The overarching goal of subatomic physics is to push the knowledge frontier of what the universe is made of to the very smallest distance scales. In doing so, subatomic physics has been able to distill and translate observations of natural phenomena into universal laws expressed by a few mathematical equations. The existence of this expansive theoretical scaffolding is the very reason specific questions about the universe can be formulated and we can advance systematically in the exploration of the unknown.

The field of subatomic physics research has progressed significantly over the past couple of decades, driven by technological advances, computing power, and theoretical developments. As a prime example, the discovery of the Higgs boson in 2012 at the LHC provided the capstone for the Standard Model of particle physics, yet many questions remain as ‘science drivers’ for the field and even the Higgs has now become a tool to push forward our understanding of subatomic physics.

The LRP Committee identified eight science drivers for the field of subatomic physics research in 2022 that encapsulate a number of underlying questions:

Science Driver —
Higgs, Physics at the Electroweak Scale, and Beyond

What is the precise nature of the Higgs sector and the flavour sector of the Standard Model? What is the physics of electroweak symmetry breaking? What lies beyond the electroweak scale?

Science Driver —
Fundamental Symmetries and Observed Asymmetries

What are the fundamental symmetries in nature, and how do we explain observed imbalances, e.g. the matter-antimatter symmetry in the universe?

Science Driver —
Neutrino Properties

What is the nature of neutrino mass, the mass hierarchy, and of neutrino interactions?

Science Driver —
Dark Matter and Potential Dark Sectors

What is the nature of dark matter in the universe and its interactions? Is dark matter part of a more extended dark sector?

Science Driver —
New Physical Principles and Structures

A broad range of theoretical questions, including what formal theoretical principles and structures underly the forces and matter in the universe?

Science Driver —
Hadron Properties and Phases

How do quarks and gluons give rise to the properties of nucleons and other hadrons, and to the hadronic phases of matter in extreme conditions?

Science Driver —
Nuclear Structure

How does nuclear structure emerge from nuclear forces and ultimately from quarks and gluons?

Science Driver —
Cosmic Formation of Nuclei

How do the properties of nuclei explain the formation of the elements in the universe?

These science drivers are deeply inter-connected and in combination define three broad science directions in subatomic physics, as illustrated in Figure 1. To address the breadth of these science drivers requires a diversified research program of bold projects with complementary objectives, exploiting a variety of different techniques. In the rest of this section, these science drivers are described in more detail, focusing on recent scientific progress as well as Canadian activities and achievements. Indeed, Canadian subatomic physics has an enviable global reputation, with impact on many of the major projects that have pushed our understanding forward in recent decades. The Council of Canadian Academies’ 2018 report “Competing in a Global Innovation Economy: The Current State of R&D in Canada” highlights the global impact of Canadian subatomic physics research, as measured by average relative citations which grew from 1.79 to 2.05 compared to the Canadian average of 1.43. Given its global impact, but relatively small community size, physics and astronomy was highlighted in the report as a research opportunity for Canada, and future opportunities and plans will be described in h 3.

Science Driver —
Higgs, Physics at the Electroweak Scale, and Beyond

The discovery of the Higgs boson in 2012 identified the remaining missing ingredient in the Standard Model of particle physics. It also identified one of the main agents for the breaking of the fundamental electroweak symmetry in nature. Yet, the electroweak sector remains one of the most puzzling aspects of the Standard Model. The Higgs boson is a type of matter that has never been seen before and its properties are yet to be fully studied. Its mass, for example, is not constrained by any symmetry in the Standard Model, and unlike the mathematical structure of the other forces of nature that are fully specified based on symmetry properties, the addition of Higgs interactions leads to a large number of undetermined parameters in the Standard Model. This makes our current understanding of the role the Higgs boson plays in the universe particularly ad hoc and incomplete, and in stark contrast with the structural simplicity of other aspects of the Standard Model. In particular, this raises the fundamental question of what underlying principles determine the properties of the Higgs boson. This question motivates the possible existence of new physics phenomena beyond those described by the Standard Model, but also identifies the Higgs boson as a unique probe to explore physics processes at and beyond the electroweak energy scale.

Exploration of physics phenomena at and beyond the electroweak scale is taking place in proton-proton collisions at the LHC and will continue in the coming years at the High-Luminosity LHC, through both the measurement of known electroweak processes and searches for signatures of new phenomena. Looking forward, a future electron-positron collider, such as the proposed ILC in Japan or FCC-ee in Europe, would operate as a Higgs factory, producing an enormous number of Higgs bosons, thereby making it possible to measure Higgs properties to an unprecedented level of precision, and possibly uncovering hints of physics phenomena beyond those predicted in the Standard Model.

Precision measurements of physics processes at lower energies also provide a complementary window into new physics at or beyond the electroweak scale. Indeed, the degree of precision of both measurements and Standard Model predictions is an aspect of subatomic physics research that is unique among all the sciences, and can be used to reveal small discrepancies arising due to new physics. This sensitivity can be achieved through the study of rare or forbidden processes in the Standard Model; for example, in the decays of tau leptons, kaons, bottom and charm hadrons, or the study of theoretically well-understood processes such as electron-electron scattering.

