# Particle Physics at the European Spallation Source

H. Abele  A. Alekou  A. Algora  K. Andersen  S. Baeßler  L. Barron-Pálos  J.
Barrow11footnotemark: 122footnotemark: 2 E. Baussan  P. Bentley  Z. Berezhiani
Y. Beßler33footnotemark: 3 A. K. Bhattacharyya  A. Bianchi  J. Bijnens  C.
Blanco  N. Blaskovic Kraljevic  M. Blennow  K. Bodek  M. Bogomilov  C.
Bohm44footnotemark: 4 B. Bolling  E. Bouquerel  G. Brooijmans55footnotemark: 5
L. J. Broussard66footnotemark: 6 O. Buchan  A. Burgman  H.
Calén77footnotemark: 7 C. J. Carlile  J. Cederkall  E. Chanel  P. Christiansen
V. Cirigliano  J. I. Collar  M. Collins  C. B. Crawford  E. Cristaldo Morales
P. Cupiał  L. D’Alessi  J. I. M. Damian88footnotemark: 8 H. Danared  D.
Dancila  J. P. A. M. de André  J. P. Delahaye  S. Degenkolb  D. D. Di Julio
M. Dracos  K. Dunne99footnotemark: 9 I. Efthymiopoulos  T. Ekelöf  L.
Eklund1010footnotemark: 10 M. Eshraqi  I. Esteban  G. Fanourakis  A. Farricker
E. Fernandez-Martinez  M. J. Ferreira  M. Fertl  P. Fierlinger  B. Folsom  A.
Frank  A. Fratangelo  U. Friman-Gayer  T. Fukuda  H .O .U. Fynbo  A. Garcia
Sosa  N. Gazis  B. Gålnander  Th. Geralis  M. Ghosh  G. Gokbulut  J .J. Gomez-
Cadenas  M. Gonzalez-Alonso  F. Gonzalez1111footnotemark: 11 L. Halić  C.
Happe1212footnotemark: 12 P. Heil  A. Heinz1313footnotemark: 13 H. Herde  M.
Holl1414footnotemark: 14 T. Jenke  M. Jenssen  E. Jericha  H. T.
Johansson1515footnotemark: 15 R. Johansson  T. Johansson1616footnotemark: 16
Y. Kamyshkov1717footnotemark: 17 A. Kayis Topaksu  B. Kildetoft  K. Kirch  B.
Kliček  E. Klinkby  R. Kolevatov  G. Konrad  M. Kozioł  K. Krhač  A.
Kupść1818footnotemark: 181919footnotemark: 19 Ł. Łacny  L. Larizgoitia  C. M.
Lewis  M. Lindroos  E. Lychagin  E. Lytken  C. Maiano  P. Marciniewski  G.
Markaj  B. Märkisch  C. Marrelli  C. Martins  B. Meirose2020footnotemark:
202121footnotemark: 21 M. Mezzetto  N. Milas  D. Milstead2222footnotemark: 22
F. Monrabal  G. Muhrer  A. Nepomuceno2323footnotemark: 23 V.
Nesvizhevsky2424footnotemark: 24 T. Nilsson2525footnotemark: 25 P. Novella  M.
Oglakci  T. Ohlsson  M. Olvegård  A. Oskarsson  T. Ota  J. Park262626Now at
The center for Exotic Nuclear Studies, Institute for Basic Science, 34126
Daejeon, Korea D. Patrzalek  H. Perrey  M. Persoz  G. Petkov  F.M. Piegsa  C.
Pistillo  P. Poussot  P. Privitera  B. Rataj2727footnotemark: 27 D. Ries  N.
Rizzi  S. Rosauro-Alcaraz  D. Rozpedzik  D. Saiang  V. Santoro  U. Schmidt  H.
Schober  I. Schulthess  S. Silverstein2828footnotemark: 28 A. Simón  H. Sina
J. Snamina  W. M. Snow2929footnotemark: 293030footnotemark:
303131footnotemark: 31 T. Soldner  G. Stavropoulos  M. Stipčević  B. Szybiński
A. Takibayev  Z. Tang  R. Tarkeshian  C. Theroine  J. Thorne  F. Terranova  J.
Thomas  T. Tolba  P. Torres-Sánchez  E. Trachanas  R. Tsenov  U. I. Uggerhøj
G. Vankova-Kirilova  N. Vassilopoulos  R. Wagner  X. Wang  E. Wildner  M.
Wolke3232footnotemark: 32 J. Wurtz  S. C. Yiu3333footnotemark: 33 S. G. Yoon
A. R. Young3434footnotemark: 34 L. Zanini3535footnotemark: 35 J. Zejma  D.
Zerzion  O. Zimmer3636footnotemark: 36 O. Zormpa  Y. Zou  Department of
Physics and Astronomy, Aarhus University, Aarhus, Denmark  University of
Cukurova, Faculty of Science and Letters, Department of Physics, 01330 Adana,
Turkey  Institute of Nuclear and Particle Physics, NCSR Demokritos, Neapoleos
27, 15341 Agia Paraskevi, Greece  Laboratory for High Energy Physics and
Albert Einstein Center for Fundamental Physics, University of Bern, 3012 Bern,
Switzerland  Ikerbasque, Basque Foundation for Science, Plaza Euskadi 5,
E-48013 Bilbao, Spain  Department of Physics, Indiana University, 727 E. Third
St., Bloomington, IN 47405, USA  Indiana University Center for Exploration of
Energy & Matter, Bloomington, IN 47408, USA  Indiana University Quantum
Science and Engineering Center, Bloomington, IN 47408, USA  Mirrotron Ltd.,
29-33 Konkoly Thege Miklós út, 1121 Budapest, Hungary  Centre for Energy
Research, 29-33 Konkoly Thege Miklós út, 1121 Budapest, Hungary  Massachusetts
Institute of Technology, Dept. of Physics, Cambridge, MA 02139, USA
Department of Physics, University of Virginia, Charlottesville, VA 22904, USA
Enrico Fermi Institute and KICP, University of Chicago, Chicago, IL 60637, USA
Center for Cosmology and AstroParticle Physics (CCAPP), Ohio State University,
Columbus, Ohio 43210, USA  Department of Physics, Ohio State University,
Columbus, Ohio 43210, USA  Spallation Neutron Science Center, Dongguan 523803,
China  Donostia International Physics Center (DIPC), Paseo Manuel Lardizabal
4, 20018 Donostia-San Sebastian, Spain  Joint Institute for Nuclear Research,
141980 Dubna, Russia  Physikdepartment/E66, Technische Universität München,
James-Franck-Str. 1, 85748 Garching, Germany  Physik-Department ENE,
Technische Universität München, James-Franck-Str. 1 85748 Garching, Germany
CERN, 1211 Geneva 23, Switzerland  Institutionen för Fysik, Chalmers Tekniska
Högskola, Gothenburg, Sweden  Departamento de Física Atómica, Molecular y
Nuclear, Universidad de Granada, Granada, Spain  Institut Laue-Langevin, 71
Avenue des Martyrs, 38042 Grenoble, France  Institute for Experimental
Physics, Hamburg University, 22761 Hamburg, Germany  Physikalisches Institut,
Universität Heidelberg, 69120 Heidelberg, Germany  Forschungszentrum Jülich,
52425 Jülich, Germany  Department of Physics and Astronomy, The University of
Tennessee, Knoxville, TN 37996, USA  AGH University of Science and Technology,
al. Mickiewicza 30, 30-059 Krakow, Poland  Marian Smoluchowski Institute of
Physics, Jagiellonian University, 30-348 Krakow, Poland  INFN, Laboratori
Nazionali del Gran Sasso, Assergi, 67100 L’Aquila, Italy  Dipartimento di
Scienze Fisiche e Chimiche, Universita’ di L’Aquila, Via Vetoio, Coppito 1,
67100 L’Aquila, Italy  Molecular Nanophotonics Group, Peter Debye Institute
for Soft Matter Physics, Faculty of Physics and Earth Sciences, Universität
Leipzig, Germany  Scads.AI (Center for Scalable Data Analytics and Artificial
Intelligence), Leipzig, Germany  University of Kentucky, Lexington, KY 40504,
USA  Luleå University of Technology, 97187 Luleå, Sweden  Department of
Physics, Lund University, P.O Box 118, 221 00 Lund, Sweden  Faculty of
Engineering, Lund University, P.O Box 118, 221 00 Lund, Sweden  Department of
Astronomy and Theoretical Physics, Lund University, Box 43, SE 221-00 Lund,
Sweden  European Spallation Source ERIC, Box 176, SE-221 00 Lund, Sweden
European Spallation Source Consultant, Norway  Departamento de Fisica Teorica
and Instituto de Fisica Teorica, IFT-UAM/CSIC, Universidad Autonoma de Madrid,
Cantoblanco, 28049, Madrid, Spain  Department of Chemistry - TRIGA site,
Johannes Gutenberg University Mainz, 55128 Mainz, Germany  Institute of
Physics, Johannes Gutenberg University Mainz, Staudinger Weg 7, 55099 Mainz,
Germany  Instituto de Física, Universidad Nacional Autónoma de México,
Apartado Postal 20-364, 01000, México  University of Milano-Bicocca and INFN
sez. di Milano-Bicocca, Milano, Italy  Department of Physics, Nagoya
University, Nagoya 464–8602, Japan  Los Alamos National Laboratory, New Mexico
87544, USA  Department of Physics, Columbia University, New York, NY 10027,
USA  Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA  Pôle Théorie,
Laboratoire de Physique des 2 Infinis Iréne Joliot Curie (UMR 9012)
CNRS/IN2P3, 15 rue Georges Clemenceau, 91400 Orsay, France  INFN sez. di
Padova, Padova, Italy  Laboratoire de Physique Nucléaire et de Hautes Énergies
(LPNHE), Sorbonne Université ,Université Paris Cité, CNRS/IN2P3, Paris, France
Department of Physics, Princeton University, Princeton 08544, NJ USA
Department of Physics, North Carolina State University, Raleigh, NC
27695-8202, USA  Departamento de Ciências da Natureza, Universidade Federal
Fluminense, Rua Recife, 28890-000 Rio das Ostras, RJ, Brazil  DTU Physics,
Technical University of Denmark, Frederiksborgvej 399, DK-4000 Roskilde,
Denmark  Institute for Nuclear Theory, University of Washington, 3910 15th Ave
NE, Seattle, WA 98195, USA  Sofia University St. Kliment Ohridski, Faculty of
Physics, 1164 Sofia, Bulgaria  IPHC, Université de Strasbourg, CNRS/IN2P3,
Strasbourg, France  Department of Physics, School of Engineering Sciences, KTH
Royal Institute of Technology, Roslagstullsbacken 21, 106 91 Stockholm, Sweden
Department of Physics, Stockholm University, 106 91 Stockholm, Sweden  The
Oskar Klein Centre, AlbaNova University Center, Roslagstullsbacken 21, 106 91
Stockholm, Sweden  School of Physics and Astronomy, Tel Aviv University, Tel
Aviv 69978, Israel  Department of Physics and Astronomy, Uppsala University,
Box 516, 75120 Uppsala, Sweden  Uppsala University, P.O. Box 256, 751 05
Uppsala, Sweden  Instituto de Fisica Corpuscular, CSIC-Universitat de
Valéncia, E-46071 Valéncia, Spain  Paul Scherrer Institute, 5232 Villigen PSI,
Switzerland  Cockroft Institute (A36), Liverpool University, Warrington WA4
4AD, UK  National Centre for Nuclear Research, Pasteura 7, 02-093 Warsaw,
Poland  TU-Wien, Atominstitut, Stadionallee 2, 1020 Wien, Austria  Center of
Excellence for Advanced Materials and Sensing Devices, Ruđer Bošković
Institute, 10000 Zagreb, Croatia  Institute for Particle Physics and
Astrophysics, ETH Zürich, 8093 Zürich, Switzerland

###### Abstract

Presently under construction in Lund, Sweden, the European Spallation Source
(ESS) will be the world’s brightest neutron source. As such, it has the
potential for a particle physics program with a unique reach and which is
complementary to that available at other facilities. This paper describes
proposed particle physics activities for the ESS. These encompass the
exploitation of both the neutrons and neutrinos produced at the ESS for high
precision (sensitivity) measurements (searches).

###### Contents

  1. 1 Glossary
  2. 2 Introduction
  3. 3 The European Spallation Source
    1. 3.1 The Accelerator and the target area
    2. 3.2 The ESS instrument suite
    3. 3.3 The ESS lower moderator
    4. 3.4 ESS timescales and accelerator power usage projections
  4. 4 Theory
    1. 4.1 Neutrons
      1. 4.1.1 Precision measurements in neutron beta decay
      2. 4.1.2 Searches for a non-zero neutron electric dipole moment
      3. 4.1.3 Neutron oscillations to anti-neutrons or to sterile neutrons
      4. 4.1.4 Searches for extra fundamental interactions, gravitational spectroscopy, Lorentz invariance tests
      5. 4.1.5 Studies of hadronic parity violation
    2. 4.2 Neutrinos
      1. 4.2.1 Coherent neutrino-nucleus scattering
      2. 4.2.2 Neutrino oscillations, leptonic CP violation, non-standard neutrino interactions with matter
  5. 5 ANNI
    1. 5.1 Introduction
      1. 5.1.1 Benefits of pulsed neutron beams for particle physics experiments
      2. 5.1.2 ANNI design guidelines and preliminary design
    2. 5.2 Precision neutron decay
      1. 5.2.1 Introduction
      2. 5.2.2 ep/n separator
      3. 5.2.3 BRAND
      4. 5.2.4 Experiments with Cyclotron Radiation Emission Spectroscopy
    3. 5.3 Electric dipole moment of the neutron
      1. 5.3.1 The Beam EDM experiment
      2. 5.3.2 EDM with _in-situ_ UCN production
    4. 5.4 Neutron electric charge
    5. 5.5 Hadronic weak interaction
      1. 5.5.1 Improvement of the SNS experiments NPDGamma and n3He
      2. 5.5.2 New experiments: NDTGamma, spin rotation
      3. 5.5.3 Hadronic TRIV measurements
    6. 5.6 ANNI summary tables
  6. 6 The HIBEAM/NNBAR program
    1. 6.1 Introduction
    2. 6.2 HIBEAM
      1. 6.2.1 Search for $n\rightarrow n{{}^{\prime}}$ via disappearance
      2. 6.2.2 Search for the regenerative $n\rightarrow n{{}^{\prime}},\bar{n}^{\prime}\rightarrow n$ process
      3. 6.2.3 Search for $n\rightarrow\bar{n}$ by regeneration through mirror states
      4. 6.2.4 Detectors for sterile neutron searches
      5. 6.2.5 HIBEAM sensitivity
    3. 6.3 NNBAR at the ESS - measurement methodology
    4. 6.4 NNBAR design
      1. 6.4.1 The NNBAR Large Beam Port
      2. 6.4.2 NNBAR optics
      3. 6.4.3 Magnetic shielding and vacuum
      4. 6.4.4 Preliminary detector design
    5. 6.5 Previous free neutron oscillation searches and current limits
    6. 6.6 NNBAR sensitivity at the ESS
    7. 6.7 The gain from using the ESS
    8. 6.8 Comparison with other future experiments
    9. 6.9 An option to use the coherent reflection of antineutrons and neutrons
  7. 7 UCN/VCN
    1. 7.1 Implementing a UCN source at the ESS
    2. 7.2 Measurements of the neutron lifetime
    3. 7.3 Gravitational spectroscopy with neutrons
    4. 7.4 Measurements of the neutron’s permanent electric dipole moment (EDM)
    5. 7.5 Study of non-stationary quantum effects
    6. 7.6 Implementation of a VCN Source at the ESS
    7. 7.7 Scientific Prospects for Use of VCN
  8. 8 CE$\nu$NS at the ESS
    1. 8.1 Introduction
    2. 8.2 CE$\nu$NS at the ESS
    3. 8.3 Timeline and expected sensitivity
  9. 9 The ESS neutrino Super Beam (ESS$\nu$SB)
    1. 9.1 Instrumentation
      1. 9.1.1 Proton Driver
      2. 9.1.2 Accumulator Ring
      3. 9.1.3 Short pulses for neutron production
      4. 9.1.4 Target Station
      5. 9.1.5 Detectors
    2. 9.2 Optimizing the neutrino baseline
    3. 9.3 Physics reach of the ESS$\nu$SB experiment
    4. 9.4 ESS$\nu$SB Synergies with Future Projects
      1. 9.4.1 Low Energy nuSTORM
      2. 9.4.2 A Proton Complex Test Facility for a Muon Collider at ESS
    5. 9.5 Proposed Project Time Line
  10. 10 Conclusion

