2

The Next 40 Years

The next 40 years of particle physics promise to be a period of profound exploration and discovery as well as groundbreaking technological development. Research in the field will be driven by the quest to answer fundamental questions about matter, energy, space, and time. This chapter lays out a strategy for the next 40 years that can realize the stunning scientific opportunities ahead and achieve the vision described in the Summary.

The strategy builds on the program in place and planned for the next decade (summarized in Appendix E), and it comprises six recommendations described in this chapter and two additional recommendations in Chapters 3 and 6. The committee’s recommendations call for two new particle colliders, further building on the increasingly important discoveries and approaches that do not involve colliders, taking advantage of new connections with other fields, significant investments in research and development (R&D), and attention to the highly skilled workforce needed for progress.

THE SCIENCE DRIVING THE STRATEGY

As described in Chapter 1, the current understanding of the universe is not only spectacularly successful but also opens up entirely new questions that could not have even been posed 50 years ago. Some of these involve completions and extensions of the current paradigm: What explains the relatively simple but bizarre properties of matter and forces seen in the real world? Why is there more matter than antimatter, making our existence possible? What comprises dark matter, and what is the nature of dark energy? Is there a deeper unification of particles and forces, as strongly suggested by observed regularities connecting quarks and leptons, and the strong and electroweak interactions close to the Planck scale? Are the forces further unified with gravity, as suggested by string theory?

There are also profound new questions that involve seeking a deeper understanding of the inter-relations between matter-energy and space-time, which may call for a revolutionary change in our formulation of space and time. Space and time are central concepts for understanding the universe, but what is their origin? Intertwined with the origin of space and time are questions about the origin and the ultimate fate of the universe, which are in turn related to a more fundamental understanding of dark energy and the quantum vacuum.

Getting at the latter involves a deeper understanding of dark energy. Dark energy appears to be an energy associated with the quantum vacuum. The same violent quantum fluctuations that appear to doom space-time at short scales should also endow the vacuum with a gargantuan energy, inconsistent with what is observed. Further-

more, if the Higgs is point-like, as it is in the Standard Model, these fluctuations would give the Higgs, and all other elementary particles tied to the Higgs, an enormous mass compared to what is observed. Are the mysteries of vacuum energy and the Higgs mass related?

Direct experimental investigations of the Planckian regime are out of reach, and the vacuum energy that drives the accelerated expansion of the universe cannot be experimentally manipulated but only observed. This leaves us with the Higgs particle, as the most important character in this drama, amenable to direct, controlled experimental investigation.

The Higgs Is Special

The Higgs is the simplest of elementary particles, and its very simplicity is what makes it perplexing (see Box 2-1). There is nothing like it elsewhere in nature. All other elementary particles have an intrinsic quantized “spin”—leptons and quarks have spin 1/2, while the force-carrying particles have spin 1. In concert with the laws of relativity and quantum mechanics, non-zero spins are associated with deep symmetry principles that both mandate the existence of spinning particles and largely dictate the structure of their interactions. In sharp contrast, the Higgs is the first point-like particle with no spin that has ever been discovered. Its existence is

BOX 2-1
The Higgs Boson

The Higgs boson is the simplest of elementary particles, and its very simplicity is what makes it perplexing (Figure 2-1-1). All other elementary particles—quarks, leptons, and gauge bosons—have an intrinsic quantum-mechanical spin; the Higgs does not. Its interactions with other particles are not dictated by symmetries, whereas those of the other elementary particles are. While it gives mass to the other elementary particles, its own mass remains a mystery. The Higgs field that fills the vacuum today and gives masses to the other particles came into existence a fraction of a second after the Big Bang and may have yet-to-be-discovered cosmic connections. In short, the Higgs boson is central to moving beyond the Standard Model and to revealing connections between the birth and evolution of the universe and the particles and their interactions.

not mandated by known symmetries. While other elementary particles acquire their mass from their interactions with the Higgs, the nature of these interactions, as well as the self-interaction of the Higgs, are not totally dictated by known principles.

There are good reasons to expect other spin-zero particles to exist as well. Cosmological observations give strong evidence for a period of explosive accelerated growth in the very early universe, driven by a vastly larger vacuum energy than exists today. The simplest picture for the dynamics controlling the beginning, duration, and ending of this period of “inflation” is associated with a spin zero “inflaton” particle. There are also arguments that what appear to be constants of nature, controlling the strength of particle interactions, are determined by other spin zero particles in much the way that particle masses are determined by the Higgs. The corresponding particles are known as the “axions” and “moduli” of string theory.

Studying the Higgs represents the first foray into a new era, not only in understanding the nature and interactions of elementary particles, but in exploring the dynamics that determine the structure of the vacuum and the fundamental constants of nature. Since its discovery at the Large Hadron Collider (LHC) in 2012, the Higgs has been under intensive study there.

The 10 TeV Frontier

The LHC collides protons at 14 TeV, but since the proton is composed of quarks and gluons, the energy is shared between them, so that the actual energies involved in the collision of these constituents only provide a definitive probe of physics at the 1 TeV scale. There are pressing reasons to push forward by another order of magnitude in the journey to ever-shorter distances and to explore the 10 TeV frontier. While the LHC was powerful enough to produce Higgs particles, and with its upgrade, the High-Luminosity LHC, to perform first detailed studies of the Higgs particle features, it has only produced a fuzzy picture of how truly point-like the Higgs is. The mysteries of vacuum fluctuations affecting the Higgs would be less glaring if it was determined that the Higgs is not elementary but has substructure, helping explain its light mass. Therefore, the Higgs must be put under the most powerful microscope available in order to get a much sharper picture of it.