Canadian Contributions
and Achievements

Canadian researchers have been and continue to be at the forefront of experimental investigations of physics at the electroweak scale and beyond. They hold leadership roles in several different complementary international projects at the energy and precision frontiers located at unique off-shore facilities. Specific achievements of Canadians in the past five years include the following:

• The ATLAS experiment is designed to study the results of proton-proton collisions produced by the LHC at the highest energy ever achieved in a laboratory. Canadians have and continue to play a key role in all aspects of this international research program. Major achievements in the past five years include:
  • Canadians have directly contributed to the analysis of ATLAS data resulting in the publications of 120 refereed papers on a wide range of topics including the measurement of Higgs boson properties, studies of the electroweak sector, and searches for hints of new physics phenomena.
  • Concurrently, the ATLAS-Canada team has also undertaken the development and construction of novel detector elements with significantly improved performance in order to upgrade the ATLAS detector in preparation for HL-LHC data taking.
    • The ATLAS-Canada team has built and delivered to CERN one quarter of all required muon detector elements, and is now completing their integration into ATLAS. These new muon detecting elements will provide the ATLAS experiment with the capability to identify in real-time proton collisions of interest that should be recorded for future detailed offline data analysis.
    • The ATLAS-Canada team has taken on responsibilities for the construction of a new state-of-the-art particle tracking system that will make it possible to precisely reconstruct the trajectory of thousands of charged particles simultaneously created in proton-proton collisions at the HL-LHC.
    • The ATLAS-Canada team is also developing a new electronics readout for the ATLAS calorimeter system that will significantly improve the ability to precisely measure the energy of particles, under the harshest experimental conditions foreseen at the HL-LHC.
  • In addition, TRIUMF is developing and will provide crab cavity cryomodules for the HL-LHC as part of a Canadian contribution to the upgrade of the accelerator.
• The Belle II experiment at the KEK laboratory in Japan searches for evidence of new physics in a wide range of final states where the Standard Model predictions are well understood. Its physics program is based on the study of a record-breaking quantity of electron-positron collisions at a specific energy enhancing the production of B-hadrons, and is complementary to the LHC physics program. Canadians have been leading the development of key aspects of the Belle II experiment, and are now contributing to its operation. Sample achievements during the past five years include:
  • The Canadian team provided beam background shields for the endcap calorimeters which protect the apparatus against the high level of radiation generated from the intense accelerated particle beams. These shields additionally contain monitors used to characterize backgrounds during beam injection to assist in collider operations.
  • Canadians developed the reconstruction code for the Belle II calorimeter successfully exploiting the full waveform information to produce significantly better energy resolution in the presence of backgrounds and uniquely providing new hadron identification capability. This contribution positively impacts the entire Belle II program, increasing the overall sensitivity of physics studies.
  • The interpretation of collision data requires detailed simulation of known physics processes, for example, to estimate backgrounds. The Canadian team wrote and now maintains the virtual model of the Belle II detector necessary for enabling the entire Belle II physics program.
  • Canadians have already started exploiting the new and growing Belle II data set and published timely results in the search for new particles belonging to a possible ‘dark sector’ in the universe.
  • Canadians have been leading the development of the international Chiral-Belle project, a proposal to upgrade the SuperKEKB e+e− collider with polarized electron beams. The main goal of Chiral-Belle is to precisely measure the weak mixing angle, a fundamental parameter of the Standard Model, at energy scales complementary to other measurements, to search for evidence of new physics beyond the Standard Model. The Canadian team is leading the study of the accelerated particle beam dynamics around key components of this future accelerator infrastructure; the Spin rotators used to align the polarized electrons at the collision point, and the Compton polarimeter used to continuously monitor the polarisation of the electron beam with high precision.
• The NA62 experiment at CERN is designed to measure rare kaon decay branching fractions with high precision. The experiment took data during 2016–2018 and a future data taking period is planned for 2022–2025. Canadians contributed to operational and development activities related to the calorimeter and tracking systems. In the past five years, the Canadian team has focused on the primary objective of the experiment, the measurement of the ultra-rare kaon decay mode K+ → π+ νν. The decay process is highly suppressed in the Standard Model, yet its probability of occurrence is precisely calculated at the 10^-10 level. The measurement of this ultra rare decay process provides a unique opportunity to probe for new physics at very high mass scales in a complementary way to searches conducted at the LHC.
• The goal of the MOLLER experiment is to make the world’s most precise off-resonance measurement of the weak mixing angle, using polarized electron-electron scattering at the Jefferson Laboratory (JLab) in the USA, as a sensitive test for physics beyond the Standard Model. The experiment is under development and scheduled to begin data taking in 2027. Since the last LRP, the Canadian team has made significant progress in leading the design of the magnetic spectrometer and the integrating detectors and associated electronics. The Canadian team has also established leadership roles in simulation and analysis software.
• The MoEDAL experiment at the LHC is a dedicated detector array designed to detect magnetic monopoles and other highly ionizing massive particles hypothesized in a number of physics scenarios beyond the Standard Model. During the past five years, Canadians have participated in the experiment’s data taking and contributed to the publications of the collaboration’s first physics results providing some of the most stringent constraints to-date on the existence of monopoles. Canadians have also led the development, construction and now, current installation of a new detector system to significantly expand the physics program of the experiment during the future LHC Run-3 data-taking campaign.
• The MATHUSLA experiment proposal has been developed during the last LRP period. The proposed experiment is a dedicated large volume detector to be located on the surface above one of the interaction regions at the LHC. The goal of the experiment is to search for neutral long-lived particles hypothesized to exist in various new physics scenarios beyond the Standard Model. Canadians have been instrumental in developing the physics case for this experimental proposal through various sensitivity studies. Canadians have also recently begun to participate in the construction and commissioning of a demonstrator unit and will contribute to the analysis of preliminary data recorded with this demonstrator.
• The development of a future Higgs factory is identified by the international community as a top priority. The ILC is the most advanced and mature proposal on the world-stage that, if approved, would be located in Japan. There are also complementary proposals for electron-positron machines, such as the post HL-LHC Future Circular Collider (FCC-ee) that could eventually be transformed into the next energy frontier hadron machine. In the past 5 years, Canadians have continued to contribute to R&D work for the design of tracking and calorimeter systems, and to improve performance of superconducting radio-frequency (SRF) cavities for a future ILC detector. More recently, Canadians have joined international efforts towards the development of semi-conductor sensor devices that can tolerate very high radiation levels and be used in the design of tracking systems at future colliders. Moreover, TRIUMF is a member of an international collaboration on the development of SRF crab cavities for the ILC. This collective R&D program will build on existing Canadian infrastructure and enable Canadians to take on a central role in a future international collider project.
• The Canadian particle theory community has been active in proposing ways to test whether the Higgs boson discovered in 2012 is the same as the one predicted by the SM using data from the LHC and beyond, and is exploring novel new physics signatures that motivate analyses at colliders.