##  1 Glossary

Acronym/term |  Meaning
---|---
ANNI |  Pulsed cold neutron beam facility for particle physics at the ESS
aCORN |  Spectrometer for measuring the electron-neutrino correlation coefficient $a$ in neutron decay
$a$SPECT |  Spectrometer for measuring the electron-neutrino correlation coefficient $a$ in neutron decay
BD |  Beam Dump
Beam EDM |  Experiment to measure the nEDM using a pulsed neutron beam
BRAND |  Spectrometer for measuring correlation coefficients in neutron decay ($BRAND$ is a subset of the targeted correlation coefficients)
CAD |  Computer Aided Design
CCW |  Counter Clock Wise
CE$\nu$NS |  Coherent Elastic Neutrino-Nucleus Scattering
CKM |  Cabibbo–Kobayashi–Maskawa
COHERENT |  Experiment to measure CE$\nu$NS at the SNS
CDR |  Conceptual Design Report
CP |  Charge-Parity
CPT |  Charge-Parity-Time Reversal
CRES |  Cyclotron Radiation Emission Spectroscopy
CW |  Clock Wise
DDH |  Desplanques-Donoghue-Holstein
DE |  Dark Energy
DM |  Dark Matter
DPA |  Displacements per Atom
DTL |  Drift Tube Linac
EDM |  Electric Dipole Moment
EDMn |  Concept for a scalable multi-chamber experiment to measure the nEDM
EFT |  Effective Field Theory
emiT |  Spectrometer to search for TRIV in neutron beta decay ($D$ coefficient)
ep/n separator |  Electron Proton / Neutron separator (magnet separating charged neutron decay products from the neutron beam)
ESS |  European Spallation Source
ESS$\nu$SB |  European Spallation Source Neutrino Super Beam
FnPB |  Research Neutron Source Heinz Maier-Leibnitz at SNS
FOC |  Frame Overlap Chopper
FODO |  FOcussing DEfocussing
FRM II |  Research Neutron Source Heinz Maier-Leibnitz
FUNSPIN |  Polarised cold neutron beam at PSI
GEANT4 |  A Monte Carlo simulation program for GEometry ANd Tracking
GENIE |  GEnerator for NeutrIno Events
GRANIT |  GRAvitational Neutron Induced Transitions
GRS |  Gravity Resonance Spectroscopy
HBL |  High Beta Line
HIBEAM |  High Intensity Baryon Extraction and Measurement - the first stage of NNBAR
HighNESS |  HIGH intensity Neutron source at the ESS
HWI |  Hadronic Weak Interaction
ILL |  Institut Laue-Langevin
J-PARC |  Japan Proton Accelerator Research Complex
LANL |  Los Alamos National Laboratory
LANSCE |  Los Alamos Neutron Science Center
LBP |  ESS Large Beam Port
LD2 |  Liquid Deuterium
LEBT |  Low Energy Beam Transport
LINAC |  LInear ACcelerator
MAC-E Filter |  Magnetic Adiabatic Collimation combined with an Electrostatic Filter
MCNP |  Monte Carlo N-Particle program for particle transport
MEBT |  Media Beta Beam Transport
n3He |  Experiment to measure the proton asymmetry in thermal neutron capture by 3He, ${}^{3}{\rm He}(n,p)t$
nEDM |  Neutron Electric Dipole Moment
NINJA |  Neutrino Interaction research with Nuclear emulsion and J-PARC Accelerator
NG-C |  Neutron beam line at NIST
NIST |  National Institute of Standards and Technology
NNBAR |  An experiment to search for neutrons converting to anti-neutrons at the ESS
NoMoS |  Neutron decay prOducts MOmentum Spectrometer
NO$\nu$A |  Neutrinos Off-axis $\nu_{e}$ Appearance
NPDGamma |  Experiment to measure the $\gamma$ asymmetry in thermal neutron capture by hydrogen, $p(n,\gamma)d$
NDTGamma |  Experiment to measure the $\gamma$ asymmetry in thermal neutron capture by deuterium, $d(n,\gamma)t$
nTRV |  Spectrometer to search for TRIV in neutron beta decay ($R$ coefficient)
NuSTORM |  Neutrino from STOred Muons
PDC |  Pulse-Defining Chopper
PERC |  Proton Electron Radiation Channel (ep/n separator at the FRM II)
Perkeo II, III |  Spectrometer for measuring correlation coefficients in neutron decay (generation II or III)
PF1B |  Cold neutron beam facility for particle and nuclear physics at the ILL
PF2 |  UCN and VCN facility at the ILL
PHITS |  Particle and Heavy Ion Transport code System
PMT |  Photo-Multiplier Tube
PS |  Power Supply Unit
PSB |  Proton Synchrotron Booster
PSC |  Pulse-Suppressing Chopper
PSI |  Paul Scherrer Institut
PV |  Parity Violation/Violating
qBOUNCE |  Quantum bounce experiment with UCN
QCD |  Quantum Chromodynamics
QNeutron |  Experiment to measure the neutron electric charge
RAL |  Rutherford Appleton Laboratory
RFQ |  Radio Frequency Quadrupole
RF |  Radio Frequency
sFGD |  super Fine Grained Detector
SM |  Standard Model
SNS |  Spallation Neutron Source
T2K |  Tokai to Kamiokande
TPC |  Time Projection Chamber
TRIV |  Time Reversal Invariance Violation/Violating
UCN |  Ultra-Cold Neutron(s)
UCNA |  Spectrometer for measuring the beta asymmetry coefficient $A$ with UCN
VCN |  Very Cold Neutrons

##  2 Introduction

Progress in particle physics has traditionally been achieved by a symbiosis of
experiments at the energy and intensity frontiers and model-building. This has
led to the current situation of the Standard Model (SM) representing our best
knowledge of particle physics but which leaves a number of open questions to
be resolved. These include the composition of dark matter, the dynamic origin
of the observed matter-antimatter asymmetry, and the fine-tunings needed for a
light Higgs and no observable CP violation in the strong sector. Furthermore,
the SM is itself known not to be complete by the existence of massive
neutrinos and offers no explanation for the smallness of their masses. There
thus exist many problems requiring hitherto unobserved particles and physics
processes. Appropriate facilities are needed to maximise the chance of
observing new physics. As the world’s brightest neutron source, the European
Spallation Source (ESS) [1] offers unique capabilities at the intensity
frontier in addressing a range of the aforementioned open questions.

Presently under construction, the ESS in Lund, Sweden, is a multi-disciplinary
international laboratory with 13 European member states. At design
specifications, the ESS will operate at 5 MW using a proton linac of beam
energy 2 GeV, leading to spallation neutrons that are steered into a suite of
instruments. In addition to providing the most intense neutron beams, the ESS
also provides a large neutrino flux. While the ESS will start with fifteen
instruments used for neutron scattering research, a particle physics program
is part of the ESS statutes [2] and is identified as missing capability of the
highest importance [3].

Unsurprisingly, given the opportunities provided by the ESS, a number of
proposed experiments and activities at the ESS are being developed by the
community373737Several of these, ESSnuSB [4] and HighNESS [5] (NNBAR [6]
together with a dedicated UCN source), are funded by Horizon 2020 actions for
research leading to conceptual design reports. The construction of advanced
high-pressure noble gas, cryogenic CsI, and low-noise germanium detectors for
CE$\nu$NS studies at the ESS (Section 8) is supported by two Horizon 2021
actions.. It is timely to describe the various ideas put forward. Proposed
activities include the use of dedicated instruments for long-term projects
such as ANNI [7] and HIBEAM/NNBAR [6]. The ANNI project can encompass
precision measurements of neutron properties including decays and experiments
with ultra-cold neutrons (UCN) such as a search for a non-zero electric dipole
moment of the neutron. The HIBEAM/NNBAR program provides a series of searches
for baryon number transformation processes via neutron conversions, with
increasing sensitivity and ultimately providing an improvement in sensitivity
of three orders of magnitude compared with the earlier searches [8]. The
possibility of a high-flux dedicated UCN source is also considered and it is
currently under study as a part of the HighNESS project - more details are
given in Section 7. The nuESS experiment [9] can exploit the ESS’ ability to
provide the largest pulsed neutrino flux suitable for the detection and
measurement of coherent elastic neutrino-nucleus scattering. The ESSnuSB
project [4] is a large scale endeavor to use the proton linac to produce the
world’s most intense neutrino beam to measure neutrino oscillation parameters
and the leptonic CP phase.

This paper is organised as follows. A section on the ESS and related
infrastructure is given. The ESS configuration and specifications of the ESS
for the start of operations are described. Any infrastructure changes leading
to operations at full design specifications are regarded as upgrades. New
infrastructures required for the various particle physics projects are briefly
described in the ESS section, with further details given where needed in the
following sections. After the ESS section, a theory review is given of topics
in particle physics which are relevant for the proposed activities. Each
activity is then described in dedicated sections. A description of the
apparatus and experimental methods used in the project is given, together with
a quantification of the physics potential and how it fits into the worldwide
landscape of experiments (current and planned).

##  3 The European Spallation Source

Presently under construction, the European Spallation Source (ESS) in Lund,
Sweden, is a multi-disciplinary international laboratory and will be one of
Europe’s flagship scientific facilities. The ESS is organised as a European
Research Infrastructure Consortium (ERIC) and currently has 13 member states:
Czech Republic, Denmark, Estonia, France, Germany, Hungary, Italy, Norway,
Poland, Spain, Sweden, Switzerland and the United Kingdom. Sweden and Denmark
are the host countries. The facility’s unique capabilities, when completed at
full specifications, will both exceed and complement those of today’s leading
neutron sources, enabling new opportunities for researchers across a broad
variety of scientific fields including materials, life sciences, energy,
environmental technology, and particle physics.

An overview of the ESS facility is shown in Figure 1 where the basic building
blocks of the facility are shown: a proton linac, a target and a set of
instruments located in the experimental halls.

Figure 1: Layout of the ESS infrastructure.

###  3.1 The Accelerator and the target area

The ion source is the origin of the ESS proton beam. The beam begins as a
plasma of protons, which is created by “boiling off" the electrons from
hydrogen molecules using rapidly varying electromagnetic fields. The plasma is
guided into the accelerator beamline where a conducting radio frequency
quadrupole (RFQ) section is followed by a Drift Tube Linac (DTL) section that
accelerate the ions supplied by the electron cyclotron source up to a kinetic
energy of 90 MeV.

Figure 2: They layout of the ESS linac.

The rest of the acceleration is achieved with superconducting accelerating
structures of three different types. “Spoke” cavities are used for energies up
to 200 MeV, followed by medium-$\beta$ 6-cell elliptical cavities up to 570
MeV and finally high-$\beta$ 5-cell cavities up to 2 GeV. There is a cryogenic
installation that provides the cooling power required to keep the
superconducting cavities at a temperature of 2 K and water cooling is used for
the normal conducting structures and all high power equipment like klystrons,
RF loads, etc. The ESS linac layout is shown in Figure 2. The high neutron
flux from the ESS is due to the fact that the ESS, at full specifications,
will possess the world’s most powerful accelerator and the highest beam power
on target. The proton beam of 62.5 mA is accelerated to 2 GeV with a 14 Hz
pulse structure (with each pulse 2.86 ms long). This will give 5 MW 383838Note
that the ESS is currently committed to delivering 2 MW as accelerator power. A
power of 5 MW is part of the upgrade plan (see Section 3.4).  average power
and a peak power of 125 MW. Once the proton beam has reached its final energy
the beam hits a rotating tungsten target to produce neutrons by spallation
(see Figure 3). These are predominately evaporation neutrons at energies
around 2 MeV. Tungsten blocks mounted on a wheel rotating at 23.3 revolutions
per minute successively intercept the proton beam. Pressurized helium gas is
used as a cooling fluid, reducing the peak temperature by 150∘ between two
shots. Most of the beam power is dissipated in heat in the target which is
located inside a 6000 tons shielding configuration known as the monolith. The
target station converts the proton beam from the accelerator, through the
spallation process, into a number of intense beams of slow neutrons delivered
to the instruments. The high-energy spallation neutrons are slowed down in the
neutron moderators located inside the moderator-reflector plug shown in Figure
3. Initially, the ESS will be equipped with only a single compact low-
dimensional moderator, which has been designed to deliver the brightest
neutron beams for condensed matter experiments [10], optimized for small
samples, flexibility, and parametric studies. This moderator will be located
above the spallation target and due to its shape it is called the butterfly
moderator (see Figure 4). It is a cold parahydrogen moderator, 3 cm thick with
a single vessel and light water moderators. Its shape has been optimized after
an intense design study optimization, allowing beam extraction in the 42 beam
ports available at the ESS arranged in two 120∘ sectors. The space below the
target is initially occupied by a steel plug that later can be removed and
accommodate a second moderator system (see Section 3.3).

Figure 3: Overview of the ESS target area. Figure 4: Overview of the ESS upper
moderator. Left: MCNP model of the ESS target area in its initial
configuration with only a moderator located about the spallation target.
Right: Top view of the butterfly moderator. The dark blue represents para
hydrogen, while the light blue is water.

The target area is surrounded by the monolith, a 3.5 m thick steel structure
that also contains the neutron beamports necessary to extract thermal and cold
neutrons from the target. The beamport system of the ESS is arranged around
the moderators and allows the extraction of neutrons above and below the
target, a feature that is currently being investigated with the design of a
lower moderator below the target. At the end of the monolith the beamlines are
housed in the so-called bunker (see Figure 5). The bunker is a common
shielding area that surrounds the ESS monolith to protect the instrument area
from the high dose of ionizing radiation produced during operation. The
shielding structure of the ESS bunker consists of heavy magnetite concrete
walls of 3.5 m thickness, and a roof, also of heavy concrete, of variable
thickness.