There are two aspects of this question: Does the Higgs look point-like to other particles, and does it look point-like to itself? The first question is ideally studied at Higgs factories discussed in greater detail below. The second can be studied by seeing how the Higgs interacts with itself, in a process with Higgs particles meeting at a point in space-time. The LHC will give some rough indication of whether this interaction exists but will not determine it with any accuracy. Elementary particle collisions at the 10 TeV scale will be able to measure Higgs self-interactions to an accuracy of a few percent and will largely settle the issue.

Collisions at 10 TeV will also directly probe the unity of the electromagnetic and weak interactions at high energies; for instance, by observing coherent radiation of W and Z particles mirroring electromagnetic radiation. There are also several well-motivated scenarios where new particles would be too heavy to have been produced at the LHC but must show up at the 10 TeV scale. As one example, one of the simplest candidates for dark matter are weakly interacting particles with a mass between 1–3 TeV, too heavy to be produced at the LHC, but which would either be directly produced or conclusively excluded by 10 TeV collisions.

UNDERSTANDING THE HIGGS AND EXPLORING THE 10 TEV FRONTIER

Colliders will play a critical role in answering the big questions of particle physics. In particular, the two colliders discussed below, a Higgs factory and a 10 TeV muon collider, will fully reveal the properties of the Higgs boson and explore the 10 TeV frontier to search for new particles and phenomena beyond the reach of the LHC. Together, they form the cornerstone of the committee’s plan. While the operational phase of a Higgs factory is likely to precede that of a muon collider, the muon collider is discussed first because of the urgency of the investments that must be made to determine its feasibility.

A Muon Collider

It is possible to reach the 10 TeV frontier by building a more powerful version of the LHC, colliding protons in a larger tunnel, about 100 km in size, with collision energies near 100 TeV, so that the quark and gluon constituents collide at 10 TeV energies. This is currently being discussed as the Future Circular Collider (FCC-hh, for hadron–hadron collisions) program at CERN, and the Super Proton-Proton Collider in China. A different possibility is to reach 10 TeV collisions between electrons and positrons using “laser plasma wakefields,” an acceleration technique exploiting the large electric fields produced by lasers. More information about these approaches is provided in the Snowmass 2021 Accelerator Frontier Report.¹

A completely different path to the 10 TeV scale has recently inspired a great deal of excitement—the possibility of a muon collider. Muons are heavier cousins of electrons that decay in about a millionth of a second when at rest. But a 10 TeV muon collider accelerates them to 0.9999999998 times the speed of light so that by relativity they live for about a tenth of a second, long enough to send them around a 10 km ring and smash them together over and over again.

A muon collider combines many of the scientific advantages of both electron/positron and proton colliders in a single machine. Like protons, the heaviness of muons relative to electrons makes them easier to accelerate to high energies without energy loss to electromagnetic radiation. But, unlike protons (and like electrons), muons are point-like, so their collisions provide the same kind of precision measurements made in electron–positron accelerators. A muon collider will thus be able to plumb the most fundamental mysteries of the Higgs while at the same time rocketing to the energy frontier and giving a robust probe of the 10 TeV scale.

A muon collider also has significant advantages in operating costs and energy consumption. At 10 km in size, it is 10 times smaller than proton machines probing the same energies and has concomitantly smaller demands on power consumption. In this way, it not only provides a new path to the 10 TeV scale as an immediate next step but also offers a way forward for continued exploration even beyond the 10 TeV scale in the long-term future. A muon collider is especially opportune in the United States. The footprint of a muon collider may fit on the site of the Fermi National Accelerator Laboratory (Fermilab) site, and the path to a 10 TeV collider would pass through intermediate stages producing novel neutrino beams for new neutrino oscillation experiments, leveraging Fermilab’s existing strength in neutrino physics (see Box 2-2).

The immense potential for scientific discovery and demand for technological innovation offered by the muon collider leads to the committee’s first recommendation.

Recommendation 1: The United States should host the world’s highest-energy elementary particle collider around the middle of the century. This requires the immediate creation of a national muon collider research and development program to enable the construction of a demonstrator of the key new technologies and their integration.

Challenges of a Muon Collider

Part of what makes the muon collider so exciting is that it is so novel—unstable particles in such huge numbers and concentrations have never been collided before. But this also means it is unknown whether such colliders can be made to work. There are important technical challenges that must be overcome to produce, compress, control, and collide the large number of muons necessary to make such a collider possible. A demonstration that these challenges can be overcome must be achieved before there is full confidence the machine can be built.

Systematic study of muon colliders began more than 20 years ago and has continued in the United States and in Europe. Most of the challenges have been identified, and the roadmap for the necessary R&D has been established. To achieve the beam required to produce enough collisions, many muons must first be produced by colliding a high-intensity proton beam on a target.

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¹ S. Gourlay, T. Raubenheimer, V. Shiltsev, et al., 2022, “Snowmass ’21 Accelerator Frontier Report,” https://doi.org/10.48550/arX-iv.2209.14136.