Science Driver —
Fundamental Symmetries
and Observed Asymmetries

Principles of symmetry play a fundamental role in dictating the laws of nature; yet, the full realization of our universe also relies on subtle mechanisms via which symmetry is broken or hidden. As such, precision experimental tests of both observed symmetries and known symmetry violations provide a powerful and complementary approach to the search of new physics phenomena beyond the Standard Model. More specifically, tests of invariance under the discrete transformations of charge conjugation (C), parity (P), and time reversal (T) provide important probes for new physics. Experimental observations have established that the symmetry associated with the individual P and combined CP transformations is violated in nature, and these effects are incorporated in the Standard Model, although their fundamental origin remains unknown. Moreover, the observed magnitude of CP violation in nature is insufficient to explain the predominance of matter over antimatter observed in the universe. Sources of CP (or T) violation due to new physics phenomena can be searched for through a number of different experimental approaches, including: precision measurements of CP violation in Kaon and B-meson decays; searches for CP violation in neutrino oscillations in long-baseline experiments; and searches for the existence of electric dipole moments violating time-reversal symmetry in neutrons, atoms, and molecules. Interestingly, the violation of parity symmetry provides for an extremely sensitive means to study the neutral current weak interaction, which is otherwise generally masked by the dominant electromagnetic processes. As a result, precision tests of the weak interaction can be achieved using parity violating measurements made in electron-electron scattering, electron-proton scattering, atomic systems, and using cold neutrons. Other important tests of symmetry properties of the Standard Model include lepton flavour universality and lepton number conservation, that can be explored in various particle decays and experiments studying the nature of neutrinos. Finally, the combined CPT symmetry, believed to be an exact symmetry of nature, can be tested in spectroscopy experiments using anti-hydrogen atoms, and any observed deviation would imply a breakdown of relativistic quantum field theory.

Canadian Contributions
and Achievements

The following describes some of the Canadian contributions and achievements in the past five years related to the exploration of fundamental symmetries.

• ALPHA is an experiment at CERN that aims to test CPT symmetry and the universality of gravitational interactions between matter and antimatter using anti-hydrogen spectroscopy. With strong leadership from Canadians, the ALPHA collaboration has produced a series of noteworthy achievements such as a test of anti-hydrogen charge neutrality, the measurement of the anti-hydrogen 1s–2s transition frequency and a demonstration of anti-hydrogen laser cooling.
• TUCAN is an experiment at TRIUMF that aims to measure the neutron electric dipole moment with unprecedented precision using ultra-cold neutrons. Canadians achieved important milestones in the establishment of this physics program: a new fast kicker magnet was built feeding a new proton beamline with a high-power spallation target, and the first ultra-cold neutrons were successfully produced at TRIUMF and their interactions with superfluid helium characterized.
• The goal of the FrPNC collaboration is to search for evidence of new physics phenomena through the study of neutral-current weak interactions with atomic physics methods. Canadians have successfully established a laser trap facility at TRIUMF and recently achieved a major milestone, the detection of the highly forbidden 7s−8s transition Francium, paving the way to future parity violation measurements.
• Canadians have used the TRINAT facility at TRIUMF to study the decays of short-lived isotopes produced at ISAC in the search for new physics. The recently added capacity to efficiently optically pump trapped atoms has enabled Canadians to achieve the most precise measurement of the beta decay asymmetry to date using 37K.
• Using cold neutrons produced at the Oak Ridge National Laboratory, Canadians have contributed to the first measurement of parity violation in the neutron-proton and neutron-3He systems, providing the most stringent constraints to date on the weak nucleon-nucleon coupling constants. Following in the footstep of these efforts, Canadians have also participated in the development of the future Nab experiment that will test for physics beyond the Standard Model through the study of cold neutron beta decay. Specifically, Canadians have developed a 30 keV proton accelerator at the University of Manitoba that will be used to characterize the large area silicon detectors used in the Nab experiment.
• Canadians have also made significant progress in the development of experiments capable of testing, and measuring, fundamental symmetries as part of a variety of other research programs such as ATLAS, Belle II, Chira Belle, MOLLER, NA62, T2K, Hyper-K, DUNE, SNO+, nEXO and LEGEND, and experimental programs at radioactive beams facilities. The specific Canadian achievements on each of these projects are presented as part of the descriptions of other science drivers.
• A primary motivation for exploring new sources of CP violation and lepton number violation is their connection to the matter antimatter asymmetry in the universe. Canadian theorists have been actively analyzing the physics signatures of these potential mechanisms, their associated cosmological implications, and new opportunities for experimental tests.

Science Driver —
Neutrino Properties

In recent decades, studies of neutrinos have revealed many of the properties of these elusive particles, from the paradigm-changing discovery that neutrinos have non-zero mass to the measurement of the surprisingly large mixing angles between the different neutrino species. Still, there is much to learn. We do not yet know the absolute scale of the neutrino mass which has an important bearing on the impact neutrinos have on the evolution of the universe, which of the neutrino species is the lightest, or even whether neutrinos and antineutrinos are distinct particles. We also don’t yet know whether neutrinos violate CP symmetry in a way that could help explain the excess of matter over antimatter in the universe.

The most promising experimental approach to determining whether neutrinos are their own antiparticles or not is through the search for neutrinoless double beta decay (0vββ). Observation of this lepton number violating process would be clear evidence for physics beyond the Standard Model, and clearly demonstrate that neutrinos are Majorana-type particles and hence potentially obtain their masses in a manner completely independent of the much celebrated Higgs mechanism. The observed rate of 0vββ would also constrain the absolute neutrino mass. A number of experiments around the world are searching for 0vββ using different technologies and different candidate isotopes. Canada is playing a leading role in this effort as SNOLAB provides an exceptional low background site.