Figure 5: The ESS bunker wall.

Outside of the bunker, the beamlines are placed in the instrument halls. The
long instruments are located in the west sector, the short instruments in the
north and east sector while the instruments with an intermediate length are
located in the south sector (see Figure 6) .

###  3.2 The ESS instrument suite

The ESS will start with fifteen instruments for neutron scattering (indicated
in yellow in Figure 6). These represent only a subset of the full
$22$-instrument suite required for the facility to fully realize its
scientific objectives, as defined in the ESS statutes [2]. The ESS mandate
includes a particle physics program, and the current lack of an appropriate
beamline for particle physics has been identified as one of the most important
missing capabilities [3]. In Figure 6 the location for the ANNI beamline is
shown. This is a proposed particle physics instrument optimised for precision
measurements of neutron beta decay, hadronic weak interaction and
electromagnetic properties of the neutron (for a description of the layout of
the beamline and the proposed experiments see Section 5). Figure 6 also shows
the position of the NNBAR beamline where the test beamline (TBL) is currently
located. The TBL will be used at the start of ESS operations to characterize
the target-reflector-moderator system. Once the TBL has completed its task,
the NNBAR experiment could be placed at that position, at the Large Beam Port
(LBP). The LBP, so named after its size compared to the standard ESS
beamports, has been included to allow the extraction of a large integrated
neutron flux- The LBP covers a frame as large as three normally-sized
beamports (for more details see Section 6). The LBP could also be used as an
infrastructure for Ultra Cold Neutron production (see Section 7) or as a
generic particle physics beamline with high integrated flux.

Figure 6: The ESS instrument layout.

###  3.3 The ESS lower moderator

As outlined in Sections 3.1 and 3.2, the configuration of the ESS source
offers the possibility of upgrades, including the design of a dedicated high
intensity moderator. In fact, so far, only the upper moderator is under
construction [10] and the space below the spallation target is available for
an additional moderator system. The design of the lower moderator is a part of
a design study project termed HighNESS [11, 5] funded as a Research and
Innovation Action within the EU Horizon 2020 program. The ESS second moderator
will serve two classes of applications: particle physics (the moderator is
currently optimized for the NNBAR experiment but it could in principle serve
every particle physics application where high integrated flux is required) and
neutron scattering applications. In the present configuration two emission
windows opposite to each other are under study as can be seen in Figure 7.
From a first round of optimization, the lower moderator MCNP6 model is a
${45\times 48.5\times 24}$ cm3 box (respectively, along and transverse to the
proton beam and vertical dimension) filled with LD2 at
$20\text{\,}\mathrm{K}$. The moderator is surrounded by a light water pre-
moderator ($2.5\text{\,}\mathrm{c}\mathrm{m}$ thick facing the target and
$1\text{\,}\mathrm{c}\mathrm{m}$ in all the other directions) and a water-
cooled room-temperature beryllium reflector. The dimensions of the openings
are ${40\times 24}$ cm2 and ${15\times 15}$ cm2, for NNBAR and neutron
scattering, respectively. Optimization of the high-intensity moderator is
still on-going and the final design will be part of the Conceptual Design
Report of the ESS upgrade due at the end of the HighNESS project in October
2023. In addition to the high intensity liquid deuterium (LD2) moderator, part
of the HighNESS project is also dedicated to the design of a UCN and very cold
neutrons (VCN) source that will make use of the LD2 moderator as a primary
source. Several options are currently under study as discussed in Section 7.
Beyond its potential for neutron physics, the ESS will also offer exceptional
opportunities for particle physics with neutrinos due to its intense neutrino
flux (Section 8) and its powerful accelerator (Section 9).

Figure 7: A lower moderator for the ESS.

###  3.4 ESS timescales and accelerator power usage projections

Owing to delays due to the Covid-19 pandemic and technical challenges, the ESS
has recently conducted a rebaseline exercise to revise its construction and
commissioning schedule. The newly revised baseline plan introduces a two year
delay and will enable the ESS to start operation and be open for scientific
users working with up to fifteen instruments in late 2027. The maximum
accelerator power and proton beam energies will be 2 MW and 800 MeV,
respectively. The possibility of operating the accelerator at 2 GeV beam
energy, with 5 MW power would then be part of an ESS upgrade project.

##  4 Theory

The Standard Model (SM) of particle physics [12, 13, 14] describes a very
large body of experimental results but it has a number of shortcomings and
issues to which it does not have a good answer. One of the shortcomings is the
large number of free parameters, especially in the so-called flavour sector
where the pattern of quark and lepton masses and mixing is simply put in by
hand, see e.g. [15]. A related issue is the origin of neutrino masses and
mixing, see Section 4.2.2 and e.g. [16]. These issues could be described as
"close to the SM" questions. There is also the QCD-theta parameter leading to
CP-violation in the purely strong sector which is unnaturally small.393939See
however references [17, 18, 19, 20] which using different methods suggest that
CP is conserved in strong interactions.

The next class of issues concerns those related to the universe and the
question of why matter exists. We know that a large part of the energy density
of the universe is not normal matter, i.e. it cannot be explained by particles
and fields present in the SM. This consists of two types, dark matter and dark
energy. The former is most likely due to some particles only interacting
weakly with normal matter while the nature of the latter is fully unclear, but
compatible with a simple cosmological constant, see e.g. [21]. The question of
why matter and anti-matter are not created in equal amounts in the early
universe also falls into this class.

The third class of issues is that where we have little experimental clue as to
what to expect. These include quantum gravity, searching for violations of
Lorentz and CPT symmetries and in general searching for processes and
phenomena not present in the SM.

The last class is related to studying effects of the strong interaction,
especially in ways that help to answer some of the experimental uncertainties
appearing for the others, but also interesting in their own right.

The resolution of the above-mentioned SM shortcomings likely requires new
degrees of freedom and new dynamics. This strongly motivates a broad search
for new physics, by either performing precision measurements of SM-allowed
phenomena or by searching for phenomena that are ‘rare’ or forbidden, because
they violate approximate or exact symmetries of the SM. One should of course
also be on the look-out for surprises, completely unexpected new results.

In broad brush terms one can expect that new physics has escaped detection so
far because the new particles are either very heavy or very weakly coupled.
Traditionally, there are two routes to search for new physics in laboratory
experiments: one is to increase the energy of particle accelerators so as to
try to directly produce new particles – this is known as the “energy
frontier". The other approach is to perform very precise and sensitive
measurements in low invariant mass systems, which allows one to indirectly
access the virtual exchange of heavy degrees of freedom or directly excite
light and weakly coupled particles – this is known as the “precision
frontier”. This second route requires using ultra-sensitive detectors and/or
powerful particle accelerators to generate large fluxes of particles such as
neutrinos, muons, mesons, neutrons, etc. – hence sometimes the name “intensity
frontier”. In this language, the ESS is an intensity frontier facility.

We emphasize that both energy and precision/intensity frontiers are needed to
infer structure, symmetries, and parameters of the underlying new physics. For
example, while high-energy colliders are the most powerful probe of new
particles associated to the electroweak symmetry breaking mechanism, precision
frontier experiments typically provide the strongest probes of lepton ($L$)
and baryon ($B$) number violation, CP violation, flavor violation in the quark
and lepton sectors, charged- and neutral-current weak interactions, neutrino
properties, and dark sectors.

In the context of the intensity frontier, the ESS will provide a number of
exciting opportunities, due to the high neutron and neutrino fluxes. First,
precision measurements of neutron decay will probe non-standard interactions
in the charged-current sector and help to determine the mixing element
$V_{ud}$ precisely, Section 4.1.1. Second, measurements of the neutron
electric-dipole moment, Section 4.1.2, provide the most sensitive probe for
CP-violation beyond the SM, as well as stringently bounding the QCD-theta
parameter. Baryon number violation has been strongly probed in proton decay
but alternatives that do not contribute to this exist and can be probed via
neutron oscillations to anti-neutrons or sterile neutrons (see Section 4.1.3).
Both of these will contribute to the understanding of net baryon number
generation in the universe. Another strength of the ESS will be the searches
for extra fundamental interactions and other phenomena discussed in Section
4.1.4. The nucleon-nucleon weak interaction is expected to have a number of
nontrivial features and possible measurements are discussed in Section 4.1.5.
Moreover, neutrino oscillation measurements will be sensitive to CP violation
in the lepton sector and non-standard neutrino interactions with matter (see
Section 4.2.2). Precise measurements of coherent neutrino-nucleus scattering
will test neutrino couplings to quarks and help in determining reaction rates
for dark matter experiments, as outlined in Section 4.2.1.

In the theory part of this review we have chosen to discuss the physics
relevance for the different experimental activities mainly in terms of
specific models when we address sensitivities to physics beyond the Standard
Model. An alternative way to do this is to use effective field theory (EFT)
methods, see e.g. [22] for a general introduction. There are several reasons
why we did not choose this method for comparison with e.g. direct searches:

  * 1.

Each experiment typically comes with its own relevant EFT or at least its own
relevant combination of coefficients in the EFT. Examples are Chiral
perturbation theory for a lot of hadron physics, chiral (nuclear) effective
theory for nuclear effects, Standard Model Effective Field Theory (SMEFT) and
Higgs Effective Field Theory (HEFT), see e.g. [23], for LHC physics, Low-
Energy effective field theory below the electroweak scale [24] for neutron
beta decay.

  * 2.

Comparison with direct searches for mediator particles at the LHC and other
high energy colliders are typically model dependent.

On the other hand, for low-energy experiments as ESS experiments typically
qualify, putting the results in terms of the relevant EFT coefficients makes
comparison with models easier. It also shows the importance of doing complete
measurements.

Next, we discuss in greater details the opportunities discussed above.

###  4.1 Neutrons

####  4.1.1 Precision measurements in neutron beta decay

Beta decay has played a crucial role in the history of particle physics
(neutrino hypothesis, parity violation, V-A theory, …) [25, 26, 27, 28, 29,
30]. Neutron beta decay is particularly interesting for several reasons.
First, it is the simplest one from a theoretical point of view (other than the
pion beta decay, which has a branching ratio of $10^{-8}$), since nuclear
effects are absent in this case. Second, it is sensitive to a wide variety of
interactions, since both Fermi and Gamow-Teller matrix elements are non-zero.
Third, significant progress is taking place on the experimental side with the
arrival of powerful (ultra)cold neutron sources and new detection techniques
[31, 32, 33, 34].

During the last decades there were significant tensions between some of the
measurements [31, 32, 35], which inspired interesting theory developments that
illustrate the broad discovery potential of neutron beta decay measurements,
see e.g. Refs. [36, 37]. Although the internal consistency of the data has
greatly improved with the arrival of more precise measurements and the
revision of some of the older ones, some tension remains, affecting quantities
as important as the neutron lifetime [38, 39]. It would be highly desirable to
further clarify the situation.

The exquisite theory and experimental precision achievable in several
observables makes neutron beta decay sensitive to small effects generated by a
wide variety of new phenomena [40, 41, 42, 43]. These measurements can probe
heavy new particles, which can be too massive to be produced at the LHC [44].
Such particles could play a crucial role in the generation of the matter-
antimatter asymmetry or the electroweak symmetry breaking mechanism. Likewise,
beta decay measurements are sensitive to the effects of new light particles
with very small couplings to the known fields, opening an interesting
connection with dark matter searches.

The physics reach of neutron beta decay goes beyond such searches of new
phenomena. It gives us access to the mixing matrix element $V_{ud}$, one of
the fundamental parameters of the electroweak sector in the SM. Recent studies
have increased the accuracy of the radiative corrections to neutron beta
decay, while revealing new uncertainty sources in nuclear decays,
strengthening the case of the former to extract $V_{ud}$ [45, 46, 47]. Testing
the unitarity of the CKM quark mixing matrix, whose $(1,1)$ element is
$V_{ud}$, represents a crucial check of theory [43]. It should be clarified
whether recent tensions in this test are unaccounted SM effects or hints of
new phenomena [48, 49, 50]. Neutron decay is also of the highest importance
for the study of strong interactions thanks to the precise extraction of the
axial nucleon charge $g_{A}$ and the study of the above-mentioned radiative
corrections. The comparison with QCD predictions is a challenging test [51,
52] that is sensitive to nonstandard effects [43]. Finally, neutron decay
measurements are relevant as well for nuclear physics, astrophysics and
cosmology, where $g_{A}$ and $V_{ud}$ play a crucial role [31, 32, 53].

As explained in Sections 5.2 and 7.2, the ESS offers a unique possibility to
improve our knowledge of fundamental properties of the neutron beta decay.
Significant improvements are expected both on the SM parameters and the BSM
searches, with the many and varied implications that were mentioned above.

####  4.1.2 Searches for a non-zero neutron electric dipole moment

Permanent electric dipole moments (EDMs) of non-degenerate quantum systems,
such as the neutron, would signal the breakdown of time-reversal (T) and
parity (P) invariance, or equivalently (due to the CPT theorem) of CP
invariance, where C is the charge conjugation operation that exchanges
particles and antiparticles. Given the un-observably small contribution to
EDMs induced by the SM weak interactions, the current null EDM results and
prospective sensitivities have far-reaching implications for fundamental
interactions and cosmology, as briefly summarized below (for more extended
discussions see Refs. [54, 55, 56]).

First, the existing upper limits on neutron EDM ($|d_{n}|<1.8\times 10^{-26}$
$e$ cm at 90% CL[57]) imply that CP-violating effects in the SM strong
interaction are extremely small ($|\theta_{\rm QCD}|<10^{-10}$). This is
already pointing to something very deep and historically, even before the
bound became so stringent, has led to the idea of a new broken symmetry whose
Goldstone boson – the axion – is a viable candidate for the dark matter in the
universe [58, 59, 60]. Second, the current null EDM results severely constrain
extensions of the SM that include CP-violation at the TeV scale, and probe
very strongly the CP properties of the recently discovered Higgs boson and
possible extended Higgs sectors. Finally, EDM searches shed light on the
origin of the matter-antimatter asymmetry of the universe, which cannot be
explained within the SM and requires the presence of new CP violation,
according to Sakharov’s conditions [61].

To pin down the nature of new sources of CP violation, multiple EDM searches
are needed, as EDMs of different particles species posses different
sensitivity to possible contributions from quark EDMs and color-EDM, purely
gluonic CP-violating interactions, and CP-violation in the lepton sector [56].
In this context the neutron stands out as the theoretically cleanest hadronic
system. In fact, there are good prospects to reduce the uncertainty associated
with non-perturbative QCD effects in the near future with lattice QCD [62, 63,
64, 65], thus enhancing the model-diagnosing power of neutron EDM searches
(both in case of positive and null signal).