Operational experience at current and planned high-power accelerators (the Spallation Neutron Source at Oak Ridge National Laboratory [ORNL], the Proton Improvement Plan II [PIP-II] at Fermilab) forms the basis to achieve the necessary high-power beams. The muons must be focused into a dense beam, packing many muons into a tiny volume with very little spread in their energy. This can be accomplished by ionization cooling, which uses an absorber to slow down the muons in all directions, while the momentum along the beam is regenerated by the accelerating cavity. This may be the most challenging aspect of the muon collider design since the beam must be squeezed by a factor of a million to achieve the required collider luminosity. A proof-of-concept has been demonstrated by the Muon Ionization Cooling Experiment. The radio frequency systems needed for muon production, acceleration, ionization cooling, and beam manipulation must operate over a wide range of frequencies, from a few megahertz to a few gigahertz, and under a wide range of conditions and require both room-temperature and superconducting technology. The short muon lifetime, even stretched by relativistic time dilation, implies that their acceleration and collision must be accomplished extremely rapidly. The technical progress needed to meet these challenges, and the muon collider demonstrator itself, will inevitably result in significant advances in accelerator technology with implications far beyond the field of particle physics, such as adiabatic demagnetization refrigeration and fusion magnets.²

Moving Forward

A muon collider is a bold and innovative approach to getting to the 10 TeV energy scale. Its origins trace to the United States, and it could be sited in the United States at Fermilab. The significant technological challenges in determining whether or not a muon collider can be built demand the initiation of an R&D phase (circa 7 years), followed by a demonstrator phase (circa 10 years), as quickly as possible. Doing so will ensure that making a decision on the feasibility of a muon collider and whether or not to build one in the United States will not delay getting to the 10 TeV frontier.

A Higgs Factory

Determining whether the Higgs is elementary or has substructure has huge ramifications for the future of particle physics. The Higgs interacts with all the other elementary particles, and measuring these interactions allows us to learn whether the Higgs looks point-like to external probes.

This defines the program for a “Higgs factory,” where electrons and positrons are collided in a large 100 km ring at energies about twice the mass of the Higgs, producing millions of Higgs particles, enabling high-precision measurements of their production and decay. This allows a precise measurement of the interactions of the Higgs with leptons, quarks, photons, W and Z bosons, and gluons for which there are also precise Standard Model predictions.

The discovery of Higgs substructure would define an extensive experimental program for future colliders to produce and study the Higgs constituents. Decisive evidence for a point-like Higgs would force theorists to think in radically new directions about the origin of the Higgs.

A number of proposals have been made for Higgs factories, some of which have mature designs and are currently under serious consideration, including the following:

• The Future Circular Lepton Collider (FCC-ee), a circular electron–positron collider under study for CERN (see Figure 2-1), would occupy a new 90 km tunnel and would have four interaction points, allowing for up to four detectors. Science could begin as early as the mid-2040s. The same tunnel could in the future be repurposed for a proton–proton collider (FCC-hh) referred to above, at an energy of 100 TeV, with science operations commencing toward the end of the century.

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² National Academies of Sciences, Engineering, and Medicine, 2024, The Current Status and Future Direction of High-Magnetic-Field Science and Technology in the United States, The National Academies Press, https://doi.org/10.17226/27830.

• The International Linear Collider (ILC) consists of two linear accelerators with a combined length of 21 km that accelerate beams in opposite directions to provide collisions at their intersection. The ILC could accommodate upgrades to higher energies, possibly employing new acceleration technologies. The design is mature and was a global effort, involving scientists from Asia, Europe, and the United States. But neither Japan nor any other nation has offered to host the ILC.
• The Circular Electron Positron Collider (CEPC) is a circular collider that has been identified by the Chinese Academy of Sciences as its top priority for a future particle accelerator. It would have two rings in the same 100 km tunnel and two interaction points. It could be repurposed as a proton–proton collider, known as the Super Proton-Proton Collider. While the CEPC has invited international participation, the participation of U.S. scientists is uncertain.

Several other Higgs factory concepts are in earlier stages of development. Some strive to increase the accelerating gradient of a linear collider to reduce their linear size or to provide an upgrade path to higher energies. These include the Cool Copper Collider, which would use cryogenically cooled copper accelerating cavities, and the Higgs-Energy Lepton collider, which would use traveling-wave superconducting accelerating cavities. Other

proposals involve using energy recovery linear accelerators or recirculating linear accelerators to reduce power consumption. These include the Circular Energy Recovery Collider, the Energy Recovery Linear Collider, and the Recycling Linear e+e− Collider. The Compact Linear Collider, developed at CERN, uses normal-conducting acceleration to achieve a very-high accelerating gradient. More details about all these concepts can be found in the Snowmass 2021 accelerator frontier report.

Active participation in a Higgs factory is crucial for the U.S. particle physics community, not only for the scientific advances it promises but also for the continuing benefits of international collaboration. Furthermore, U.S. involvement would ensure a leading role in cutting-edge technology and provide valuable training for the next generation of physicists. This leads to the committee’s second recommendation.

Recommendation 2: The United States should participate in the international Future Circular Collider Higgs factory currently under study at CERN to unravel the physics of the Higgs boson.

The highest scientific priority with Recommendation 2 is to help ensure that an international Higgs factory be built in a timely manner and that the United States participate in a significant way. The committee is singling out the FCC-ee project to this end, because it is the most advanced Higgs factory project in terms of implementation, having recently completed a geological, environmental, technical, and financial feasibility study.

It is notable that the FCC-ee has capabilities in addition to use as a Higgs factory; it can be used for conducting precision electroweak measurements and top quark studies, and it could extend searches for new physics, including in rare b decays. There is also a special relation between the United States and CERN, which includes very significant and mutually beneficial U.S. participation in the LHC and High Luminosity LHC (HL-LHC), as well as very significant contributions by CERN to the Long-Baseline Neutrino Facility/Deep Underground Neutrino Experiment (DUNE). This was recognized in 2024 by the U.S. government when it issued the following statement of support for the FCC-ee:³

All of this forms the basis for Recommendation 2.

Timing

The committee’s first two recommendations ask for U.S. involvement and leadership in new accelerator projects that will realize the stunning opportunities ahead to advance particle physics. The timeline for these colliders will stretch decades into the future. Projecting that far in time is difficult because of the many uncertainties—scientific, technological, decision-making, and budgetary.

The relative sequencing of the projects ahead and important decision points can be discussed with more certainty. Currently, construction is taking place on both DUNE at Fermilab and HL-LHC at CERN; each should begin science operations around 2030 and continue for 10 years or more.