Precision measurements of neutrino oscillations provide the potential for further fundamental breakthroughs. Neutrino oscillation experiments, such as those based on high luminosity neutrino beams, reactor anti-neutrinos, and atmospheric neutrinos, will attempt to determine the neutrino mass hierarchy and CP-violating phase. They will also search for signs of new physics such as the existence of sterile neutrinos and non-standard neutrino-matter interactions.

Neutrinos can also act as ‘messengers,’ providing to us otherwise inaccessible information about such things as supernova explosions, the composition of the interior of the Earth, the solar core, and high energy particle acceleration processes in the cosmos. Such natural neutrinos also provide an opportunity to study the properties of neutrinos and search for beyond-the-standard model physics.

Canadian Contributions
and Achievements

Canadian researchers are at the forefront of experimental investigations into the properties of neutrinos. Specific achievements of Canadians in the past five years include the following:

• The Canadian-led SNO+ experiment at SNOLAB will search for 0vββ in ¹³⁰ Te. It will also contribute to neutrino oscillation studies through measurements of reactor anti-neutrinos and low energy solar neutrinos. Significant milestones in the development of this research program have been achieved. The SNO+ experiment began operation in 2017 with a water-fill phase and, after a successful data-taking run with water, the transition of the detector to a scintillator fill was completed in 2021.
• The goal of the EXO-200 and proposed future nEXO experiments is to search for 0vββ in xenon. The EXO-200 experiment concluded its operation in 2018 at the Waste Isolation Pilot Plant (WIPP) in New Mexico. Canadians have played a leadership role in both the operation of the detector and subsequent data analysis, achieving sensitivity similar to the most sensitive searches and finding no statistically significant evidence for 0vββ. In parallel, Canadians have contributed to the development of the next generation nEXO experiment, to possibly be sited at SNOLAB, and have taken responsibility for the delivery of key components of the detector such as the outer detector muon veto, water circulation and assay systems and photon sensor testing.
• LEGEND is a program of 0vββ experiments based on ⁷⁶Ge. There is the potential that the proposed future LEGEND-1000 experiment could be located at SNOLAB. A small effort on this research program has recently been established in Canada with contributions initially focused on the development and characterization of specialized germanium sensors.
• The T2K experiment is an ongoing long-baseline neutrino experiment in Japan. Canadians have played an active role in this experiment at all stages, contributing to multiple aspects of construction and analysis, with their work culminating in the publication of the first significant constraint on the neutrino CP-violating phase, a result which is having a profound impact on the community at large and the planning for the next generation of oscillation experiments.
• The future Hyper-K project in Japan builds on the successes of the T2K experiment with construction of an eight times larger far detector and upgrades to the JPARC beam intensity to build a world-leading neutrino experiment. The Hyper-K project was approved and construction of the detector began in 2020. Canada has taken a leading role in Hyper-K since its conception. The Canadian team’s recent activities have focused on various initiatives aimed at suppressing sources of systematic uncertainties that may ultimately limit the precision of Hyper-K measurements. For example, Canadians have led the proposal for a new hadron production experiment to gather hadron interaction data in phase space regions relevant to Hyper-K measurements. Canadians developed the concept of moving the near detector to different off-axis positions to sample different neutrino energy spectra. Canadians have also been leading a proposed test experiment at CERN to establish the detector technologies, calibration methods and detector models of the intermediate water Cherenkov detector necessary for percent level neutrino differential cross-section measurements.
• The future DUNE experiment, at the Sanford Underground Research Facility (SURF) in South Dakota, will study neutrino oscillations using an artificial neutrino beam, as well as atmospheric, solar and supernova neutrinos. Canadian participation in the DUNE experiment has recently been established with contributions around the following key areas of the physics program: near detector commissioning, development of the data acquisition, trigger and calibration systems, and development of the DUNE computing model.
• IceCube is a high energy neutrino telescope sited at the South Pole. In addition to studies of ultra-high energy neutrinos, IceCube also makes significant contributions to the precision measurement of mixing parameters at high energy. Canadians have established leadership in key data analyses such as atmospheric neutrino fluxes and oscillations, supernova neutrinos, indirect dark matter searches and tests of Lorentz invariance. Additionally, Canadians have been playing an active role in the development and use of new optical modules that will be deployed as an extension to IceCube to enhance the angular resolution of high-energy neutrino events. This IceCube upgrade work pursued by Canadians will have an extensive synergy with the work required to develop similar trigger and reconstruction algorithms for the future P-ONE detector, which will use almost identical optical modules used in the IceCube upgrade. Indeed, Canada is preparing to take on a major role with P-ONE off the coast of Vancouver Island, BC, a project that would utilize the CFI MSI-funded Ocean Networks Canada infrastructure to expand the global capabilities and sky coverage of neutrino telescopes.
• HALO is a Canadian-led supernova neutrino experiment operating at SNOLAB. The Canadian team has extended its leadership to the development of the proposed HALO-1kT experiment that would be sited at the Laboratorio Nazionale del Gran Sasso (LNGS) in Italy. HALO-1kT is a detector of opportunity being pursued because of the availability of 1000 tonnes of lead from the decommissioning of the OPERA experiment.
• The BeEST experiment aims to perform the highest-sensitivity search for keV-scale sterile neutrinos to date using the electron capture decay of ⁷Be implanted into superconducting quantum sensors. Canadians have contributed to the publication of the first limits with this technique. These new constraints improve upon previous decay measurements by up to an order of magnitude.
• The coherent elastic neutrino-nucleus scattering process provides a clean environment to search for new physics and is also astrophysically important, playing a role in supernova processes and their detection. Canadians are involved in a number of experiments studying, or planning to study, coherent elastic neutrino-nucleus scattering using different types of target nucleus. These include COHERENT, Scintillating Bubble Chamber (SBC), NEWS-G, MINER and RiCOCHET.