The gap between the existing upper limits on neutron EDM ($|d_{n}|<1.8\times
10^{-26}$ $e$ cm at 90% CL[57]) and the Standard Model expectation due to the
Kobayashi-Maskawa phase ($|d_{n}|\sim 10^{-32}$ $e$ cm [66]) provides a
compelling discovery window spanning six orders of magnitude. Current and next
generation searches will have sensitivities a few orders of magnitude below
the current limits. The major scientific merits of a one to three order of
magnitude improvement in the neutron EDM sensitivity [i.e.
$|d_{n}|\sim(10^{-29}-10^{-27})e~{}{\rm cm}$] are:

(i) Sensitivity to very high scale new physics, possibly inaccessible at
current colliders. Existing null EDM results already imply a lower bound of
several TeV on the mass scale $M$ associated with new CP violation, based on
general effective theory considerations. These model-independent
considerations are borne out in detailed studies of explicit models, such as
the minimal supersymmetric standard model [67] and the so-called split-
supersymmetry scenarios [68, 69, 70, 71, 62], where the future sensitivity
reaches up to hundreds of TeV.

(ii) Unmatched sensitivity to CP-violating interactions of the Higgs boson
[72, 73, 74] and of extended Higgs sectors [75]. This makes the neutron EDM a
key tool in characterizing the properties of the Higgs boson discovered at the
LHC in 2012 and baryogenesis, see e.g. [76].

(iii) The possibility to probe mechanisms for the generation of the baryon
asymmetry of the universe. With the observation of the Higgs boson, it is
particularly timely to ask whether the baryon asymmetry was produced during
the electroweak symmetry-breaking era that occurred roughly 10 picoseconds
after the Big Bang, involving new particles with masses around or below the
TeV scale (see Ref. [77] for a review). EDM searches provide a particularly
powerful probe of the associated CP violation, given their sensitivity to mass
scales M in the multi-TeV region. In many scenarios (with some exceptions
[78]) successful baryogenesis leads to strict lower bounds on the neutron and
electron EDMs, only a factor of 2 – 3 below the current experimental limits
[79, 77]. The new generation of neutron EDM searches will provide very
stringent tests of the origin of matter in baryogenesis mechanisms operating
near the electroweak scale.

Experimental prospects for neutron EDM searches at ESS are discussed in
Sections 5.3 and 7.4.

####  4.1.3 Neutron oscillations to anti-neutrons or to sterile neutrons

The possibility of neutron–antineutron ($n-\bar{n}$) oscillation was put
forward in Refs. [80, 81, 82], followed by a number of papers studying
different aspects of this phenomenon and its model realizations [83, 84, 85,
86, 87, 88, 89, 90]. The neutron–antineutron oscillation violating baryon
number $B$ by two units can have an intimate connection with the possibility
of neutrino Majorana masses which violate lepton number $L$ by two units (and
both violate $B-L$). In particular this connection can naturally emerge e.g.
in a left-right symmetric model or its $SO(10)$ extensions, in which
$U(1)_{B-L}$ is a local symmetry and it has to be spontaneously broken at some
scale [82].

In the SM the neutron can have only Dirac mass while the neutrinos remain
massless. But in the context of BSM theories the neutrino Majorana masses can
be induced via the effective $\Delta L=2$ operators $C_{L=2}(\ell\phi)^{2}$ of
dimension 4 involving two lepton doublets $\ell$ [91], where $\phi$ stands for
the Higgs doublet of the SM. Then the neutrino mass range $m_{\nu}\sim 0.1$ eV
implies the Wilson coefficient
$C_{L=2}=M_{L=2}^{-1}\sim(10^{14}~{}\text{GeV})^{-1}$ pointing to a lepton
number breaking scale close to the GUT scale. As for the neutron Majorana mass
term $\epsilon_{n\bar{n}}n^{T}Cn+\mathrm{h.c.}$ responsible for $n-\bar{n}$
mixing, it can be originated from the six-quark (dimension 9) operators
$C_{B=2}(udd)^{2}$ involving $u$ and $d$ quarks in combinations with different
Lorentz and color structures [88, 89, 90]. However, the determination of the
effective scales $M_{L=2}$ and $M_{B=2}=C_{B=2}^{1/5}$ is a model dependent
issue, and even in the GUT context their values can be quite different.
Namely, $\Delta B=2$ operators induce $n-\bar{n}$ mixing with
$\epsilon_{n\bar{n}}=\kappa(1~{}{\rm PeV}/M_{B=2})^{5}\times 3\cdot 10^{-25}$
eV, $\kappa=O(1)$ being the operator dependent constant in the evaluation of
the matrix element $\langle 0|udd|n\rangle$. The value of $\kappa$ is
calculated by lattice QCD and models see [92, 93]. Indirect limits from decay
of nuclei are affected by large uncertainties [94, 95]. The direct
experimental bound on the $n-n^{\prime}$ oscillation time
$\tau_{n\bar{n}}=\epsilon_{n\bar{n}}^{-1}>8.6\times 10^{7}$ s [8], implies the
upper limit $\epsilon_{n\bar{n}}<7.7\times 10^{-24}$ eV. Somewhat stronger but
indirect bounds follow from the nuclear stability, namely from oxygen
$\epsilon_{n\bar{n}}<2.5\times 10^{-24}$ eV, so that present limits point to
the effective scale of around $M_{n\bar{n}}>0.5$ PeV. (For a summary of the
present experimental situation, see the reviews [96, 97].) Therefore, the
experimental search of $n-\bar{n}$ oscillation can be meaningful if the scale
$M_{6q}$ is below around 10 PeV. On the other hand, its discovery would be a
clear evidence of $B$-violation by two units, and would have a great impact
for our understanding of the origin of the baryon asymmetry in the universe.

The last two decades showed a renaissance of the interest for new physics
related to $n-\bar{n}$ mixing, and generally for $\Delta B=2$ processes and
their role in the early universe. In particular, new theoretical schemes
involving new particle states mediating the effective six-quark operator were
proposed and their implications for the LHC searches and for primordial
baryogenesis were discussed [98, 99, 100, 101, 102, 103, 104, 105, 106, 107,
108]. Mechanisms of $n-\bar{n}$ mixing were discussed also in the context of
the theories with extra dimensions [109, 110, 111, 112]. Different theoretical
aspects of $n-\bar{n}$ oscillation were also discussed regarding the role of
discrete C, P, T symmetries [113, 114, 115, 116], as well as the possibility
of the very low scale spontaneous $B-L$ violation by two units and its
apparent effects [117, 118, 119].

Another stream of research that emerged in the last two decades is related to
a possible connection between the neutron and dark matter (DM), in particular
in the context of the scenarios where DM is represented by a hidden gauge
sector. The simplest and most economic example is related to mirror particles
[28, 120]. Namely, a dark sector represented by a mirror SM′ replica of the
SM, which means that all observed particles: the electron $e$, proton $p$,
neutron $n$ etc. must have their dark mirror twins $e^{\prime}$, $p^{\prime}$,
$n^{\prime}$ etc. which are sterile to our SM interactions but self-interact
via the SM′ gauge bosons (for reviews see [121, 122]). Mirror matter is a
viable candidate for DM with specific cosmological implications if, after
inflation, mirror sector was reheated at lower temperatures than the ordinary
world [123, 124, 125, 126, 127]. During cosmological evolution, as for
ordinary matter, the mirror nuclei and atoms, as well as stellar objects,
which are dark for an ordinary observer, should form.

Besides gravity, there can exist some feeble interactions between particles of
two sectors induced e.g. by kinetic mixing of the ordinary and mirror photons
[128, 129] and/or by gauge bosons of common flavor symmetry [130, 131]. These
interactions can provide a portal for the direct DM detection [132, 133, 134]
and induce the mixing phenomena between the neutral particles of two sectors
as pions and Kaons. Ordinary and mirror sectors can be connected also by a
common axion [135]. However, most interesting are the interactions which
violate baryon and lepton numbers of both sectors. From the one hand, such
interactions can provide a co-genesis mechanisms of baryon asymmetries both in
ordinary and mirror worlds which can naturally explain the relation between
the baryon and DM fractions in the universe [136, 137, 138]. On the other
hand, they can induce the mixing of the neutrinos and the neutron with their
dark mirror partners, exactly or closely degenerate in mass.

Namely, dimension 5 operators $C_{L=1}(\ell\phi)(\ell\phi)^{\prime}$, which
violate lepton numbers $L$ and $L^{\prime}$ of both sectors by one unit,
induce active-sterile $\nu-\nu^{\prime}$ mixings which makes mirror neutrinos
natural candidates for sterile neutrinos [139, 140, 141].

Analogously, mass mixing between the ordinary $n$ and sterile mirror
$n^{\prime}$ neutrons, $\epsilon_{nn^{\prime}}n^{T}Cn^{\prime}+\text{h.c.}$,
can be induced by dimension 9 operators
$C_{B=1}(udd)(u^{\prime}d^{\prime}d^{\prime})$ involving ordinary $u,d$ and
mirror $u^{\prime}d^{\prime}$ quarks which violate both $B$ and $B^{\prime}$
but conserve the combination $B-B^{\prime}$ [98]. As opposed to $n-\bar{n}$
mixing, the nuclear stability limits give no restriction on $n-n^{\prime}$
mixing since $n\to n^{\prime}$ transitions in nuclei are suppressed due to
kinematic reasons [98]. On the other hand, existing experimental and
astrophysical limits allow $n-n^{\prime}$ oscillation to be a rather fast
process, with the characteristic oscillation time
$\tau_{nn^{\prime}}=1/\epsilon_{nn^{\prime}}$ much smaller than the neutron
lifetime, with interesting implications for cosmic rays [142, 143] and neutron
stars [144, 145, 146, 147]. Namely, the scale of underlying new physics
inducing the mixed six-quark operators can be at TeV,
$C_{B=1}\sim(1~{}\text{TeV})^{-5}$ (cosmological limits [98, 148] do not
exclude such a possibility), in which case $n-n^{\prime}$ mixing can be as
large as $\epsilon_{nn^{\prime}}\sim 1$ neV or so.

The phenomena of $n-n^{\prime}$ oscillations can be experimentally searched
via neutron disappearance $n\to n^{\prime}$ and regeneration $n\to
n^{\prime}\to n$ [98, 149, 150]. Such transitions can also be induced via the
non-diagonal magnetic moment between $n$ and $n^{\prime}$ states [151].
Several experiments were performed searching for $n-n^{\prime}$ oscillation
with the UCN [152, 153, 154, 155, 156, 157, 158, 159], and, for a simplest
scenario of the case mass degenerate $n-n^{\prime}$ oscillation, an upper
limit was set on the oscillation time, $\tau_{nn^{\prime}}<414$ s [153].
However, this limit becomes invalid if there is some mass splitting between
$n$ and $n^{\prime}$ or $n-n^{\prime}$ oscillation is affected by the presence
of mirror magnetic fields [160]. Interestingly, some of the above experiments
show anomalous deviations [161] which will be critically tested in the new
experiments [162, 6].

The phenomena of $n-\bar{n}$ and $n-n^{\prime}$ mixings can have a common
theoretical origin which unify $\Delta B=1$ and $\Delta B=2$ interactions [98,
117]. More generally, the four states $n$, $\bar{n}$, $n^{\prime}$ and
$\bar{n}^{\prime}$ can be all mixed with each other. While the direct
$n-\bar{n}$ mixing, i.e. the neutron Majorana mass, is strongly restricted by
experimental limits, $\epsilon_{n\bar{n}}<10^{-24}$ eV or so, $n-n^{\prime}$
and $n-\bar{n}^{\prime}$ mixings can be both much larger. In this way,
significant effects of $n-\bar{n}$ transition can be induced via the above
mixings: namely, a neutron travelling to mirror world can return back as an
antineutron [163]. The probability of induced $n\to
n^{\prime}\bar{n}^{\prime}\to\bar{n}$ transition can be many orders of
magnitude larger than that of direct $n-\bar{n}$ oscillation, and this
phenomenon can be experimentally tested in new experiments which can properly
scan the range of the applied magnetic field [164].

Experimental prospects at the ESS are the HIBEAM/NNBAR projects as discussed
in Section 6.

####  4.1.4 Searches for extra fundamental interactions, gravitational
spectroscopy, Lorentz invariance tests

Fundamental interactions additional to gravitational, electromagnetic, weak
and strong are assumed in many extensions of the SM. They can arise for
various reasons, including the existence of additional elementary particles or
dimensions of space, dark matter or energy hypotheses. The existence of
additional bosons induces a spin-independent Yukawa-type interaction with a
characteristic range that is inversely proportional to the boson mass. If
heavy bosons are to be sought at high energies, weakly interacting light
bosons would elude such detection techniques. An additional boson may even be
massless [165], which would violate the equivalence principle at large
distances. Theories with extra large dimensions of space [166, 167, 168, 169,
170, 171, 172] predict observable spin-independent interactions. The light
dark matter hypothesis [173] favors them. Chameleon-type interactions [174]
are intensively researched. The existence of axion-like particles would lead
to the existence of spin-dependent extra interactions [175].

A generic functional form of a new spin-independent interactions is the one of
a Yukawa-type interaction between two particles with masses $m_{1}$ and
$m_{2}$ at a distance $r$: $V(r)=\alpha Gm_{1}m_{2}/r\cdot\exp(-r/\lambda)$,
where $\lambda=\hbar/mc$, with the mass of the new boson $m$, is the Yukawa
range of the new interaction. Here, $\alpha=1$ would mean that the new
interaction is as strong as gravity for short ranges. The most simple
functional form of a new spin-dependent short-range interaction between an
unpolarized spin-1/2 particle (1) and a polarized spin 1/2 particle (2) at a
distance $r$, mediated by a light pseudoscalar boson of mass $m$, is given by

$V(r)=g_{s}^{1}g_{p}^{2}\hbar^{2}/(8\pi
m_{2})\cdot(\sigma_{2}\cdot\hat{r})(1/r\lambda+1/r^{2})\exp(-r/\lambda).$ (1)

Here, $g_{s}^{1}g_{p}^{2}$ is the product of the relevant coupling
coefficients for the interaction between particle 1 (unpolarized) and 2
(polarized), $m_{2}$ and $\sigma_{2}$ are the mass and the spin of the
polarized particle, and $\lambda=\hbar/mc$ being the Yukawa range as above.
The Yukawa range and the mass $m$ of the new boson are used as free parameters
in the analysis. Figure 8 shows the present most constraining limits for both
of those interactions in the relevant Yukawa range. Other properties or
functional forms of new short-range interactions are discussed in [176, 177,
178].

Figure 8: Left: Current most constraining limits for new spin-independent
short-range forces. The first experiment (red line, [179]) uses free neutrons.
At higher $\lambda$ ranges, other techniques and probes are more sensitive
[180, 181, 182, 183]. Right: Current most constraining limits for new spin-
dependent interactions. Experiments [184, 185, 186, 187] use the neutron as
the polarized particle, for the first of those it is a free neutron. In [188,
189], the polarized particle is an electron.

The large number of ways to search for extra interactions is reflected in the
amount of data collected by the Particle Data Group [39], e.g., in the review
about ”Axions and other similar particles”. Depending on the type and range of
extra interactions, neutrons play a unique or competitive role in this set of
methods complementing searches at high-energy particle accelerators, in atoms,
in low-background neutrino detectors, in searches for interactions on top of
the van der Waals/Casimir-Polder interaction, measurements of gravity at short
distances, astrophysical and cosmological constraints, and others. Several
neutron experimental methods are available for such research, including
neutron gravitational quantum spectroscopy [190, 191, 192, 193, 194], neutron
scattering and interferometry [195, 196, 197, 198, 199, 200], crystal neutron
diffraction [179, 184, 201], neutron spin rotation [202, 203], and others.
They allow also testing Lorentz invariance [204, 205, 206], non-commutative
quantum mechanics [207, 208], extensions of gravitational theories and many
others.