Determining the feasibility of a muon collider is a critical decision point, and thus it is essential that R&D begin as soon as possible. Once the R&D is complete, estimated to take about 7 years, the construction of a demonstrator can begin. Ideally, that construction would start soon after DUNE begins science operations, with the demonstrator phase lasting about 10 years.

Assuming CERN moves forward with the FCC-ee, its construction could begin around the same time as the muon-collider demonstrator. Furthermore, around the time that FCC-ee science operations begin, a decision

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³ Department of State, 2024, “Joint Statement of Intent Between the United States of America and the European Organization for Nuclear Research Concerning Future Planning for Large Research Infrastructure Facilities, Advanced Scientific Computing, and Open Science,” https://2021-2025.state.gov/joint-statement-of-intent-between-the-united-states-of-america-and-the-european-organization-for-nuclear-research-concerning-future-planning-for-large-research-infrastructure-facilities-advanced-scie.

on whether or not a muon collider is feasible should be made, and, if it is feasible, construction could begin immediately.

This sequencing ensures that intensive studies of the Higgs and progress in particle physics will continue at the FCC-ee while a muon collider is being built in the United States. Ideally, the muon collider will begin operations near the end of the committee’s 40-year horizon. Just beyond the 40-year horizon, a 100-TeV proton collider could further extend the discovery reach of a 10 TeV muon collider.

The science that drives these accelerator projects is as compelling as the projects are challenging. There is both a scientific urgency and a national imperative to acting now. The United States cannot risk losing the momentum, leadership, and talent it has built up over decades. Boldly moving forward will propel the United States to making the breakthroughs and innovations of the 21st century in a highly competitive world.

EXPANDING HORIZONS OF DISCOVERY

Particle colliders will continue to play an essential role in particle physics. However, over the past two decades, the particle physics community, particularly in the United States, has diversified its approaches to addressing fundamental questions about matter, energy, space, and time. For example, in addressing the pressing questions about neutrinos, the identity of the dark matter, the nature of dark energy and cosmic acceleration, as well as the universe’s earliest moments, particle physicists are using a wide variety of tools, including neutrino and muon beams, underground dark matter searches, cosmic surveys, and novel detector technologies.

The current breadth of the U.S. program is illustrated by a recent survey of the research interests of more than 3,000 scientists involved in particle physics: energy frontier 37 percent, cosmic frontier 29 percent, theory 27 percent, neutrino frontier 24 percent, computational frontier 17 percent, instrumentation frontier 16.5 percent, rare processes 14 percent, accelerator frontier 13 percent, and underground facilities 5 percent (multiple areas of interest were permitted, so the sum is greater than 100 percent).⁴ In addition, particle physics research has now attracted scientists from many other fields, bringing new techniques and fresh perspectives. There are growing interactions with many fields, including astronomy, nuclear physics, gravitation and relativity, particle astrophysics, quantum and atomic physics, mathematics, and computer science, all of which are increasingly important for progress in particle physics.

A Variety of Approaches

There is a huge breadth of activities in particle physics in addition to colliders. The scope and timescales of these initiatives vary significantly, but they tend to be shorter than the multi-decade timescale of big accelerators. The United States has the world-leading program in non-collider particle physics, both in its breadth and its depth. This rich program not only complements and extends the reach of colliders to study fundamental questions in particle physics but also, because of the smaller scope and shorter timescales of some of the experiments, allows for faster implementation and can present attractive opportunities, especially for early-career scientists.

A number of these future opportunities for addressing many of the big questions of particle physics are discussed below. The Snowmass 2021 report⁵ provides a more expansive and detailed discussion of all of the opportunities ahead. These opportunities involve the four Department of Energy (DOE) laboratories with high-energy physics programs in addition to Fermilab—Argonne National Laboratory, Brookhaven National Laboratory, Lawrence Berkeley National Laboratory, SLAC National Accelerator Laboratory—and involve partnerships with university programs in both high-energy physics and astrophysics.

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⁴ Division of Particles and Fields, American Physical Society, n.d., “Support the 2023 P5 Report: Statistics,” https://docs.google.com/spreadsheets/d/e/2PACX-1vRaGc9kVV-uBNPJstmYcYMwiluxya7hSsgDnWB1pg44l8zxPvGl4jUSvOR0VCoa5fCetgDJCNDUJb3O/pubhtml?gid=307089066&single=true, accessed April 30, 2025.

⁵ J.N. Butler, R.S. Chivukhala, A. de Gouvêa, et al., 2023, “Report of the 2021 U.S. Community Study on the Future of Particle Physics (Snowmass 2021) Summary Chapter,” https://doi.org/10.48550/arXiv.2301.06581.

Cosmic Surveys

The distribution of matter today and the snapshot of the universe 380,000 years after the Big Bang from the cosmic microwave background (CMB) provide the means of studying dark energy and cosmic inflation through multi-wavelength surveys of the universe. The proposed program, which includes Dark Energy Spectroscopic Instrument (DESI) and the Vera C. Rubin (Rubin) Observatory Legacy Survey of Space and Time in the optical and Cosmic Microwave Background Stage Four experiment in the microwave, will reveal much about the nature of dark energy, dark matter, neutrino masses, and cosmic inflation.

Among the future opportunities are even larger redshift surveys, from tens of millions to billions of redshifts, and a new generation of surveys that use line intensity mapping, a promising technique for mapping the large-scale structure of the universe using mean intensity fluctuations of atomic and molecular lines.

Dark Matter

The quest to understand dark matter is a central challenge in both particle physics and cosmology because it accounts for the bulk of the matter in the universe and is not comprised of Standard Model particles. Its nature remains one of the great puzzles in both fields and a window to physics beyond the Standard Model.