Science Driver —
Dark Matter and Potential Dark Sectors

Compelling data from galactic rotation curves, the dynamics of galaxy clusters, the large scale structure of the universe, and the cosmic microwave radiation demonstrates that ~ 85% of the matter in the universe today is non-baryonic dark matter. Furthermore, neutrino measurements and large-scale structure indicate that only a small fraction of dark matter can be in the form of neutrinos. A global experimental and theoretical effort is testing many hypotheses concerning the nature of dark matter, including thermal relics from the early universe, a category which includes weakly interacting massive particles (WIMPs), and a range of theoretically motivated lighter mass scenarios such as axions, sterile neutrinos, dark photons, and other dark sector degrees of freedom including the mediators of new forces through which dark matter may interact.

Experiments can search for dark matter in at least three ways: through direct detection of ambient dark matter in the galactic HALO, production and detection in accelerator-based experiments, and through observation of dark matter annihilation signatures.

Direct searches for dark matter candidates are carried out in large ultra-clean underground observatories or through their possible interactions with strong magnetic field. The most sensitive searches for high-mass WIMPs use noble liquids as a target while direct searches for low-mass WIMPs use a variety of techniques and materials including searches for scattering off electrons. Searches for WIMPs interacting with nucleon spin use targets such as fluorine. The direct searches for axions, on the other hand, typically rely on the possible axion-to-photon conversion that could take place in a strong magnetic field such as that present in a resonant cavity or in the vicinity of a nucleus in a target material.

Dark matter particles and particles related to a possible dark sector could be produced in accelerator-based experiments in particle collisions or beam dump experiments. The strategy with this experimental approach is to search for visible or invisible decays of a dark mediator particle that would couple to both dark matter and known Standard Model particles.

Indirect searches for dark matter are also carried out by astronomical observatories looking for signatures of dark matter annihilation, including cosmic rays and neutrinos.

Canadian Contributions
and Achievements

The presence of SNOLAB gives Canada a prime position from which to take a leading role in the direct search for dark matter. Canadians have been particularly productive in the past five years and the following list highlights some recent achievements.

• The Canadian-led DEAP-3600 experiment uses a large liquid-argon detector at SNOLAB to search for high-mass WIMPs. It has been in operation since 2017 and successfully demonstrated the very low background levels achievable in liquid argon, based in part on the use of advanced pulse-shape discrimination techniques. The DEAP-3600 collaboration has published the best dark matter limits in liquid argon; these are complementary to limits obtained with other target materials. Canadians have also contributed to the interpretation of these limits in the context of effective field theories and the velocity distribution of dark matter given uncertainties in galactic dynamics.
• The Canadian-led PICO bubble-chamber program at SNOLAB employs superheated fluorinated targets to search for spin-dependent WIMP-nucleus interactions. The PICO-40 detector is in operation and the PICO-500 detector is under construction. The PICO collaboration has published the most stringent direct-detection constraint on the WIMP-proton spin-dependent cross-section.
• The SuperCDMS experiment, which is currently being deployed at SNOLAB, will use germanium and silicon detectors to search for low-mass WIMPs. Canadians have contributed significantly to the analysis of the data taken during previous deployments at Soudan Mine, USA and the resulting publications of the results of detectors operating with a high-voltage bias, exploiting the Luke-Neganov effect. This work forms the basis of the deployment of SuperCDMS-SNOLAB. In addition, the Canadian Cryogenic Underground Test Experiment (CUTE) at SNOLAB has been built and commissioned which will allow for thorough pre-testing of crystals before deployment in SuperCDMS-SNOLAB and for early dark-matter results.
• Canadians researchers have contributed to the publication of a joint analysis with the IceCube and Antares neutrino observatories searching for dark-matter annihilation in the centre of the Milky Way galaxy. While no excess over the expected background is observed, these limits present an improvement of up to a factor of two in the relevant dark matter mass range with respect to the individual limits published by both collaborations.
• The Canadian-led NEWS-G experiment at SNOLAB searches for low-mass WIMPs using spherical proportional counters filled with light atomic mass gases, such as neon, methane, and helium, and thus features particular sensitivity to low mass WIMPs. Canadians have contributed to the publication of the first dark matter search results with a spherical proportional counter at the Laboratoire Souterrain de Modane in France. At the time of publication, the results set new constraints on the spin-independent WIMP-nucleon scattering cross-section for WIMP masses under 0.6 GeV. Canadians have also been significantly contributing to the installation and commissioning of the experiment at SNOLAB that will operate shortly.
• Canadians initiated and developed the new SBC international collaboration for the development of a scintillating bubble chamber that will combine the scintillation of noble liquids with the rejection of electromagnetic backgrounds found in bubble chambers, to search for low mass WIMPs. Canadians have been involved in the development of all aspects of the experiment.

Canadian theorists have been actively involved in developing models for dark matter over the full mass range, studying a range of astrophysical and terrestrial constraints, and have proposed many novel ideas for direct and indirect detection.

Science Driver —
New Physical Principles and Structures

Theoretical physicists are driven to explore fundamental questions about the structure of relativistic quantum field theory itself, the foundation that underlies the Standard Model (SM) of particle physics. These questions cover a particularly wide scope and have the ambitious goals to understand the ultimate nature of physics at high energies, and the unification of particle physics with gravity.

While the SM is a remarkable scientific achievement, and a high degree of quantitative control has been achieved in a number of regimes, a full understanding of its quantum field theoretic building blocks has yet to be achieved and there are mysteries to be understood. Examination has revealed surprising connections, e.g. dualities, between seemingly unrelated theories leading to new calculation techniques at both weak and strong coupling. Important recent progress in the study of strongly-coupled field theory has involved the so-called conformal bootstrap approach, where analyticity and unitarity constraints are used to extract information about quantum field theories even in the absence of a traditional perturbative expansion. Lattice gauge theory is a more direct approach to understanding strong dynamics in gauge theories and Quantum Chromodynamics (QCD) in particular, and is also the subject of considerable theoretical development, e.g. to understand chiral fermions, and indeed as a potential application for quantum computing. Another focus of recent research has been the study of scattering amplitudes, yielding new insights into underlying geometric structures and possibly even the nature of spacetime as well as practical methods for doing calculations in QCD and gravity. Notably, many of these approaches rely on deep and growing links between the formal and the phenomenological approaches to particle theory.