ESS can play a unique role among neutron sources if the experimental methods
critically use the pulsed structure of ESS neutron fluxes, or unique ESS
sources that can provide intense neutron fluxes with wavelengths unavailable
today. In particular, this refers to the possibility of constructing an
intense source of very cold neutrons. A broad window of opportunity for
neutron experiments is open to constrain new interactions in the nanometer
range and below, where neutrons are the best or competitive; the sensitivity
of neutron experiments is rapidly improving for ranges up to about several
micrometers, and is competitive for a number of scenarios. A distinct
advantage of the neutron as a test particle is the absence of an electric
charge and a small magnetic moment, respectively, and therefore the smallness
of systematic effects. An important drawback is the low neutron flux,
especially for neutrons with wavelengths optimal for these experiments. The
ESS can remove precisely the most critical of the limitations of these
experiments and allow a major increase in sensitivity, promising discovery
potential. More details on ESS expectations are in the experimental Section
5.4.

####  4.1.5 Studies of hadronic parity violation

Nucleon nucleon (NN) weak amplitudes offer a unique, dynamically-rich regime
in which to test the standard electroweak model. NN weak interactions provide
a new opportunity to develop theoretical methods in low energy strong
interaction theory such as effective field theory [209, 210] and lattice gauge
theory [211] and make predictions in a challenging but calculable system [212,
213, 214, 215, 216, 217], a recent review is [218]. The NN weak interaction is
also a test case for our ability to trace symmetry-violating effects of a
known quark-quark interaction in nuclei, which is of great interest also for
electric dipole moments and neutrinoless double beta decay. NN weak
interactions will soon become experimentally accessible due to recent advances
in atomic and molecular optics (AMO) physics through the effects of parity-odd
nuclear anapole moments [219, 220, 221, 222, 223, 224] on atomic and molecular
structure. Advances in laser cooling also allow to detect other effects via
mixing of opposite-parity states in molecules [225, 226, 227, 228, 229].

The value of the ESS for this physics lies in its unparalleled combination of
high intensity slow neutron beams, needed to reach the statistical accuracy to
see NN weak effects, and neutron energy information using neutron time of
flight from this pulsed neutron source, needed for the suppression of
systematic errors. The experimental aspects are discussed in Section 5.5.

Examples of possible NN weak experiments which can take special advantage of
the strengths of the ESS are: (1) neutron-proton parity-odd spin rotation,
which can access the $\Delta I=2$ NN weak amplitude that can most easily be
calculated in lattice gauge theory, (2) parity-odd gamma asymmetry in
$\vec{n}+D\to T+\gamma$, which is a sufficiently simple system to be treatable
using effective field theory techniques in terms of two-body NN weak
amplitudes, (3) a remeasurement of the parity-odd gamma asymmetry in
$\vec{n}+p\to D+\gamma$ recently measured at the Spallation Neutron Source
(SNS) at ORNL [230], which can determine the very important weak pion exchange
amplitude with higher precision, and (4) a repeat of the
$\vec{n}+{}^{3}He\to{}^{3}H+p$ parity violation experiment, which was also
recently measured at the SNS [231] and can be done with higher precision.

###  4.2 Neutrinos

The ESS will provide the largest pulsed neutrino flux, opening unprecedented
opportunities to study their interaction with matter and oscillations. The
main theory aspects are introduced in this section, whereas experimental
details will be discussed in Sections 8 and 9.

####  4.2.1 Coherent neutrino-nucleus scattering

In the SM neutrinos interact with matter not only through charged current but
also through neutral current via the tree-level exchange of a $Z$ boson.
Interestingly enough at low energies the neutrino cannot resolve the nucleus,
i.e., the neutrino interacts coherently with all the nucleons in the atomic
nuclei, with the resulting enhancement in the cross section [232]. The
challenging detection of the experimental signal of this Coherent Elastic
Neutrino-Nucleus Scattering (CE$\nu$NS) was recently achieved by the COHERENT
collaboration at the Oak Ridge National Laboratory [233], opening exciting
opportunities both at the technological and scientific levels.

The ESS is particularly well suited for this kind of measurements thanks to
its very high yield of low-energy neutrinos, which will allow for high-
statistics measurements [9]. It is worth noting that the use of multiple
targets would allow us to disentangle various physics effects. These are
discussed more in Section 8.

Concerning fundamental physics, CE$\nu$NS measurements offer interesting
information about the nuclear structure of the target, such as the nuclear
neutron distribution. Moreover, once such effects are properly parameterized,
CE$\nu$NS measurements represent a unique probe of the interactions between
neutrinos and quarks. Some applications include the extraction of the weak
mixing angle at very low momentum transfer, the study of the neutrino
electromagnetic properties and the search of non-standard interactions and new
light particles (sterile neutrino, dark matter, etc) [9]. More details about
the experimental opportunities are in Section 8.

####  4.2.2 Neutrino oscillations, leptonic CP violation, non-standard
neutrino interactions with matter

The quantum mechanical phenomenon of neutrino oscillations has been
experimentally observed by several different so-called neutrino oscillations
experiments, including the Super-Kamiokande and SNO experiments [234, 235]. In
the past decades, using data from atmospheric, solar, accelerator, and reactor
neutrino experiments, the various parameters that describe neutrino
oscillations have been measured to excellent precision. These parameters are
two mass-squared differences $|\Delta m_{31}^{2}|$ and $\Delta m_{21}^{2}$ as
well as three leptonic mixing angles $\theta_{12}$, $\theta_{13}$, and
$\theta_{23}$. Nevertheless, at the moment, at least three parameters remain
to be determined, i.e. the mass ordering of neutrinos, the octant of the
mixing angle $\theta_{23}$, and most importantly, the leptonic CP-violating
phase $\delta_{\rm CP}$. Presently, there are many dedicated proposed
experiments in order to measure these parameters.

The ESSnuSB [4, 236] is a proposed experiment at the ESS. Its main aim is to
discover and measure leptonic CP violation, i.e., to determine the leptonic
CP-violation phase $\delta_{\rm CP}$, with unprecedented sensitivity and
related to that the matter-antimatter asymmetry of the Universe. Due to the
fact that the leptonic mixing angle $\theta_{13}$ is unexpectely large, the
ESSnuSB is optimal for obtaining maximal sensitivity in measuring leptonic CP
violation at the so-called second neutrino oscillation maximum, see for
example Refs. [237, 238, 239, 240]. Currently, there are two different
baseline lengths that are under investigation: 360 km (Zinkgruvan, Sweden) and
540 km (Garpenberg, Sweden), which are both situated at distances from the ESS
that are suitable to the second neutrino oscillation maximum. During
2018–2021, the ESSnuSB has been investigated by a European Design Study
project financed by the European Commission by its Horizon 2020 Framework
Programme. Comparative studies between the ESSnuSB and other proposed
experimental setups in determining the leptonic CP-violating phase have been
carried out [241, 242, 243]. It has also been argued [244] that the choice of
the second neutrino oscillation maximum could reduce statistics and make
complementary searches of e.g. the octant of $\theta_{23}$ less fruitful, thus
opting for shorter baselines (such as the baseline length of the Zinkgruvan
choice).

What is the difference between the first and the second neutrino oscillation
maxima? For vacuum neutrino oscillations, the first oscillation maximum is
defined as $|\Delta m_{31}^{2}|L/(4E)=\pi/2$, where $L$ is the length of the
baseline and $E$ is the average neutrino energy, whereas the second
oscillation maximum is given by $|\Delta m_{31}^{2}|L/(4E)=3\pi/2$. Using the
characteristic values of the ESSnuSB ($E\simeq 0.36$ GeV), we find that the
first and second oscillation maxima are situated at $\hat{L}_{1}\simeq 180$ km
and $\hat{L}_{2}\simeq 530$ km, respectively, for $\Delta m_{31}^{2}=2.5\cdot
10^{-3}\,{\rm eV}^{2}$ [245]. Indeed, the value of second oscillation maximum
is close to the baseline length of the Garpenberg choice (of the detector). It
should be noted that taking into consideration matter effects and three-flavor
neutrino oscillations, the definition of the neutrino oscillation maxima will
change quantitatively, but not qualitatively.

In addition to measuring leptonic CP-violation, the ESSnuSB is an ideal
experimental setup to investigate other new physics scenarios such as non-
standard neutrino interactions, sterile neutrino, and neutrino decay. For
recent reviews on, for example, non-standard neutrino interactions, see Refs.
[246, 247, 248]. In phenomenological studies, so-called source and detector
non-standard neutrino interactions have been explored [249], the sensitivity
to light sterile neutrinos has been studied [250, 251], and the search and
possibility of invisible neutrino decay has been investigated [252, 253, 254].
Furthermore, it has been proposed to use the ESSnuSB to test lepton flavor
models [255, 256]. Such models, which give rise to a non-zero leptonic Dirac
CP-violating phase, could be related to the matter-antimatter asymmetry of the
Universe [257, 258, 259] and are basically testable with the ESSnuSB. In
comparative studies, the ESSnuSB has also been used to put stringent
constraints on fundamental symmetries such as potential CPT violation in
neutrino oscillations [260, 261]. The experimental aspects of ESSnuSB are
discussed in Section 9.

##  5 ANNI

###  5.1 Introduction

ANNI [262, 7] is a facility providing a cold pulsed and eventually polarised
neutron beam for a multitude of experiments in particle physics with neutrons.
These experiments cover a broad physics program (see also Section 4.1) and
bring their own dedicated instrumentation, as outlined in Sections 5.2-5.5.3
and 6.2. ANNI is therefore a “user instrument” in the spirit of the ESS as a
user facility [2]. It consists of a neutron guide transporting cold neutrons
from the ESS “butterfly” upper moderator (see Section 3.1) to the experiment
while suppressing other radiation from the spallation source by its S-shaped
curvature, a chopper system to tune the neutron pulses, an optional
supermirror neutron polariser, and an area for the installation of experiments
of up to 50 m length.

Comparable facilities exist or have been operated at continuous neutron
sources404040Only the latest facility at the respective neutron source is
listed.: PF1B [263] at the Institut Laue Langevin (ILL), FUNSPIN [264] at the
Paul-Scherrer Institute (PSI), the fundamental neutron physics station NG-C
[265] at the National Institute of Standards NIST, Mephisto [266] at the
Forschungsreaktor München II (FRM II), as well as at pulsed spallation
sources: the Fundamental Neutron Physics Beamline FnPB [267] at the Spallation
Neutron Source (SNS), the pulsed cold neutron beam line FP12 at LANSCE [268],
and the neutron optics and physics beam line NOP [269] at J-PARC.

Many particle physics experiments with cold neutrons are limited by
statistics. Beam facilities at the strongest continuous neutron sources so far
provide an order of magnitude higher time-averaged neutron flux compared to
beam facilities at the strongest pulsed sources. Pulsing the beam at a
continuous source costs typically two orders of magnitude in intensity since
both, the beam energy and the time structure, need to be restricted. In spite
of the lower statistics available so far with pulsed beams, several
experiments have employed them in order to overcome sources of significant
systematic uncertainty, see Section 5.1.1. ANNI promises to be the first
pulsed beam facility whose time-averaged flux surpasses that of the best
continuous beam facilities, providing simultaneously the advantages of pulsed
beams and the world-leading neutron flux.

####  5.1.1 Benefits of pulsed neutron beams for particle physics experiments

Pulsed neutron beams have been used at continuous sources in spite of the
substantial reduction of intensity, thanks to their benefits (updated from
[7]):

Localisation in space:

In contrast to a continuous beam, a neutron pulse is not only limited in its
transverse but also in its longitudinal direction. This allows observing
neutrons in a region of well-defined response, free of edge effects. It has
been used in pulsed beam measurements of the neutron lifetime [270, 271] where
decays of cold neutrons were detected with $4\pi$ angular coverage for the
neutron pulse being fully inside a strong magnetic field or a time projection
chamber (TPC), respectively. At a continuous beam, edge effects need to be
corrected which leads to uncertainties and usually requires dedicated
measurements, for example by varying the length of the proton trap used in
[272]. A new project at J-PARC implements the TPC technique at a pulsed source
[273, 274]. Measurements with Perkeo III [275] have used a pulsed beam at the
continuous facility PF1B in order to avoid regions of ill-defined spectrometer
response, resulting in the presently most accurate measurement of the beta
asymmetry parameter $A$ [276] and a limit on the Fierz interference term $b$
[277].

Localisation of neutrons in time:

If the neutron intensity arrives within a short time span, the signal-to-
background ratio is increased compared to a continuous beam of the same time-
averaged intensity (assuming similar levels of environmental background). The
environmental background can be measured during the absence of the neutron
pulse, in time intervals very close to the signal windows, allowing to
subtract slowly-changing environmental background. This was exploited in [276,
277]. (Note that at a pulsed source a part of the environmental background is
pulsed, too. It can be measured by omitting pulses in the experiment.)
Neutrons may create beam-related background with time constants large compared
to the pulse duration, e.g. by activating windows or beta-active isotopes in a
target or charging unwanted Penning traps in retardation spectrometers such as
$a$SPECT [278]. This background is diluted in time compared to the signal,
which increases the signal-to-background ratio for beam-related background.
The localisation of the neutron pulse in time can also be beneficial for data
acquisition and reduce the data volume, see Section 5.2.4.

Known velocity for each neutron:

Assuming the absence of frame overlap, the arrival time of a neutron at a
given distance from a pulsed source is directly related to its velocity (or
energy or wavelength). This can be exploited to calculate velocity-dependent
signal or suppress systematic effects, as proposed for the Beam EDM experiment
[279], see Section 5.3.1, or for accurate neutron polarimetry [280]. Employing
time-dependent neutron optics, manipulation can be optimum for each individual
neutron, e.g. by adapting the amplitude of an oscillating magnetic field of a
resonance spin flipper to the neutron velocity [281].

####  5.1.2 ANNI design guidelines and preliminary design

ANNI was designed to provide all benefits of pulsed beams to a multitude of
experiments. It was not optimised for a particular experiment but as best
compromise for a reference suite of topical experiments. The reference
experiments were chosen to represent all different requirements of neutron
particle physics experiments with cold beams:

$a$SPECT [278]:

neutron decay experiment with short decay volume, potentially profiting from
the localisation of the neutron pulse in time,

NPDGamma [282, 283]:

target experiment, profiting from neutron velocity information (see Section
5.5.1),

PERC [284, 285] and Perkeo III [275]:

neutron decay experiments with long decay volume, optimised for pulsed beams
and exploiting neutron pulse localisation in space (see Section 5.2.2),

Beam EDM [279]:

experiment featuring a very long neutron flight path, exploiting neutron
velocity information and time-dependent neutron optics (see Section 5.3.1).

The Beam EDM experiment was so far only taken into account to define the space
needed for ANNI, but not in the beam line simulations. Its requirements as
well as those of new proposals such as BRAND (Section 5.2.3), Cyclotron
Radiation Emission Spectroscopy (CRES, Section 5.2.4), the EDMn experiment
(Section 5.3.2) and HIBEAM (Section 6.2) will be included in the final
optimisation of the beam line.