The current program, which includes accelerator searches, underground detectors, and astrophysical measurements, has the potential to discover the two most motivated candidates—weakly interacting massive particles and quantum chromodynamics (QCD) axions. The absence of any compelling signal to date has pushed theorists to explore many other interesting possibilities, spanning a mass range of more than 40 orders-of-magnitude, with a wide range of interactions with normal matter, including wave-like dark matter or micro black hole dark matter. A natural possibility is that dark matter is not merely a single particle add-on to the Standard Model but is part of a rich, new dark sector with its own panoply of particles and forces.

The future of dark matter research will include novel collider searches for long-lived particles, a new generation of ultra-sensitive quantum sensors and detectors, and even table-top experiments, capable of probing a broader spectrum of masses and interaction strengths.

Neutrinos

Neutrinos are special in many ways. Their masses are minuscule, and they only interact with other matter via the weak force, making them feebly interacting and thus challenging to detect. There is much that is still unknown about neutrinos. They have tiny masses and “mix” with each other as they propagate through space, but this only determines the difference between their masses, not the overall mass scale, or even the ordering of their masses. The mixing between neutrinos provides a new source of charge parity (CP) violation that may be connected to the asymmetry between matter and antimatter in the universe, but this CP violation in the neutrino sector has yet to be conclusively observed. The current neutrino program, headlined by DUNE at Fermilab, should resolve the question of the mass ordering and definitively detect CP violation with a plan to run to the 2040s.

Since neutrinos are neutral, they might be their own antiparticles (much as photons are). This attractive and economic possibility may also help explain their miniscule masses. If they are not their own anti-particles, there must instead be additional, light particles beyond the Standard Model. This important and fundamental question can be settled by planned experiments in the U.S. nuclear physics program searching for neutrino-less double beta decay.

In addition, future CMB experiments and other cosmic surveys have on their agenda measuring the sum of the neutrino masses or searching for evidence of additional light particle species. Perhaps the grandest challenge is the detection of the background of approximately 300 neutrinos per cubic centimeter of space that are likely left as relics from the Big Bang, whose observation would give a direct window into the early universe going to much earlier times than can be accessed with photons.

Particle Astrophysics

The universe functions as a high-energy accelerator producing energetic cosmic rays. Thus, particle astrophysics has always been an exciting collaborative effort. The first evidence for new particles beyond ordinary matter was obtained by studying cosmic ray collisions in the atmosphere.

The study of the highest energy cosmic rays, gamma rays, and neutrinos is enabled by detector technology developed for particle physics, offering new opportunities for fundamental physics. For example, the annihilation or decay of dark matter particles may produce such particles, and currently the best constraints on very-high-mass dark matter particles beyond the reach of colliders are derived from searches for their indirect detection using gamma rays and neutrinos. Stars are capable of producing copious numbers of feebly interacting new particles, which place stringent limits on their existence and open new avenues for their detection. While the uncertainties on their properties are currently a limiting factor, astrophysical phenomena, such as supernovae and black holes, provide novel environments to test the properties of dark matter and are sources of high-energy particles that allow for searches of new physics, such as Lorentz violation or the conversion of photons into axions.

Rare Decays and Precision Measurements

There are a number of processes whose rates are either forbidden or highly suppressed within the Standard Model. Experimental searches for these processes thus provide a unique opportunity for discovering new physics, since even tiny new effects can be dominant. For example, experimental measurements of the distribution of charge in the electron—its “electric dipole moment”—would give indirect evidence for new, very massive, particles that are inaccessible to current accelerators. The probes of electric dipole moments of the electron and the neutron have made enormous progress by more than two orders of magnitude over the past decade. Similar scales could be indirectly probed by the observation of rare decays, such as the muon decaying into an electron (Mu2e) and a photon. Deviations in the predicted magnetic properties of the muon would also give a powerful probe of new physics. There are also two experiments using intense muon beams produced at Fermilab; Muon g-2 is finishing its analysis, and Mu2e is still under construction. There is an ongoing and planned program on precision quark flavor based outside the United States.

Observation of electric dipole moments, rare muon decays, or deviations in the magnetic properties of the muon would not only be electrifying discoveries in their own right; they would suggest a definitive scale for new particles within reach of future colliders and set a much more precise target for their optimal collision energies.

Finding: A broad set of experiments that does not involve particle colliders are critical to addressing many of the most urgent questions in particle physics.

Recommendation 3: The United States should continue to pursue and develop new approaches to questions ranging from neutrino physics and tests of fundamental symmetries to the mysteries of dark matter, dark energy, cosmic inflation, and the excess of matter over antimatter in the universe.

Connections and Exchanges with Other Fields

Particle physicists are often early adopters and adapters of advances in other areas of science and technology. The methodologies of particle physics are closely related to nuclear physics, atomic physics, particle astrophysics, and astronomy, and many connections have been and are being made with these disciplines. Particle physicists have also rapidly deployed developments in computational science, materials science, quantum many-body physics, quantum information science and engineering, and microelectronics to advance their science.

These fields also benefit from the ambitious and demanding scientific goals of particle physics. For example, particle physics continues to provide a testbed and incubator for complex computational systems and approaches, including exascale and high-performance computing, big data, and artificial intelligence (AI)/machine learning (ML) methodologies. Connections between particle physics and other subfields of physics are crucial for expanding

the mutual intellectual and technological benefits. The number and importance of these connections is growing. In the following text, some of the most promising connections and exchanges are described. Doubtless, others will arise.