Developing a consistent and complete understanding of gravity at the quantum level remains one of the grand challenges in physics. String theory provides a theoretical framework which accommodates both classical general relativity and quantum mechanics, but is a rich mathematical structure and its concrete application to subatomic physics remains less clear. Most recently exploration of string theory has been productive in elucidating many nontrivial aspects of and connections between quantum field theory, QCD, condensed matter physics, black holes, spacetime, quantum information, and formal mathematics. Perhaps the most far-reaching and nontrivial structure to emerge in this way is the AdS/CFT correspondence or holography, which ties together theories of gravity with quantum field theories in lower dimensions. This discovery nearly 25 years ago continues to stimulate a vast body of theoretical work touching on strong dynamics in quantum field theories relevant to particle and condensed matter physics, thermal dynamics, hydrodynamics and the quark-gluon plasma, and black holes. In recent years, this approach to thinking about the (quantum) physics of black holes has led to new connections to quantum information theory and quantum computing, and new insights about Hawking radiation and a possible resolution of the information loss paradox. Some of these new ideas can be formulated in the traditional language of gravitational path integrals, pointing once again to the power of this dual perspective to provide a novel and productive viewpoint on deep puzzles in conventional physics. Beyond gravity itself, the internal consistency of string theory has provided pointers for where to look for new physics beyond the SM. For example, extra dimensions constitute a new viewpoint from which to consider the sensitivity of the electroweak scale to quantum corrections and the origin of the flavour symmetry structure in the SM.

The synergy between particle physics and early cosmology also provides fertile ground for formal theoretical research that seeks to understand the very early universe. Current cosmological data requires an early epoch of inflation or an alternative description that produces the large scale features observed today and the origins of structure. A full theoretical understanding of early cosmology, and its initial conditions, remains an active research area and one of the few areas where very high scale subatomic physics may leave observable imprints. Indeed, the origins of structure may give us clues to the particle nature of dark matter, while evidence for inflation can provide knowledge about the very high energy structure of subatomic physics. Various early universe scenarios also lead to new predictions, such as the formation of primordial black holes, phase transitions, or topological defects, that are now topical as potentially observable sources of gravitational waves. Finally, understanding the nature of dark energy, and/or the small size of the cosmological constant, remains another grand challenge under study that lies at the intersection of quantum field theory and gravity, and may be a window to understand other deep aspects of fundamental physics.

Canadian Contributions
and Achievements

The Canadian formal theory community has actively contributed to, and indeed provided leadership for, many of the topical directions of research progress outlined above. Specific examples of developments since the last LRP include the following:

• New insights into the structure of scattering amplitudes in quantum field theory and gravity, and associated foundational components of field theory and conformal field theory.
• Developments in the basic understanding of thermal systems, the relativistic hydrodynamic regime, and its applications e.g. to the quark-gluon plasma.
• New understanding of the phase structure and dynamics of strongly-coupled gauge theories.
• Developments in understanding holography, and the connections of black holes and spacetime structure to quantum information theory.
• New insight into the quantum features of black holes, entropy, and low dimensional models of quantum gravity.
• Varied developments in understanding quantum field theory in the very early universe, in de Sitter space times, and the implications for gravitational wave signatures.

Canada has high-profile theory centres, including the Perimeter Institute, but the formal theory community is diverse, and widely distributed across Canada. Researchers actively collaborate in small teams that are often international with members in multiple countries.

Science Driver —
Hadron Properties and Phases

The nature of quarks and gluons, the fundamental constituents of hadrons, is one of the major unsolved problems of modern physics. Strong interactions between quarks and gluons at very high energies (short distance scales) are described within the Standard Model by the theory of Quantum Chromodynamics (QCD), but a full understanding of the strong force at long distances, where quark confinement dominates, is one of the major unsolved problems of subatomic physics.

To gain insight into the strongly interacting, non-perturbative regime of QCD, where quark (colour) confinement dominates, a number of different approaches are being followed. One strategy is to measure hadron properties such as mass, spin and polarizability, in electron scattering and photoproduction experiments. Another is to search for hybrid mesons predicted to exist by lattice QCD calculations as a means to understand how the quark and gluonic degrees of freedom that are present in the fundamental QCD Lagrangian manifest themselves in the spectrum of hadrons. Evidence for new types of hadrons, including tetraquark and pentaquark state, are exciting discoveries which strongly motivate further study. Measurements of the electromagnetic form factors of mesons, such as the charged pion and kaon, will elucidate the role of confinement and chiral symmetry breaking in fixing the hadron’s size and mass as well as the transition from the perturbative-QCD to strongly-coupled domains (short to long distances). Exotic matter can also be created by colliding nuclei at relativistic energies, creating conditions similar to those that existed shortly after the Big Bang, which informs the construction of the phase diagram of nuclear matter.

Canadian Contributions
and Achievements

Canadians are at the forefront of the quest to understand the properties of hadrons, on both the experimental and theoretical fronts. Canadian achievements in the past five years include the following.

• The Canadian theoretical community leverages a range of calculational approaches, including Lattice QCD, Light Front Holographic QCD and Chiral Pertubation Theory to advance the field and to support the Canadian experimental efforts. For example, recent achievements include the first direct lattice QCD calculation predicting the existence of tetraquarks with valence content udbb, and calculations of the Standard Model predictions for the differential branching ratio of the rare decay Bs → ϕμ+μ−.
• The GlueX project currently taking place at Jefferson Lab aims to measure the properties of hybrid mesons produced through photo-production. Canadians have maintained responsibility for the gain calibrations of the silicon PMTs for the Barrel calorimeter which was designed and built in Canada. The Canadian team also led the measurement of the photon-beam asymmetry for η and η′ mesons, concluding that this photoproduction process is dominated by natural parity exchange with little dependence on momentum transfer.
• The pion form factor program at Jefferson Lab has been led by Canadians, garnering over 1,000 citations for their work collecting and analyzing the data from various experiments.
• Canadians have conducted a program of measurements to extract the spin polarizabilities of the proton at the Mainz Mictrotrom (MAMI) in Germany. Such polarizabilities are fundamental observables of hadron structure, and are amenable to calculation with various QCD-inspired models and effective theories. Several measurements have been published and shown to be in agreement with several different types of predictions obtained using different theoretical approaches.
• Canadians continue to play a pivotal role in the investigation of ultra-relativistic heavy ion collisions in general, and the properties of the quark-gluon plasma in particular, through the calculations of relevant experimental observables using hydrodynamics techniques and the development of this formalism. Canadian involvement in these efforts has spurred the development of the requisite detector concepts at past and future heavy ion colliders, as well as advancing our knowledge of hadron structure.