We note that most of the experiments call for a rather short beam line. This
is caused by two reasons: (i) The neutron pulse created by the source is
polychromatic and dilutes in space and in time with increasing distance from
the source. Ref. [286] discusses this effect at the example of PERC. Only
experiments requiring monochromatic neutrons or a very high velocity
resolution profit from large distances. This is not the case for most
experiments in neutron particle physics. (ii) Although the source pulse
frequency of the ESS of 14 Hz is lower than that of the SNS or the J-PARC
neutron source, frame overlap between subsequent pulses limits the maximum
distance of an experiment. Frame overlap for the wavelength band of 2-8 Å
(which includes 90% of the cold capture flux) sets in at 34 m from the
moderator and prevents unique wavelength information from the arrival time at
larger distance. For these reasons the ANNI guide ends at 22 m from the ESS
moderator. The experiment typically starts at 26 m from the moderator; 4 m are
reserved for beam preparation or can be bridged by a straight guide section.
Following ESS recommendations, the ANNI guide avoids direct view on the
moderator two times, assuring that secondary showers produced by high-energy
particles from the source do not reach the guide exit directly. This requires
a strongly curved guide which was achieved by two benders forming an S-shaped
guide in the vertical plane (vertical bending is optimum for the flat
butterfly moderator). The detailed guide geometry and coatings were optimised
by McStas simulations for the upper, butterfly moderator (Section 3.1), see
Ref. [7]. Future optimisations utilising MCNP/PHITS simulations are required
to minimise the background from the spallation source and from the guide
itself. A scheme of the proposed facility is shown in Figure 9.

Figure 9: Top: Side view of the proposed ANNI beam line. Trumpet, Bender 1,
Bender 2 and Antitrumpet assure neutron transport. For experiments with
polarised neutrons, Bender 2 is replaced by a polarising bender. PDC1 and PDC2
indicate pulse-defining choppers, FOC1 and FOC2 frame overlap choppers and PSC
pulse-suppressing choppers. The vertical scale is stretched by a factor of 4
for better readability. Bottom: Schematic floor plan of the ANNI facility. The
magenta area indicates the footprint of PERC with a secondary spectrometer as
example for an experiment. The upgrade area is needed for long experiments
such as Beam EDM or HIBEAM. Taken from [7].

We note that a larger, integral-flux optimised moderator as proposed for the
lower moderator position (see Section 3.3) increases the filling of the guide
[287] and may be exploited to increase the guide cross-section (which however
implies an even stronger curvature and larger neutron transport losses).
However, most of the experiments at ANNI have a limited acceptance in terms of
beam divergence and therefore profit from the high brightness and the
directionality of the butterfly moderator, whereas unaccepted neutrons may
increase backgrounds. Detailed studies based on reference experiments will
finally identify the best moderator option for ANNI.

Many experiments in particle physics require polarised neutrons. In order to
offer the optimised polarised beam for each experiment, different polariser
options are included in the design of the ANNI facility:

Moderate polarisation at maximum flux:

The second bender of the guide is replaced by a polarising bender of the same
geometry, see Figure 9, yielding a polarisation of $>95$%.

Maximum polarisation with negligible angular and wavelength dependence:

The X-SM geometry of two supermirror benders [288] can be implemented by
combining the polarising bender mentioned above with a second polarising
bender installed in the beam preparation area (this deflects the beam in the
horizontal plane). Alternatively, an advanced compact solid-state supermirror
polariser with its high magnetising field can be used, yielding a polarisation
of $>99.9$% [289, 290].

Polarisation with well-defined wavelength dependence:

The non-polarising guide is combined with a polarised-[3]He spin filter
installed in the beam preparation area. This enables certain techniques for
precision neutron polarimetry as described in [280].

Finally, choppers are needed in order to tune the pulse emitted by the
spallation source and adapt it to the requirements of the respective
experiment. The chopper system consists of two frame overlap choppers (FOCs),
two pulse-defining choppers (PDCs) that can run at multiples of the ESS pulse
frequency of 14 Hz and a pulse-suppressing chopper (PSC), see Figure 9. Higher
rotational frequencies of the PDCs reduce the transition times of opening and
closing and thus increase the statistics since the full pulse intensity can be
present for a longer period. The PSC suppresses higher-order pulses created by
this operation mode of the PDCs. The following chopper modes are enabled:

Full intensity:

All choppers are parked in open position. Frame overlap impairs unambiguous
wavelength information.

Maximum intensity with wavelength information:

The FOCs are running, preventing frame overlap up to 130 Å and simultaneously
selecting a wavelength band of 6 Å width.

Localisation in time:

Frame overlap is suppressed by the FOCs. The second pulse-defining chopper
PDC2 is running with large opening adjusted to the highest intensity of the
beam.

Monochromatic:

All choppers are phased to wavelength $\lambda_{0}$. The PDCs run at high
frequency, in combination with the PSC, in order to maximise the resolution.

Localisation in space:

As Monochromatic mode, but the opening angles and phases of the PDCs are tuned
to the dimensions of a spectrometer such as PERC or Perkeo III, see [286].

Experiment | Gain in event rate | Comment
---|---|---
$a$SPECT | 1.3 | Full spectrum
| 2.8 | Localisation in time to 1/3 of ESS period
NPDGamma | 27↑ | Wavelength information
PERC | 15↑ | Localisation in space
Perkeo III | 17↑ | Localisation in space
Table 2: Simulated gains in event rate for the reference experiments at ANNI
(ESS at 5 MW) relative to the respective presently used facility. Gains marked
by ↑ refer to polarised beams. Taken from [7].

Table 2 lists the simulated gains for the reference experiments at ANNI
compared to the presently used facilities. More details on the ANNI design can
be found in [7]. The following Sections discuss experiments proposed for the
ANNI facility.

###  5.2 Precision neutron decay

####  5.2.1 Introduction

Excellent reviews of precision measurements in neutron beta decay and their
analysis within and beyond the SM are available [34, 38, 43, 42, 33, 41, 32,
31]. We provide an overview in the context of the experiments that have been
proposed for ANNI so far (see Sections 5.2.2-5.2.4).

A free neutron decays into a proton, an electron and an antineutrino,
$n\rightarrow p^{+}e^{-}\bar{\nu}_{e}$. In addition to the neutron lifetime
$\tau_{n}$ (and decay branches involving the emission of a photon or into a
hydrogen atom [291, 292]), correlations between the decay products can be
observed. They are defined by combining momenta or spin vectors of the
involved particles into dimensionless quantities and are quantified by
correlation coefficients. The orientation of the neutron spin
$\bm{\sigma}_{n}$ can be controlled by beam polarisation and magnetic guiding
fields, the electron’s momentum $\bm{p}_{e}$ and projections of its spin
$\bm{\sigma}_{e}$ can be measured and the antineutrino momentum
$\bm{p}_{\bar{\nu}}$ can be reconstructed from observing electron and proton,
whereas the spins of proton and antineutrino are difficult to measure.
Combining the 4 accessible vectors and axial-vector, 6 twofold, 4 threefold, 5
fourfold and 1 fivefold scalar combinations can be defined, see [32].
Threefold and fivefold combinations test time reversal invariance.
Furthermore, the electron spectrum may deviate from the pure phase space
factor $\rho(E_{e})$, which is described by the Fierz interference term $b$.
The equations for differential decay rates of the neutron can be found in the
classical papers [293, 294, 295] (see also [296]). For illustration, we show
the five “classical” correlations, quantified by the correlation coefficients
$a$-$D$, and the terms that depend explicitly on the transverse component of
the electron polarisation:

$\displaystyle\mathrm{d}\Gamma_{n}$ $\displaystyle\propto$
$\displaystyle\rho(E_{e})\left\\{1+a\,\frac{\bm{p}_{e}\cdot\bm{p}_{\bar{\nu}}}{E_{e}E_{\bar{\nu}}}+b\,\frac{m_{e}}{E_{e}}+\right.\frac{\langle\bm{\sigma}_{n}\rangle}{\sigma_{n}}\cdot\left[A\,\frac{\bm{p}_{e}}{E_{e}}+B\,\frac{\bm{p}_{\bar{\nu}}}{E_{\bar{\nu}}}+D\,\frac{\bm{p}_{e}\times\bm{p}_{\bar{\nu}}}{E_{e}E_{\bar{\nu}}}\right]\;+$
(2)
$\displaystyle\quad\langle\bm{\sigma}_{e,\perp}\rangle\cdot\left[H\,\frac{\bm{p}_{\bar{\nu}}}{E_{\bar{\nu}}}+L\,\frac{\bm{p}_{e}\times\bm{p}_{\bar{\nu}}}{E_{e}E_{\bar{\nu}}}+\right.$
$\displaystyle\quad\qquad\left.N\,\frac{\langle\bm{\sigma}_{n}\rangle}{\sigma_{n}}+R\,\frac{\langle\bm{\sigma}_{n}\rangle\times\bm{p}_{e}}{\sigma_{n}\,E_{e}}+S\,\frac{\langle\bm{\sigma}_{n}\rangle}{\sigma_{n}}\frac{\bm{p}_{e}\cdot\bm{p}_{\bar{\nu}}}{E_{e}E_{\bar{\nu}}}+\left.U\,\bm{p}_{\bar{\nu}}\frac{\langle\bm{\sigma}_{n}\rangle\cdot\bm{p}_{e}}{\sigma_{n}\,E_{e}E_{\bar{\nu}}}+V\,\frac{\bm{p}_{\bar{\nu}}\times\langle\bm{\sigma}_{n}\rangle}{\sigma_{n}\,E_{\bar{\nu}}}\right]\right\\},$

where $\bm{\sigma}_{e,\perp}$ represents a unit vector perpendicular to the
electron momentum $\bm{p}_{e}$. Seven of the correlation coefficients and the
kinematically dependent proton asymmetry $C=x_{C}(A+B)$ (with
$x_{C}=-0.27484$) have been measured, see Table 3 in Section 5.6.

In the SM with its $V-A$ structure, all correlation coefficients depend only
on the ratio of axial-vector and vector coupling constants, $\lambda\equiv
g_{A}/g_{V}$, or vanish. Here, $g_{A}$ accounts for the internal structure of
the nucleons (compared to the quarks with axial-vector coupling 1) and can be
calculated by lattice QCD, currently with precision of a few percent [297].
Experimental determination is the benchmark, and today is more precise by 1-2
orders of magnitude. The beta asymmetry coefficient
$A=-2\lambda(\lambda+1)/(1+3\lambda^{2})$ and the electron-antineutrino
correlation coefficient $a=(1-\lambda^{2})/(1+3\lambda^{2})$ have similar
intrinsic sensitivity. Since effects of CP violation on neutron decay are
negligible within the SM, the time reversal violating parameters $D$ and $R$
are driven by final state effects [298, 299, 300] which are one order of
magnitude below the present level of experimental precision. Integrating
Equation 2 yields the neutron lifetime:

$\tau_{n}^{-1}=\frac{G_{F}^{2}\left(mc^{2}\right)^{5}}{2\pi^{3}\hbar(\hbar
c)^{6}}V_{ud}^{2}\left(1+3\lambda^{2}\right)f\left(1+\delta_{R}^{\prime}\right)\left(1+\Delta_{R}\right),$
(3)

with the Fermi coupling constant $G_{\mathrm{F}}$, the CKM matrix element
$V_{ud}$, the phase space factor $f$ and the radiative corrections
$\delta_{R}^{\prime}$ and $\Delta_{R}$ (see [34] for a recent discussion).
From measuring $\tau_{n}$ (see Section 7.2) and $A$ (or $a$) the SM parameter
$|V_{ud}|$ can be determined. The uncertainty is presently 2.5 times higher
than from $0^{+}\rightarrow 0^{+}$ nuclear transitions [301, 34], but nuclear-
structure corrections are absent. In order to match experimentally the
precision of today’s radiative correction calculations for neutron decay,
$\tau_{n}$ and $\lambda$ need to be measured with relative uncertainties of
$1.9\times 10^{-4}$ and $1.1\times 10^{-4}$, respectively [302]. Today’s world
averages of the experimental results have relative uncertainties of $5.7\times
10^{-4}$ and $1.0\times 10^{-3}$, respectively, where the uncertainties of the
experimental inputs are scaled by factors of 1.8 and 2.7, respectively,
according to the Particle Data Group procedures for averaging data [303].

Interactions beyond the SM can be expanded into $V+A$, scalar, tensor and
pseudoscalar operators as corrections to the SM Hamiltonian. This modern EFT
approach yields the most general Hamiltonian of beta decay already considered
by Lee and Yang [28]. The classical papers [293, 294, 295] have related the
coefficients of the operators – which can be translated into the Wilson
coefficients of the EFT language – and the observable correlation
coefficients. Thus, correlation coefficients can be analysed for physics
beyond the SM in a model-independent way [34, 38, 43, 304, 305].

Whereas high-energy physics experiments are more sensitive to right-handed
neutrinos [34], superallowed $0^{+}\rightarrow 0^{+}$ nuclear beta decays to
scalar interactions [301], and neutron beta decay is highly relevant in
searches for exotic tensor interactions. The Fierz interference term describes
scalar–vector and tensor–axial-vector interference and is therefore linear in
the scalar and the tensor coefficients, making it particularly interesting for
searching for these exotic interactions [43]. It can be measured from the beta
spectrum or from the electron-energy dependence of beta, antineutrino or
proton asymmetry. The $D$ coefficient tests time reversal violation at the TeV
scale. In general, EDMs provide more stringent constraints [306] but not if
right-handed neutrinos are involved [307]. Within the $V-A$ model and
neglecting electromagnetic effects and recoil order corrections which can in
principle be calculated, electrons emitted in beta decay are longitudinally
polarised and correlation coefficients relating the transverse electron
polarisation $\bm{\sigma}_{e,\perp}$ to $\bm{p}_{e}$, $\bm{p}_{\bar{\nu}}$ or
$\bm{\sigma}_{n}$ vanish. Transverse electron polarisation can arise from
scalar and tensor interactions beyond the SM. Said correlation coefficients
have different sensitivities to the real and the imaginary parts of the scalar
and the tensor couplings. Their experimental values may thus be used to
establish constraints on all relevant theory parameters from neutron decay
alone [308]. Ref. [34] (Table 5) compares today’s best results on the EFT
Wilson coefficients from experiments at low and at high energy.

Experimentally, strong magnetic fields have been used to collect charged decay
products from cold neutron beams or volumes of ultracold neutrons in
measurements of spectra or asymmetries ($a$ from proton spectrum [278, 309],
$b$ [277, 310], $A$ [276, 311, 312], $B$ [313], $C$ [314]) because of their
benefits in terms of statistics and systematics (e.g. separation of charged
decay products according to their emission direction with respect to the
neutron spin – as already contemplated by Lee and Yang [28], intrinsic
determination of solid angle, substantial improvement of signal/background).
At a pulsed source, experiments with the field longitudinal to the neutron
beam profit in particular from spatial localisation of the neutron pulse, see
Section 5.2.2 and Refs. [277, 276, 315]. Spatial resolution, in some cases
including electron tracking, yields complementary systematics and is required
in measurements of triple correlations [316, 299, 317] or of correlations
involving the transverse electron polarisation [299], see Section 5.2.3. All
experiments may profit from time localisation of the neutron pulse for
background suppression or, in case of CRES, to reduce the data volume (Section
5.2.4).