Nuclear Physics

Elementary particle physics arose from the field of nuclear physics with the advent of cosmic ray experiments and higher energy accelerators that could explore scales smaller than the neutron and proton. Today, nuclear physics remains a vital field of research. Its focus includes understanding how the mass and spin of the proton is generated, the nature of the quark–gluon plasma, the limits of nuclear stability, the formation of the chemical elements, fundamental symmetries, and neutron-star physics.

Since the strong interaction physics is described by QCD, the direct links between nuclear physics and particle physics are essential. Nuclear theory is now endeavoring to calculate the properties of nuclear matter from first principles. Current areas of intense experimental research include the nature of the quark–gluon plasma and the phase structure of QCD, the mass and spin of the proton, and the spectrum of hadronic states. At CERN, the LHC supports an active program on nuclear physics in addition to the high energy physics (HEP) program. In the United States, the Electron-Ion Collider will advance the understanding of proton and nuclear structure at very short distances, which complements the probes of strong interactions at high-energy proton colliders.

Another important area of common interest is neutrino physics, with nuclear physicists developing ton-scale experiments searching for neutrino-less double beta decay.⁶ This process can only proceed if the neutrino is its own anti-particle, and since the rate for this process depends on the electron neutrino mass, these experiments are also sensitive to the scale of neutrino masses.

Astronomy, Astrophysics, and Cosmology

Broad connections with the astronomy community have been established through particle physicists participating in cosmology-oriented, optical surveys, notably the Sloan Digital Sky Survey, Dark Energy Survey, and DESI. The Legacy Survey of Space and Time (LSST) at the Rubin Observatory involves both particle physicists, who built the 3.2-gigapixel camera, and astronomers. LSST was designed for various science goals, including two of high interest to particle physics: investigating the nature of dark energy and dark matter. The high-resolution studies of individual galaxies will enable detailed investigations of the dark matter distribution in galaxies, providing valuable information about the nature of dark matter. For instance, measurement of dwarf galaxies and tidal streams within and near the Milky Way (such as by the European Space Agency’s Gaia mission) can be used to constrain the properties of dark matter.

The detection of gravitational waves by the Laser Interferometer Gravitational Wave Observatory has opened a new window on the universe. In addition to gravitational wave observatories, the study of gravitational waves is also carried out by pulsar timing array projects such as the North American Nanohertz Observatory for Gravitational Waves. Future gravitational-wave detectors will provide even more powerful probes into the early universe and may be a source of surprising discovery, including the detection of gravitational waves from cosmic strings, cosmic inflation, and the phase transitions associated with the Higgs boson. Such observations could shed light on the conditions and processes taking place during the universe’s infancy, providing insights into both fundamental physics and cosmology.

Beyond their shared scientific interests, astronomers and particle physicists collaborate closely on instrumentation and data analysis.

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⁶ Nuclear Science Advisory Committee, 2023, “A New Era of Discovery: The 2023 Long Range Plan for Nuclear Science,” https://doi.org/10.2172/2280968.

Atomic and Condensed Matter Physics

Atomic physics has had a long relationship with particle physics, going back to the measurement of the Lamb shift, propelling the development of quantum electrodynamics in the 1940s, to the decisive evidence for the electroweak theory provided by measurements of atomic parity violation in the 1970s. Recent years have seen remarkable new applications of atomic physics and quantum metrology, in precision measurements, table-top probes of new physics, and laboratory experiments designed to detect dark matter.

Condensed matter physics and elementary particle physics have had common threads since the 1950s. The Bardeen–Cooper–Schrieffer theory of superconductivity, which was related to a spontaneously broken gauge symmetry, motivated the study of spontaneous symmetry breaking in particle physics and played a key role in the invention of the “Higgs” mechanism that underpins the electroweak theory. The deep understanding of the “renormalization group,” which explains the scale dependence of physical phenomena in quantum field theory, led to a comprehensive theory of continuous phase transitions of ordinary matter and has become an essential component of fundamental physics. More recently the study of “topological” phases of matter has brought condensed matter physicists, quantum field theorists, and mathematicians together in productive dialog.

Finally, there are unexpected and exciting new connections emerging between quantum information science and quantum gravity. They involve the interplay of quantum entanglement and geometry. These new connections are bringing together string theorists, condensed matter theorists, and atomic experimental physicists to understand profound ties between seemingly disparate areas of research.

Mathematics

The laws of physics are written in the language of mathematics, and fundamental physics has long had a vigorous and stimulating interaction with pure mathematics. The still incompletely understood physical principles underlying quantum field theory and string theory involve many deep mathematical ideas, which have for decades led to unanticipated insights in mathematical fields ranging from algebraic geometry to topology and number theory. More recently, surprising new mathematical structures in algebra, geometry, and combinatorics have been uncovered in studying the basic physics of elementary particle scattering processes, bringing theoretical physicists and mathematicians together in a common quest to understand their physical and mathematical implications. It is easy to predict that the deepest ideas in physics and mathematics will continue to be even more tightly intertwined in the coming decades.

Computation

Advances in scientific computing and networking have always been crucial to particle physics research. Looking ahead, the focus shifts beyond current practices to advanced computation, data science, and AI/ML methods. Key areas include cost-effective, large-scale computing facilities for data analysis; high-performance hybrid computing; advanced networking; and sophisticated data management. Collaborations among computational scientists, data scientists, and physicists will drive innovation, workforce development, and strong partnerships across academia, laboratories, and industry.

Elementary particle physics has always had an outward-looking stance, engaging with other areas of physics, astronomy, and computer science to great mutual benefit. These interactions are expected to become even stronger and more diverse in the coming decades.

Finding: Elementary particle physics is already adapting innovative tools from other areas of physics and computer science to the mutual benefit of both fields.

Recommendation 4: The United States should explore new synergistic partnerships across traditional science disciplines and funding boundaries.