Science Driver —
Nuclear Structure

Atomic nuclei, the core of all visible matter, constitute unique many body systems of strongly interacting fermions. The properties and structure of nuclei are of paramount importance to many aspects of physics, at scales from 10⁻¹⁵m (the proton radius) to 10⁴m (neutron star radius), and to the evolutionary history of the universe. Many of the phenomena encountered in nuclei also share common basic physics ingredients with other mesoscopic systems, thus making nuclear structure research relevant to other areas of contemporary science, for example in condensed matter and atomic physics.

A wide variety of nuclei exist in the universe, but traditional nuclear models are based on the properties of just those that exist on Earth or can be created artificially with relatively long half-lives. The rare isotopes, with nuclei towards the limit of nuclear binding, provide a new window into nuclear structure. Their observed properties are showing unexpected deviations from current models, thereby challenging our fundamental understanding of nature’s principles in building these many-body quantum systems.

Current research in low-energy nuclear physics addresses the existence of atomic nuclei, their limits, and their underlying structure. It also aims to describe interactions between nuclei and dynamical processes such as fission. The ultimate goal is to develop a predictive understanding of nuclei and their interactions grounded in fundamental QCD and electroweak theory. The current challenges of nuclear structure are captured by the following overarching questions. How does the structure of nuclei emerge from nuclear forces? What new features and phenomena emerge with large neutron-proton asymmetry in rare isotopes? A third question, concerning the role of rare isotopes in shaping the visible matter in the universe, leads to the final science driver discussed in the next subsection.

Answers to these questions will follow from a broader and deeper understanding of atomic nuclei, both experimentally and theoretically. The last decades have seen progress in our understanding of the strong nuclear force. However, studies of exotic nuclei, enabled by the developments of rare isotope beams, are changing the conventional knowledge of how protons and neutrons are organized, especially with a large neutron-to-proton asymmetry at the limits of nuclear binding. For example, new forms of nuclei, nuclear halos and neutron skin appear. The well-established shell gaps near stability are also eroded by the spin-isospin effects of the two-nucleon (2N) and three-nucleon (3N) forces and new magic numbers appear far from stability.

Exploration of rare isotopes towards the extreme limits of N and Z binding will provide the insights needed for a comprehensive understanding of nuclei. This exploration is revealing novel quantum many-body features and leading us toward the true global understanding of complex quantum systems and of the mechanisms responsible for the emergent features found in atomic nuclei. Furthermore, it will open new avenues to cross-discipline contributions in basic sciences and societal applications.

Canadian Contributions
and Achievements

Canada is a world-leader in the theoretical descriptions of atomic nuclei from first principles. The ultimate goal of these efforts is to develop a predictive ab-initio theory of nuclear structure and nuclear reactions, to understand nuclei studied at rare isotope facilities. A strong collaboration between Canadian experimentalists and theorists exists and has led to feedback on the quality of inter-nucleon interactions used as input to these calculations, improving the knowledge of the 2N and 3N forces. The following list highlights recent Canadian achievements in the past five years.

• Canadians have helped reveal the imprints of the nuclear force from a study of proton elastic scattering on 10C. The Canadian led experiment, carried out with the IRIS facility at the TRIUMF-ISAC laboratory, measured the shape and magnitude of the differential cross section. Ab-initio nuclear reaction calculations performed by a collaboration led by the TRIUMF theory group, showed that those observables are strongly sensitive to the nuclear force prescription. Comparison with the data suggests that the N²LOsat chiral effective interaction does a better job, compared to the other forces, but is still not an adequate description of the nuclear force.
• The observed β-decay rates in nuclei, found to be systematically smaller than for free neutrons, implies apparent quenching of the fundamental coupling constant. An international theory collaboration, with key contributors from the TRIUMF nuclear theory group, has recently solved this 50-year-old puzzle from first-principles. Their work showed that this quenching arises to a large extent from the coupling of the weak force to two nucleons as well as from strong correlations in the nucleus. Combining effective field theories of the strong and weak forces with powerful quantum many-body techniques, the group carried out ab-initio calculations of β-decays from light- and medium-mass nuclei up to ¹⁰⁰Sn that are consistent with experimental data. These results also have implications for heavy element synthesis in neutron star mergers and predictions for the neutrino-less double-β-decay.
• Canadians have also made important contributions to the measurement and understanding of HALO nuclei. For example, recent studies with Canadian leadership with the Radioactive Ion Beam Factory (RIBF) at the RIKEN Nishina Centre in Japan have unveiled a two-neutron HALO in ²⁹F. It is the heaviest and the first Borromean HALO observed in the proton sd-shell to date. While the results are explained by state-of-the-art shell model calculations with effective interactions, ab-initio predictions are challenged in explaining the HALO in ²⁹F, pointing once more to our limited knowledge of the nuclear force from first principles.
• Canadians contributed to high-precision mass measurements of ^50–55Sc isotopes at LEBIT and the TITAN facilities at TRIUMF. This work added important information to the understanding of emerging closed-shell phenomena at N=32 and N=34 above the Z=20 magic number. Specifically, the new data enabled a complete and precise characterization of the trends in ground state binding energies along the N=32 isotone, confirming that the empirical neutron shell gap energies peak at the doubly magic ⁵²Ca. Furthermore, the results suggest that closed-shell behavior only appears in the mass surface for N < 20.
• Canadians led the recent study of the structure of ⁸⁰Ge using the GRIFFIN spectrometer at TRIUMF-ISAC. The new experimental evidence combined with shell model predictions clearly indicated that low-energy shape coexistence is not present in ⁸⁰Ge, in contrast to previously reported results.