The most precise published experimental results for correlation measurements
in neutron beta decay are included in Table 3 of Section 5.6. Until
experiments can start at ANNI, progress is expected from several ongoing and
planned activities: The Perkeo III collaboration is analysing data for the
proton asymmetry $C$ [318] and for the Fierz interference term $b$ from
measurements with polarised and unpolarised neutrons, respectively, at PF1B
(ILL). The Nab experiment is setting up at the FnPB (SNS) for measurements of
$a$ and $b$ with target uncertainties of $\delta a/a\sim 10^{-3}$ and $\delta
b\sim 3\times 10^{-3}$, respectively [319]. The uncertainty of the aCORN
experiment at NG-C (NIST) of 1.7% for $a$ [320] might be improved and, using a
polarised neutron beam, the apparatus might also be used to measure $B$ with a
final uncertainty of $<0.3$% [321]. PERC [284, 285] at Mephisto (FRM II) aims
for measurements of $a$, $b$, $A$, and $C$ with uncertainties of $\delta
a/a\sim 10^{-3}$, $\delta b\sim 2\times 10^{-3}$, $\delta A/A\sim 5\times
10^{-4}$ and $\delta C/C\sim 10^{-3}$, respectively. BRAND plans to obtain
improved results for many correlation coefficients, in particular those
involving the transverse electron polarisation, within their R&D program at
PF1B (ILL), see Section 5.2.3 and Ref. [308]. Concerning correlation
measurements with UCN, there is an R&D program at LANSCE to explore an upgrade
to UCNA [311] (UCNA+) with sensitivity for $\delta A/A\sim 2\times 10^{-3}$.

####  5.2.2 ep/n separator

The ep/n separator, see Figure 10, uses a high magnetic field in order to
collect and magnetically guide charged decay products to both ends of a long
neutron decay region and to separate them from the neutron beam. It builds on
the experience with the experiments Perkeo III [275] and PERC [284, 285]. The
time correlation between electron and proton is washed out in the magnetic
field which limits measurements at high event rates to observables that can be
derived from detection of only one decay product. These are the beta and
proton asymmetries (coefficients $A$ and $C$), the Fierz interference term
$b$, and the electron-neutrino correlation coefficient $a$ measured via the
proton spectrum. The aims of the experiments are world-leading determinations
of $\lambda$, and, combined with accurate lifetime measurements, $V_{ud}$, as
well as best limits on or discovery of scalar and tensor interactions.

Both, Perkeo III and PERC, are optimised to use pulsed neutron beams already
at the continuous reactor sources of the ILL and the FRM II in order to
eliminate or control leading sources of systematic errors by spatial
localisation of the neutron pulse, as described above and in Refs. [276, 277,
275] for Perkeo III, and Ref. [284] for PERC.

In Perkeo III, the region with the magnetic field parallel to the neutron
beam, where decay is observed under well-defined conditions, is about
$2\text{\,}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{s}$ long,
corresponding to an observation time of about $2\text{\,}\mathrm{m}\mathrm{s}$
per pulse. Its successor, the new instrument PERC, which is under construction
at the FRM II, extends the length of the active volume by a factor of $\approx
3$. A non-magnetic neutron guide preserves the high neutron density while
maintaining the neutron polarisation to be stable on the $10^{-4}$ level [322,
289]. This in effect increases decay statistics by more than an order of
magnitude. While Perkeo III uses a symmetric detector setup in order to
minimise systematics, PERC makes use of an additional high magnetic field
region (“magnetic filter”) to precisely define the solid angle of the
electrons and protons detected by the downstream detector. This layout enables
the use of an asymmetric setup with a single main detector system downstream,
and also provides much enhanced shielding of the downstream detector (see Ref.
[284]). Strong magnetic fields of 1-6 T are used to reduce systematic effects
and minimise the size of the detector to about
$12\times$12\text{\,}\mathrm{c}\mathrm{m}^{2}$$. Systematics are controlled on
the $10^{-4}$ level or better [284]. The magnetic field design of PERC is
described in Ref. [285].

The magnetic filter will reflect about 95% of all protons and electrons. While
this considerably reduces the burden for the main downstream detector, all
reflected particles will need to be absorbed by an upstream particle dump. In
PERC, this will be an active electron detector system based on plastic
scintillator and located just outside the warm bore of the PERC magnet. This
detector is located close the neutron beam, though, and is hence not easy to
shield.

Figure 10: Sketch of the ep/n separator, an upgrade to the concept of the PERC
instrument [284, 285] with improved backscattering detection. Neutrons enter
from 1. The magnetic field (field lines indicated in red) guide charged decay
products either to the tunable magnetic filter 2 and downstream detector
system 3 or to the upstream detector 4. The upstream detector also detects
particles reflected by the magnetic filter and from backscattering in the
downstream detector system. Decay products are counted if the neutron pulse 5
(green) is fully inside the homogeneous region of the magnetic field
(localisation in space). The more symmetric design of the ep/n separator
compared to PERC largely improves systematics related to backscattering: the
upstream detector can be shielded against background and covers 100% of the
beam.

In Refs. [7, 286] it was demonstrated that the instruments Perkeo III and PERC
massively profit from the pulse structure of the ESS, gaining one order of
magnitude in event rate at ANNI, see Table 2. For PERC, the upstream detector
was identified as a potential limiting systematic factor. In order to match
systematics and statistics, we hence proposed the improved design of the ep/n
separator shown in Figure 10 which features a complete separation of the
charged particles from the neutron beam also for the upstream detector [262].
A longer active volume would optimise the instrument to the low repetition
rate of the ESS and hence further improve statistics.

The ep/n separator will serve as a clean, intense and versatile source of
neutron decay products. Like in PERC, decay particles will be selected by a
tunable magnetic filter and guided towards specialised downstream detector
systems: detectors based on plastic scintillator or silicon with the possible
addition of proton-to-electron conversion foils [323, 314, 324], a MAC-E
filter like $a$SPECT [278] or an advanced magnetic spectrometer like the
$\bm{R}\times\bm{B}$ spectrometer NoMoS [325, 326].

####  5.2.3 BRAND

Figure 11: Cross section of the BRAND detector - conceptual design.

BRAND [308] is a spectrometer with electron tracking and proton detection, see
Figure 11. A particular feature is the observation of the transverse
polarisation of the electron, giving access to the correlation coefficients
$H$, $N$, $L$, $R$, $S$, $U$ and $V$ of Equation 2, where only $N$ and $R$
have been measured so far [327, 299]. A weak magnetic field (of about 100
$\mu$T) is used only to guide the neutron spin and does not affect
trajectories or spins of the decay products significantly. Electron and proton
can be measured in coincidence, giving access to the neutrino (neutrino
asymmetry coefficient $B$), to correlations of two particles (electron-
neutrino asymmetry coefficient $a$ from the correlation between electron and
proton) and, last not least, to the time-reversal violating triple
correlations (correlation coefficients $D$, $R$, $L$ and $V$) allowing to
search for CP violation in neutron decay. The full approach of BRAND is
complementary to the high-magnetic-field solid-angle-integrating spectrometers
described in Section 5.2.2.

The transverse polarisation of electrons is analysed in backward angle Mott
scattering on high $Z$ nuclei (e.g. Pb or U). This method yields an
exceptionally large analysing power, approaching 0.5 at backward angles. Most
importantly, since Mott scattering is governed by the time reversal and parity
conserving electromagnetic interaction, it is insensitive (on the level of
$10^{-7}$) to false effects (e.g. geometry misalignment) from the longitudinal
electron polarisation dominating in beta decay. This feature is unique among
the techniques measuring the transverse polarisation of leptons. Mott
scattering has been successfully demonstrated in neutron decay in the
pioneering experiment [327, 328, 329, 299]. The achieved systematic
uncertainty of $5\times 10^{-3}$ for the $R$ coefficient and $4\times 10^{-3}$
for $N$ can be further improved by at least an order of magnitude. The
substantially higher angular acceptance of BRAND combined with the neutron
flux at ANNI result in an expected increase in the rate of triggered events by
a factor of at least 300. Further gains in precision are expected from the
higher analysing power of the Mott target (in case of depleted U) and neutron
polarisation at ANNI ($>99.9$% in the maximum polarisation configuration).
Thanks to its tracking capabilities, BRAND does not require the spatial
localisation provided by ANNI’s pulse structure. The signal-to-background
ratio for coincident measurements is expected to be very high thanks to a
short coincidence time window, whereas it may profit from the localisation of
the neutron pulse in time for single-particle observables.

The key features of the proposed setup are: (i) efficient cylindrical detector
geometry that approaches $4\pi$ acceptance, (ii) electron tracking in multi-
wire drift chambers with signal readout at both wire ends, (iii) detection of
both direct and Mott-scattered electrons in plastic scintillator calorimeters,
(iv) conversion of protons (accelerated to 20–30 keV) into bunches of
electrons ejected from a thin LiF layer [324] followed by acceleration and
subsequent detection of ejected electrons in a thin ($\sim$25 $\mu$m) plastic
scintillator with position sensitivity, (v) highly symmetric detector setup
(with mirror planes parallel and perpendicular to the neutron beam) for the
suppression of systematic effects.

BRAND’s detecting system will have a several meters long segmented structure
in order to efficiently utilise the decay source. Assuming $5\times 10^{4}$
decays per second in the fiducial volume expected at ANNI and two years of
data taking, one can acquire $10^{12}$ direct electrons (coefficient $A$),
$3\times 10^{11}$ protons in coincidence with direct electrons (coefficients
$a$, $B$, $D$), $3\times 10^{8}$ Mott-scattered electrons (coefficients $N$,
$R$), and $10^{8}$ protons in coincidence with Mott-scattered electrons
(coefficients $H$, $L$, $S$, $U$, $V$). These numbers are sufficient for the
anticipated sensitivity of about $5\times 10^{-4}$ for correlation
coefficients involving the transverse electron polarisation. The measurements
of $a$, $A$, $B$ and $D$ will not be limited by their statistical uncertainty
of a few times $10^{-5}$.

BRAND’s tracking capability and the ability to reconstruct the full event
kinematics permit a detailed investigation of systematic effects. BRAND will
be the only spectrometer capable of measuring the transverse electron
polarisation. The full set of accessible correlations enables sensitive self-
consistency checks as different couplings and theory corrections contribute
differently to each correlation. For these reasons BRAND is complementary to
all high magnetic field spectrometers. The proposed experiment is challenging
and not free of risks. An experimental program has been started at the PF1B
beamline of the ILL reactor in order to demonstrate feasibility and
performance of the proposed components [308].

####  5.2.4 Experiments with Cyclotron Radiation Emission Spectroscopy

The Fierz interference term $b$ is very sensitive to exotic couplings as
discussed in Section 5.2.1. Its measurement requires accurate electron energy
spectroscopy. The energy response of conventional solid state detectors for
electrons is intrinsically nonlinear because of effects such as electron
backscattering, energy losses in detector dead layers, quenching and depth-
dependent charge- or light-collection efficiencies. Cyclotron Radiation
Emission Spectroscopy (CRES) [330] is a novel spectroscopy technology that is
not subject to these effects. As a frequency-based technology, it shows an
excellent energy reconstruction [331] and energy resolution [332], making it
particularly well suited for measurements of the Fierz interference term $b$.

CRES was proposed in Ref. [330] based on the analysis of the cyclotron
radiation emitted by the accelerated motion of a decay electron, spiraling in
a magnetic field with the cyclotron frequency

$\omega_{\mathrm{c}}=\frac{e}{m_{e}\gamma}B,$ (4)

where $e$ ($m_{e}$) are the charge (mass) of the electron and $B$ is the
magnetic flux. The relativistic factor
$\gamma=\sqrt{1+\frac{E_{e,\mathrm{kin}}}{m_{e}c^{2}}}$, where $c$ is the
velocity of light in vacuum and $E_{e,\mathrm{kin}}$ is the electron’s kinetic
energy. In typical CRES experiments $\omega_{\mathrm{c}}$ is within the
microwave range of the electromagnetic spectrum. CRES was first demonstrated
using conversion electrons from a gaseous $\mathrm{{}^{83m}Kr}$ source [333].

The electron emits power into free space according to Larmor’s formula [334]

$P\left(E_{e,\mathrm{kin}},\theta\right)=\frac{1}{4\pi\epsilon_{\mathrm{0}}}\frac{2}{3}\frac{e^{4}}{m_{e}^{4}c^{5}}\left(E_{e,\mathrm{kin}}^{2}+2E_{e,\mathrm{kin}}m_{e}c^{2}\right)\sin^{2}\theta,$
(5)

where $\theta$ is the pitch angle, defined between the electron’s momentum
vector and the magnetic field. The free-space equivalent radiation power for a
$90\text{\,}\mathrm{\SIUnitSymbolDegree}$-pitch-angle,
$17.8\text{\,}\mathrm{k}\mathrm{e}\mathrm{V}$ electron in a
$1\text{\,}\mathrm{T}$ magnetic field is $1.0\text{\,}\mathrm{fW}$.

Most gaseous sources of decay electrons, and also neutrons, are transparent
such that the microwave radiation can be received by a single antenna or
antenna array surrounding the decay volume. To integrate a detectable amount
of energy the electron must be confined in a magnetic bottle that sets a lower
limit on the pitch angle $\theta_{\mathrm{min}}$. The received signal is
amplified, mixed down, and bandpass-filtered before it is digitised. The data
analysis can then be performed in the time or frequency domain. An individual
CRES signal is shown in Figure 12. The energy resolution and reconstruction of
CRES have been demonstrated, using $\mathrm{{}^{83m}Kr}$. The lines of the
conversion electron doublets at $30.2\text{\,}\mathrm{keV}$ are separated by
$52.8\text{\,}\mathrm{e}\mathrm{V}$ and resolved with a full width half
maximum of $3.3\text{\,}\mathrm{e}\mathrm{V}$ which corresponds to a relative
energy resolution of $10^{-4}$. The deviations from the predicted
$1/\gamma$-scaling of the cyclotron frequency correspond to energy
uncertainties of less than $50\text{\,}\mathrm{m}\mathrm{e}\mathrm{V}$ across
a $>$14\text{\,}\mathrm{k}\mathrm{e}\mathrm{V}$$ kinetic energy range. This
initial demonstration opens up the opportunity for CRES applications in
neutron decay spectroscopy experiments at the ANNI beamline, with
fundamentally different systematic effects as compared to solid-state-based
electron detectors. Dominant systematic uncertainties of these detectors like
electron-surface or electron-matter interactions will be completely absent.
However, new uncertainties, such as electron-gas scattering due to the
electron’s long travel path in the column, need to be considered.