Cross-disciplinary work often leads to innovation and breakthroughs but can be challenging both for the scientists involved and for those who fund it. The impediments for the scientists engaged in such work are significant, including overcoming artificial barriers between offices and agencies, obtaining funding, and achieving adequate recognition for career advancement. The challenges for the funding agencies may be even more significant. Budgetary program lines are important parts of budgetary planning and discipline, but they can result in barriers to funding interdisciplinary work, especially in its earliest stages. Particle physics is fortunate to have two major sponsors—DOE and the National Science Foundation (NSF)—with two different cultures, mission-driven and proposal-driven, as both can provide more and different means of funding cross-disciplinary research.

RESEARCH AND DEVELOPMENT INVESTMENTS

The lengthy timescales and technical challenges involved in achieving the bold objectives recommended require a sustained effort over many decades, with investment in the development of new science and technology, as well as support of the scientists who will carry out the work.

Core Research

A strength of U.S. particle physics is the synergy between the national laboratories and universities. The national laboratories provide key infrastructure and host large projects and initiatives. The DOE Office of Science supports five national laboratories engaged in particle physics research: Fermilab, the single purpose laboratory dedicated to particle physics, and Argonne National Laboratory, Brookhaven National Laboratory, Lawrence Berkeley National Laboratory, and SLAC National Accelerator Laboratory, which are multipurpose laboratories with significant particle-physics programs. Other laboratories in the DOE complex make important contributions to specific projects and needs in particle physics; for example, ORNL makes extensive contributions to accelerator science and technology.

Universities educate the next generation of scientists. University researchers, generally supported by DOE or NSF grants, have flexibility to explore new directions. Graduate students are university-affiliated, although many benefit from working at national laboratories or collaborating with scientists there. The importance and influence of the field is illustrated by the fact that the vast majority of research-intensive universities have particle physics programs.

Technical resources—accelerators, computing centers, and engineering facilities—are predominantly housed at the national laboratories. Currently, universities can host fewer such facilities than they did in the past, which negatively impacts technical training for graduate students and postdocs and research. To optimize training and education and research, it is essential to adequately support university-based facilities in addition to sending students and postdocs to the national laboratories for the larger-scale tasks.

The 2014 Particle Physics Project Prioritization Panel (P5) report⁷ made a strong case for increasing the construction line for particle physics, to enable new projects like DUNE, the Muon-to-electron-Conversion Experiment, and PIP-II, with core research support for scientists receiving lower priority. This led to a rebalancing of DOE’s HEP budget, and funding for core research has decreased to a level somewhat below the 2014 P5 recommendation (see Figure 3-1), with a slight increase in recent years to bring it back to fiscal year 2012 levels (with no adjustment for inflation). While the rebalancing achieved its goal of enabling these important projects to go forward and increased the overall HEP budget, it reduced the funding for the scientists responsible for carrying out the work. The reduction in funding for core research—even in current year dollars—has stressed the research community, and theory was especially hard hit.⁸

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⁷ S. Ritz, H. Aihara, M. Breidenbach, et al., 2014, “Building for Discovery: Strategic Plan for U.S. Particle Physics in the Global Context,” https://usparticlephysics.org/wp-content/uploads/2018/03/FINAL_P5_Report_053014.pdf.

⁸ The Particle Physics Project Prioritization Panel report recommended an increase of “$15 million per year in 2023 dollars” to “university-based theory research” being funded by DOE, which would “bring theory support back to 2010 levels” (S. Asai, A. Ballarino, T. Bose, et al., 2024, “Pathways to Innovation and Discovery in Particle Physics: Report of the 2023 Particle Physics Project Prioritization Panel,” https://doi.org/10.48550/arXiv.2407.19176.).

Theoretical particle physics plays an essential role in advancing the field. Theory provides the framework for understanding phenomena and formulating predictions that experiments can then test. For example, lattice QCD calculations connect precise measurements with fundamental theory, which is crucial to precision tests such as the Muon g-2 experiment. Increasingly, theorists are also involved in combining results of multiple experiments, the design of new experiments, and in some cases, actually leading experiments.

Some of the activities of theoretical physics are more formal, where the connections in the short term may be to other areas of theoretical science and mathematics. The United States is unsurpassed in formal theory; among the developments that have already had extraordinary impact are quantum field theory, supersymmetry, new calculational techniques for the Standard Model, and superstring theory. Without the considerable support that theoretical particle physics receives from private foundations—about 10 percent of the total, mostly from the Simons Foundation—the impact of the decrease of core funding would be even greater. To sustain the field’s vitality and U.S. global leadership, it is essential to increase its support.

If the bold opportunities that are possible for particle physics are to become reality, there must be sufficient research support for the scientists who are doing the work. The next chapter returns to this topic and discusses the disastrous impact of decreasing, or even constant funding, on the future workforce.

Critical Research and Development Investments

The committee has identified a number of areas for R&D investment that it believes are crucial for the muon collider, a Higgs factory, and the broader enterprise. This list is by no means exhaustive, not least because new R&D opportunities are certain to emerge in the coming decades. The committee’s most important message is that, in a field defined by long timescales for expensive and difficult projects, sustained investment in innovation for the future is critical. The societal benefits of this and past innovation are discussed in Chapter 5.

Advanced Detectors

Particle physics detectors of the future will have to operate in unprecedented experimental environments, challenging technology to new heights to make them possible. As two examples, future collider detectors will need to operate with higher precision and cope with higher event rates in more intense radiation environments, and dark matter detectors will need to lower their energy thresholds and improve event reconstruction.

The development of detectors and instrumentation for particle physics experiments has often pushed existing technical boundaries and have frequently resulted in innovative technologies that benefit other scientific fields and society as a whole (as discussed in Chapter 5). For example, the widespread use of application-specific integrated circuits has a long history in particle physics, allowing for more compact, reliable and radiation resistant readouts with ability to withstand cryogenic environments. This illustrates the cross-fertilization of industry advances that have been exploited and adapted by particle physics to advance experimental goals.