Science Driver —
Cosmic Formation of Nuclei

Humanity has long sought to understand the origin of visible matter and the abundance of the known stable and long-lived nuclei. While it has been firmly established that the synthesis of elements in the universe occurs through a variety of nuclear processes, from quiescent stellar burning to dynamic conditions involving the remnants of stellar explosions and compact object mergers, only half of the total number of nuclei that are expected to exist between the neutron- and proton-dripline have been discovered, about 3,450 nuclei. Much work remains to precisely understand the different nucleosynthesis processes at play.

Understanding nucleosynthesis is accomplished by a combination of astrophysical observations and simulations, nuclear physics data, and the input of nuclear theory predictions. Specifically, from a nuclear physics point of view, the study of astrophysical reactions of interest and knowledge of properties of the nuclei involved requires stopped and accelerated radioactive ion beams such as those produced by the ISAC and ARIEL facility at TRIUMF. Nuclear physics measurements can also help elucidate the physics of neutron stars, the smallest and densest objects in the universe, and supernovae explosions, in particular through precise measurements of the neutron skin thickness in neutron-rich nuclei that help constrain the equation of state of neutron-rich nuclear matter.

This field is also highly synergistic with multi-messenger astronomy, as best evidenced in the remarkable simultaneous observations of the binary neutron star merger GW170817 at multiple electromagnetic wavelengths, triggered by gravitational wave interferometry.

Canadian Contributions
and Achievements

Research efforts in the Canadian nuclear physics community cover all the processes of nucleosynthesis and associated astrophysical phenomena. The ISAC and ARIEL facilities at TRIUMF in Canada bring immense scope for such studies, and Canadians are leading many of these projects. Canadians are also involved in selected projects at offshore facilities with complementary technology. Some research highlights since the last LRP are summarized below:

• Direct measurement of the proton capture reactions at astrophysical energies are possible using the recoil spectrometers DRAGON and EMMA at TRIUMF. Using this infrastructure, Canadians have recently achieved the measurement of the ³⁸K(p,γ)³⁹Ca reaction, greatly reducing the uncertainties in the knowledge of the mechanism involved in the Ar, K and Ca synthesis. Canadians have also exploited the joint capabilities of the EMMA and TIGRESS detectors at TRIUMF to make the first measurement of the ⁸³Rb(p,γ)⁸⁴Sr reaction, an important measurement in the p-process for constraining the reverse reaction.
• Canadians have contributed to several leading studies of nuclear properties relevant to the understanding of nucleosynthesis processes. For example, Canadians performed precise mass measurements of neutron-rich Ga and In isotopes for r-process nucleosynthesis using the TITAN Penning trap and also contributed to the precise measurement of the half-life of ¹³⁰Cd with the GRIFFIN spectrometer at TRIUMF, resolving the discrepancies between previous measurements for this crucial r-process nucleus. Canadians have also been engaged in the BRIKEN project at RIBF in Japan measuring half-lives and neutron-branching ratios for the most exotic neutron-rich nuclei over a wide mass range, and have led the development of a reference database on beta-delayed neutron emitters at the International Atomic Energy Agency (IAEA).
• Canadian researchers have been developing programs to indirectly measure the rate of neutron capture in the synthesis of heavy elements using the infrastructure at TRIUMF, Michigan State University and Argonne National Lab.
• Canadian researchers have been leading ongoing efforts to measure the neutron skin thickness in ⁴⁸Ca via parity violating electron scattering using the CREX experiment.
• Canadians have continued to maintain a world-leading position in predicting nuclear structure properties that are necessary for nuclear astrophysics. For example, Canadians have achieved impressive level of precision in calculating direct capture rates of the ⁸Li(n,γ)⁹Li reaction using ab initio reaction theory. Canadians have also been pursuing astrophysical simulations of binary mergers.

Impact and Synergies with Other Fields

The overarching goal of subatomic physics, to push the frontier of our knowledge of what the universe is made of, and the associated development of specialized research tools, naturally leads to strong links with many other research fields.

Unique opportunities and synergies exist at the boundary between subatomic physics research and other fields, along both scientific and technological fronts. From the scientific point of view, findings in the fields of astrophysics and cosmology provide complementary information in addressing several of the subatomic physics science drivers, and in turn the advancement of knowledge in subatomic physics has a direct impact on models of cosmology and astrophysics phenomena. For example, the rapidly developing multi-messenger approach to study astrophysical objects lies squarely at the boundary between the fields of subatomic physics and astrophysics. From a technological standpoint, techniques and instruments developed for subatomic physics research have been, and continue to be, adapted for use in a wide range of other fields, paving the way to innovative and ground-breaking work. These fields include biology, data science, electrical engineering, material science, medical imaging and public health. Specific examples of these synergies include particle detection techniques used in medical imaging, accelerator mass spectrometry employed in biomedical research and in archaeology for radiocarbon dating, applied nuclear imaging of plants and soil and muon tomography used in several areas such as geology, security and environmental protection. In turn, developments in quantum sensing and techniques in atomic, molecular and optical physics offer novel, and possibly groundbreaking, opportunities to address science drivers in subatomic physics. Developments in accelerator technology to support subatomic physics also have applications to accelerators supporting material science, medical diagnosis and treatment as well as industrial applications such as security, environment, and food storage.

In summary, there exists valuable scientific opportunities in cross-disciplinary collaboration at the boundaries between different fields of research, and subatomic physics research is uniquely positioned to contribute to and benefit from initiatives in regions of overlap with other fields (see Figure 2).