Figure 12: (a) A CRES signal from a single conversion electron emitted by a
$\mathrm{{}^{83m}Kr}$ source confined in a microwave guide. A sudden excursion
of microwave power is detected when the electron is created in the decay. The
signal frequency slowly increases as the electron looses energy due to the
emission of cyclotron radiation. The discrete frequency jumps are related to
the collision of the electron with gas molecules in the decay volume [333].
(b) A conceptual layout of a CRES setup around a neutron guide with a magnetic
bottle field indicated symbolically.

A major challenge of CRES is the large data volume per event in sparsely
occupied spectra, requiring online triggering and fast data compression. As
the CRES events are distributed in frequency space, there is no detector dead
time inducing event or energy pile-up. In an untriggered setup the fully
differential measurement approach of CRES causes the data volume per time to
be essentially independent of rate. Experiments at a pulsed source profit from
pulse localisation in time since signal digitising is only needed during the
presence of the neutron pulse, reducing the data volume by the ratio of the
neutron pulse duration in the magnetic bottle and the pulse period. Since this
ratio increases with shorter distance to the ESS moderator, a CRES experiment
is best implemented in ANNI’s beam preparation area (see Figure 9). A non-
conducting supermirror neutron guide inside the magnetic bottle, instead of a
gap in the guide, would allow the cyclotron radiation to be detected behind
the guide walls without reducing the neutron flux. Therefore the CRES
experiment could even run in parallel to another experiment downstream. A
conceptual arrangement with typical dimensions is shown in Figure 12.

###  5.3 Electric dipole moment of the neutron

Measurements of permanent electric dipole moments (EDMs) have a key role in
fundamental particle physics, both as a precision test of the SM of particle
physics, and as a sensitive probe for new physics. As first pointed out by
Sakharov, the observed cosmological imbalance between matter and antimatter
could only arise in the presence of significant CP-violating interactions
[61]. The SM is known to violate CP symmetry in the weak interactions of
quarks, and allows CP violation in the neutrino sector, but these effects are
insufficient – by far – to explain the observed abundances of matter,
antimatter, and photons in our universe [56]. New CP-violating physics is
needed, and searches for EDMs are recognised as a “lightning-rod” that
collects contributions from the relevant sources of CP-violation [335, 336,
337]. While a non-zero EDM measurement from any single experimental system
cannot, alone, indicate the source of the CP-violation that generates it, null
EDM results frequently provide the most powerful constraints on these types of
new physics [338].

The neutron is special in this context, due to its sensitivity to the CP-
violating SM parameter $\theta_{\text{QCD}}$. Although a finite value for this
parameter could easily have resolved the matter-antimatter puzzle,
experimental measurements of the neutron’s EDM indicate that it is much too
small. Even if $\theta_{\text{QCD}}$ has a nonzero value too small to be
detected in today’s experiments, this would represent a “fine-tuning” on the
order of one part in $10^{10}$ (the so-called “strong CP problem”, however,
see also [17, 18, 19, 20]). Further details relating to theory impacts are
discussed in Section 4.1.2.

The first experimental neutron EDM limit in 1957 [339] was already a powerful
tool for testing new theories. The precision of neutron EDM experiments has
since improved by nearly seven orders of magnitude, with the most recent
result setting a limit consistent with zero at the level of
$10^{-26}~{}e\text{ cm}$ [57]. This fantastic precision, corresponding to an
energy resolution of $10^{-22}\text{ eV}$, is possible because (provided
adequate statistical sensitivity and control of systematic errors) frequency
measurements can be improved to arbitrary precision. Yet a further improvement
by a factor of approximately $10^{6}$ would be needed, to reach sensitivity
levels where the neutron EDM that arises within the SM from CP violation in
the CKM matrix can be detected [66]. The intervening range is considered a
“background-free” window in which to search for new physics.

The fundamental statistical sensitivity for measuring the neutron EDM
$d_{\text{n}}$, assuming a count-rate-limited frequency measurement, is

$\sigma(d_{\text{n}})=\kappa\frac{\hbar}{\eta ET\sqrt{N}},$ (6)

where $E=|\bm{E}|$ is an applied electric field, and $N$ is the total number
of detected neutrons. The measurement duration $T$ is the time during which an
EDM-sensitive phase can be accumulated, between the two states whose frequency
splitting is being measured. The dimensionless contrast parameter $\eta$ has a
maximum value of 1, corresponding to 100% spin-polarisation. The
proportionality constant is $\kappa=0.5$ for (a pair of) storage measurements
with ultracold neutrons, or $\kappa=2$ for the Beam EDM configuration [340].

Measurements of the neutron EDM are based on Ramsey’s Nobel prize winning
technique of separated oscillating fields, which represents a very sensitive
method to probe for spin-dependent interactions [341, 342]. In this technique
an effective Larmor precession frequency $\omega$ is measured by applying two
consecutive phase-locked $\pi/2$ radio frequency resonance pulses to an
ensemble of neutrons exposed to a magnetic field $B_{0}$ and an electric field
$E$. By measuring $\omega$ for the two cases that the orientation of these
fields is parallel ($\uparrow\uparrow$) and anti-parallel
($\uparrow\downarrow$), a value for the neutron EDM can be deduced:

$\Delta\omega=\omega_{\uparrow\uparrow}-\omega_{\uparrow\downarrow}=\frac{4d_{\text{n}}E}{\hbar}.$
(7)

This formula makes the crucial assumption that the magnetic field has not
changed over the duration of the two measurements. To achieve this condition
neutron EDM experiments are usually enclosed with multiple layers of active
and passive magnetic shielding, and the magnetic field is monitored with
various kinds of magnetic field sensors.

Early neutron EDM experiments were performed using neutron beams, while
current experiments and most new projects employ stored ultracold neutrons
(UCNs). Experiments with UCNs have the advantage of much longer interaction
times: on the order of 200 s, compared to the range of 10-100 ms for long
neutron beam experiments. By contrast, much larger neutron count rates can be
achieved in beam experiments. Higher electric fields may also be possible for
beams, since insulating wall material is not required between the high-voltage
electrodes. This is needed to confine the UCNs in storage experiments,
although high electric fields can also be achieved for storage experiments
performed under liquid helium (see reference [343] and Section 5.3.2). The
main limiting systematic effect in beam experiments so far has been the
relativistic $\bm{v}\times\bm{E}$ effect, arising from the motion of neutrons
with velocity $\bm{v}$ in the electric field [344].

####  5.3.1 The Beam EDM experiment

Figure 13: Schematic side-view drawing of the Beam EDM experiment. The
polarised pulsed beam from the ANNI beamline is separated into two beams which
pass through a neutron Ramsey spectrometer consisting of two $\pi/2$ resonance
spin flip devices and a spin analyser. The amplitudes of the radio frequency
pulses need to be modulated in order to achieve perfect $\pi/2$ flips for
neutrons of all velocities (exploiting the ESS pulse structure through use of
time-dependent neutron optics). The two beams sense an external magnetic field
$B_{0}$ and electric fields $E$ with opposite directions. By changing the
polarity of the high voltage (HV) applied to the central electrode – the outer
two electrodes are connected to ground – the electric field direction is
inverted with respect to the direction of $B_{0}$. The detector(s) counting
the two beam rates as a function of time-of-flight need to be capable of
accepting high neutron intensities. The neccessary passive magnetic shielding
and the vacuum beam pipe are not shown.

The Beam EDM experiment proposes to overcome the limitation of the
$\bm{v}\times\bm{E}$ effect by directly measuring the shift of the Larmor
frequency, i.e. the resulting phase-shift of the Ramsey interference pattern,
as a function of the neutron time-of-flight [279]. For pulsed beams the
velocity is then known for each neutron, and hence it is possible to
distinguish between the velocity-independent frequency shift caused by an EDM,
and the velocity-dependent false signal due to the relativistic
$\bm{v}\times\bm{E}$ effect:

$\Delta\omega=\frac{4d_{\text{n}}E}{\hbar}+\frac{2\gamma_{\text{n}}vE\sin\alpha}{c^{2}},$
(8)

with $v=|\bm{v}|$ the neutron velocity, $\alpha$ the misalignment angle
between the electric and magnetic fields, $\gamma_{\text{n}}$ the gyromagnetic
ratio of the neutron, and $c$ the speed of light in vacuum.

A scheme of the Beam EDM concept is presented in Figure 13. The experiment
employs two polarised neutron beams passing through a stack of electrodes and
a time-of-flight Ramsey apparatus. The “two beam method" allows to compensate
for common-noise and drifts of the magnetic field, but remains sensitive to
magnetic field gradient changes. With an optimised full-scale setup of length
$L=50$ m (using the aforementioned upgrade area of the ANNI beamline) and an
electric field $E=100$ kV/cm, it was estimated that a (one standard-deviation)
statistical sensitivity of approximately $5\times 10^{-26}~{}e\text{ cm}$ can
be reached in one day of data taking [340]. This renders this proposal
complementary to approaches using UCN, and for a 100-day dataset could even be
competitive with their current state-of-the-art statistical sensitivities.

A conceptually similar approach using very cold neutrons (VCN) is briefly
mentioned in Section 7.7; in that scenario any gain in the statistical
sensitivity (per detected neutron) would arise purely from longer observation
times. This idea would require further study to clarify whether or not it
offers any statistical or systematic advantages, in comparison to EDM
experiments using cold neutrons or UCN.

####  5.3.2 EDM with _in-situ_ UCN production

Figure 14: Schematic illustration of the EDMn experiment concept. Polarised
UCNs are directly produced from cold neutrons (the production process does not
alter the neutron spin), in many cells filled with isotopically-pure
superfluid [4]He. The EDM measurement proceeds _in-situ_ , including both
spin-precession and detection. UCN detectors in the cell walls are turned on
by applying magnetic fields that partially cancel the wall potential for the
high-field-seeking spin state, after a spin-precession cycle has finished.
Alternative approaches could exploit absorption on 3He impurities, as
described in reference [345]. Several readout mechanisms can be envisioned.

In recent decades neutron EDM experiments have relied on stored ultracold
neutrons (UCNs), and demonstrated superb control of systematic errors despite
severe statistical limitations. The advantage of UCNs mainly comes from long
observation times, as discussed in Section 5.3 above. A secondary advantage
concerns practical requirements for well-controlled experimental conditions:
these apply only in and around the restricted volume where UCNs are stored
during a measurement. However, the low densities that can be delivered from
UCN sources to external experiments represent a severe statistical limitation:
the time-averaged detection rate in UCN-based EDM measurements is typically
not more than 100 particles per second, whereas beam-based measurements with
cold neutrons may exceed $10^{8}$ counts per second [340].

Significant improvements for experiments using stored UCNs will rely, to a
large extent, on successfully confronting the challenge of low UCN densities.
Systematic errors are also impacted, via the running time required for
performing adequate supplementary studies to constrain these effects. This
concern becomes more relevant with improved precision, as ever-smaller and
more subtle systematic errors must be treated.

Cross-sections for converting cold neutrons to UCNs are intrinsically small,
and most neutrons are lost, either by exiting the source or via other
interactions. Moreover the produced in-source UCN densities suffer further
reductions, typically two orders of magnitude, in extraction and delivery to
experiments. Superthermal UCN sources, in which dissipative processes
involving inelastic scattering are exploited to populate the phase-space more
densely, provide the main avenue towards higher UCN densities. (The UCN
densities produced from standard moderators are rather low.) Due to its
vanishing neutron-absorption cross-section, superfluid [4]He is the only
superthermal converter medium compatible with the long _in-situ_ storage times
needed for sensitive EDM experiments.

The EDMn project, illustrated in Figure 14, explores the potential for much
more sensitive neutron EDM searches [346], by scalably exploiting (1) the
entire moderated neutron beam available for UCN production, and (2) the full
_in-situ_ densities already existing in UCN sources (see also Section 7.4).
There are several further incidental advantages of the _in-situ_ liquid helium
concept, most notably the high electric field strengths achievable in that
medium. Additionally, since UCN production in superfluid 4He is driven by
conversion of 8.9 Å neutrons, the signal-to-background ratio can be increased
substantially through use of a monochromatic beam – which can be produced
without loss at a pulsed source using choppers. The first point will be
addressed via modular liquid-helium based sources, using small experimental
cells in configurations that can be efficiently replicated many times along a
neutron beam. Neutrons that pass through the first cells without interacting
can still downscatter to become UCN in later cells, until the beam is depleted
by other scattering processes in the helium and cell walls. Testing and
development will focus on single cells, to be jointly optimised for both cold-
neutron transmission and UCN storage.

This approach enables thorough development of the most suitable cells,
independent from the challenges of scaling up to a multi-cell experiment. The
multi-cell concept will also be pursued in a phased approach, with the first
few-cell demonstrations already expected to be competitive in the context of
today’s present-generation neutron EDM experiments (see Figure 15).

The second point will be addressed with innovative neutron detectors, based on
cancelling neutron-optical potentials with magnetic fields (see Figure 14
inset). The requirement is polarisation-sensitive UCN detection inside the
cells, without negative impacts on the cells’ storage properties (or
unmanageable EDM systematics). Potentially low detection efficiencies are
mitigated by the possibility for UCN to interact multiple times with the
detector, until absorption occurs.

The developments for (1) and (2) will be combined, for single-cell
demonstrations of UCN production, storage, and in-situ detection. This proof-
of-principle will enable pursuing a full-scale neutron EDM experiment via a
phased approach at the ESS. Such an experiment’s improvements in sensitivity,
while initially modest, could reach nearly three orders of magnitude beyond
the present experimental limit on the neutron EDM. The only other concept so
far targeting this sensitivity level would require a dedicated spallation
source, where a very high UCN production rate offsets extraction
inefficiencies [347].

As discussed in Section 7.4, the main challenge in EDM measurements is finally
constraining systematic errors. The technological elements required to achieve
systematic uncertainties on this level have not yet been fully demonstrated,
although recent developments in magnetic shielding and magnetometry provide a
foundation for focused work in this direction [346]. These must be pursued in
parallel with the development of improved statistical reach, which as noted
above is also required for studying systematic effects.

Figure 15: Statistical reach of the EDMn concept. Each data point in the left-
hand plot corresponds to adding one additional cell pair (i.e., both electric
field states) to the linear stack illustrated in Figure 14. These calculations
assume that the cold neutron beam can be guided within the cell stack; the
impact of beam divergence in a non-guiding scenario is discussed in [346].

###  5.4 Neutron electric charge

The electric charge of the neutron is known experimentally to be zero to an
extremely high precision [348, 349] (see also [350] for a review on electrical
neutrality of atoms, neutrons and bulk matter). Nevertheless, the questions of
charge quantisation and the neutrality of neutrons, neutrinos, and atoms
remain under debate [351, 128, 352, 353, 354, 355, 356, 357, 358, 359, 360,
361]. Moreover, there exists the possibility that the charge of a free
particle might be slightly different in magnitude compared to its charge when
bound in an atom [362]. Even a tiny electric charge of the neutron would
forbid neutron-antineutron oscillations (see Section 4.1.3), due to the
conservation of electric charge. Hence, measurement of the neutron electric
charge could provide an important input for fundamental particle theory, as it
also represents a value which is not constrained to be zero in the SM [32].

The first direct measurement of the neutron electric charge using a beam of
free neutrons dates back to the 1950’s, when Shapiro and Estulin performed a
pioneering precision experiment [363]. They employed a well collimated thermal