The use of quantum sensors is becoming more widespread. In searches for dark matter, dark photons, and detection of electric dipole moments and gravitational waves, they have the potential to be a fundamental tool of particle physics. The benefits extend in both directions: fabrication of qubits can also be used to build sensors for particle physics and noiseless readout of sensors. Understanding the noise mechanisms for these applications translate to better understanding and control of qubit coherence. Single photon detection has also become feasible through use of novel semiconductor sensors, such as silicon photomultipliers, as well as superconducting sensors.

Computing

Elementary particle physics makes extensive use of computational technology. Some of the world’s most complex experiments are in particle physics, and some of the most numerically intensive and precise calculations are carried out by theorists in lattice field theory, accelerator simulation, and computational cosmology. The demands on computing will undoubtedly increase. The rapid development of computation across multiple fronts poses both a challenge and an opportunity for particle physics.

Historically, particle physics experiments relied on Moore’s law to obtain increased computing power. Moore’s law is slowing, however, and riding the wave of computational progress will require particle physicists to embrace new methods and technology.

In terms of new computing paradigms, modern AI/ML approaches have gained a large following in many areas, particularly where very large data sets can be cheaply accessed and where the system is too complex to be adequately modeled. Statistical learning approaches based on neural network architectures have shown spectacular successes in a number of domains that include scientific applications, such as protein folding, predicting weather, and targeted materials synthesis. Additionally, large language models (LLMs) have been surprisingly successful in their ability to engage with scientists on a number of important tasks, such as software translation.

It seems clear that there will be many interesting and powerful applications of AI/ML methods in particle physics, especially in areas involving both large and high-dimensional data sets. There are many research areas where close interactions among particle physicists and AI/ML practitioners may be very beneficial. These include uncertainty quantification, proper treatments of symmetries and constraints, new data representations, inclusion of insights from theory and modeling, and notions of convergence in the sense of numerical analysis. AI/ML techniques are extremely data- and compute-intensive in their training requirements, and the availability of large-scale computing resources for such tasks might ultimately become a bottleneck as it already has for academic researchers working in the area of LLMs.

Quantum computing has generated significant excitement as an essentially new paradigm of computing that is based on the foundations of quantum information. The advent of Shor’s algorithm for factoring in 1994 showed the potential power of this approach. Quantum simulation—solving quantum problems on a (digital or analog) quantum computer—is an area that holds great promise in the long term, with direct applications to particle physics. An important example is the simulation of real-time dynamics of quantum systems, such as the high-energy collision of protons; this will become important for the future collider program in the next four decades.

Accelerator Science

Current accelerator research for particle physics is driven by the need to produce and manipulate the high-energy and high-intensity beams necessary to fulfill the energy and luminosity requirements of future accelerators, including accelerator reliability to maximize science productivity, and sustainability to minimize energy consumption and environmental impacts (see Chapter 5). In the United States, much state-of-the-art accelerator R&D is associated with the planning for the Electron-Ion Collider.

Progress in accelerator R&D demands a better understanding of the fundamental dynamics of particle beams, in conjunction with the development of new technologies from magnets to radio frequency cavities and all other accelerator systems.

Advances in understanding beam dynamics are necessary to overcome accelerator performance limitations, including the preservation of beam quality in the presence of strong and non-linear fields and collective effects. The understanding of beam distributions and beam halos are necessary to understand and minimize beam losses, a necessary condition to enable high-intensity, high-power beams.

Technical progress on accelerator systems is necessary to increase accelerator performance and to ensure reliable operations. Development of high current sources, targets that can withstand high-power beams, novel materials, and instrumentation that can withstand harsh radiation environments are all necessary to enable high-intensity and high-power beams. Beam acceleration technology, which employs normal-conducting and superconducting devices operating at radio frequencies, is a cost and performance driver for any large accelerator facility.

The challenge for the future is enabling high-gradient and low-cost acceleration systems. Similarly, the development of very high-field magnets for reasonable costs is key to all proposed colliders to reach the 10 TeV scale. R&D on novel accelerating techniques that use laser and advanced concepts to enable beam acceleration to high energies over astonishingly short distances must be continued to enable the next generation of accelerators beyond the proposed high-energy colliders.

Most accelerator R&D takes place at the national laboratories, and at a few universities, enabled by their facilities and directed at the needs of anticipated accelerator-based experiments. The broad program of basic accel-

erator sciences also improves the tools that advance many other fields and industries, as described in Chapter 5. But realizing these bold objectives will demand a reinvigorated U.S. program in accelerator physics, including at universities, starting now and sustained for decades. This should include basic accelerator physics where there are opportunities for exciting advances, as highlighted by recent breakthroughs in wake-field acceleration and optical stochastic cooling. Currently, there are not enough accelerator scientists to successfully achieve the goals described thus far. Chapter 3 addresses the workforce challenges in accelerator science.

Finding: The long journey to realize the extraordinary opportunities for discovery in particle physics will require sustained and steady support of the scientists who carry out the work and targeted investments in research and development that will make the ambitious projects possible.

Recommendation 5: The United States should invest for the long journey ahead with sustained research and development funding in accelerator science and technology, advanced instrumentation, all aspects of computing, emerging technologies from other disciplines, and a healthy core research program.

Such investments are challenging to make and require discipline, especially in the face of the budgetary realities of funding ambitious projects. However, the committee firmly believes that both R&D investments and core support are essential to the future of elementary particle physics. Chapter 6 discusses other important aspects associated with planning for new large accelerators, energy management, and environmental impact.