the STFC
Boulby Underground Laboratory in the U.K., the GridPP [49, 50] and IRIS
Collaborations, in particular at Imperial College London and additional
support by the University College London (UCL) Cosmoparticle Initiative. We
acknowledge additional support from the Center for the Fundamental Physics of
the Universe, Brown University. K.T. Lesko acknowledges the support of
Brasenose College and Oxford University. The LZ Collaboration acknowledges key
contributions of Dr. Sidney Cahn, Yale University, in the production of
calibration sources. This research used resources of the National Energy
Research Scientific Computing Center, a DOE Office of Science User Facility
supported by the Office of Science of the U.S. Department of Energy under
Contract No. DE-AC02-05CH11231. We gratefully acknowledge support from GitLab
through its GitLab for Education Program. The University of Edinburgh is a
charitable body, registered in Scotland, with the registration number
SC005336. The assistance of SURF and its personnel in providing physical
access and general logistical and technical support is acknowledged. We
acknowledge the South Dakota Governor’s office, the South Dakota Community
Foundation, the South Dakota State University Foundation, and the University
of South Dakota Foundation for use of xenon. We also acknowledge the
University of Alabama for providing xenon. For the purpose of open access, the
authors have applied a Creative Commons Attribution (CC BY) licence to any
Author Accepted Manuscript version arising from this submission. We thank
Rafael Lang, Shengchao Li, Shawn Westerdale, and Joseph Bramante for
insightful discussions.

## Data release

Selected data from the following plots can be accessed at
https://tinyurl.com/LZDataReleaseRun1MIMPSearch

  * •

Figure 6: points representing the total acceptance curve for the multiple-
scatter analysis (black line).

  * •

Figure 7: points representing the 90% confidence level upper limits assuming
two contrasting dark matter models. First, a spin-independent, scattering
model in which the differential cross section for the DM-nucleus elastic
scattering scales as $A^{4}$ with the DM-nucleon elastic scattering
differential cross section ($A$ is the nuclear mass number). Second, a spin-
independent, scattering model in which no coherent enhancement of the per-
nucleon cross section is assumed. Two limits are shown in each case: the upper
limit corresponding to the MIMP search analysis (solid line), and the
extrapolated limit from the WIMP search analysis to high dark matter masses
(dashed line) [10]. The points are expressed in units of GeV/c2 and cm2 for
mass and cross section, respectively.

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