5 Explore
in Physics

illustration of the three themes of the Exploring the Quantum Universe report
Illustration by Olena Shmahalo for U.S. Particle Physics
new paradigms in physics graphic

Section 5: Explore New Paradigms in Physics

The prevailing paradigms of particle physics and cosmology—the Standard Model and ɅCDM, respectively—are triumphs of experimental ingenuity, theoretical creativity, and human curiosity. Together, these pillars of fundamental physics explain a vast range of phenomena, from the gravitational scaffolding of the universe due to dark matter, to the complex structure of nuclei due to quarks and gluons. Particle physics lays the conceptual foundations for modern science, and it exemplifies the power of multigenerational and international collaborations to tackle grand scientific challenges.

The quest to understand the fundamental structure of the universe is far from over and mysteries remain. Our existence can be traced to a tiny difference between the amount of matter and antimatter in the early universe, which can be accommodated but not explained by the ɅCDM model. The structure of atoms only requires one generation of matter particles, but the Standard Model of particle physics has three generations, with no obvious pattern or logic to the triplication. A repeated theme in the history of physics is unification, where seemingly disparate phenomena turn out to be manifestations of a common structure. While there are tantalizing theoretical opportunities for unification within these prevailing paradigms, none has thus far withstood experimental scrutiny.

Given these open questions, we explore new paradigms that might yield transformational insights into our universe. There are two broad strategies to venture into the unknown:

Search for Direct Evidence of New Particles. Experiments that seek direct evidence for new particles set the gold standard for discovery. Heavy particles can be produced at colliders with sufficiently high energies, while light but elusive particles can be produced at accelerator-based experiments with sufficiently high intensity. The discovery of new particles, or definitive evidence for their absence, would ignite major paradigmatic shifts and determine the direction of future research.

Pursue Quantum Imprints of New Phenomena. Even if new particles cannot be produced directly, they can still leave clues to their existence via quantum imprints on known particles. This is especially true if the new particles break a fundamental symmetry of the Standard Model. Many known particles were first detected indirectly through their quantum imprints, with followup direct experiments providing definitive evidence. This motivates continued investments in a broad search program for possible quantum imprints of new phenomena.

Illustration by Abigail Malate for U.S. Particle Physics

5.1Search for Direct Evidence of New Particles

5.1.1  –Science Overview

Particle physics is a field that earned its name through the discovery of many particles that were thought to be the fundamental building blocks of matter. This began with the extraordinary discovery that every object in our world is made of scores of chemical elements. Each of those chemical elements is made of a particular kind of atom, with an atomic nucleus of specific electric charge surrounded by orbiting electrons that negate that electric charge. Although the electrons are understood to be a point-like elementary particle with no internal structure, the atomic nuclei were discovered to consist of protons and neutrons. The number of protons in an atom’s nucleus determines the nature of the chemical elements that, in turn, determine the nature of every object we see. This was a unifying paradigm that explained the physical world around us.

But nature is complicated, and further discoveries revealed that the proton and neutron were made of fundamental particles called quarks bound together by a force particle called the gluon, carrier of the “strong force”. It was also discovered that many particles disintegrate over time into lighter ones. This led to the discovery of the “weak force”, which was later determined to be similar to electromagnetism. The weak force is mediated by massive W and Z bosons, as opposed to the massless photon. Through the process of direct observation of new particles, the community of particle physicists arrived at the current paradigm: the Standard Model of particle physics.

However, we also learned that the Standard Model is far from complete. From the establishment of the ɅCDM paradigm of cosmology, we need dark matter, inflation, and dark energy, none of which are part of the Standard Model. For the moment, we do not know what led to the development of our matter-dominated universe which is suitable for life. When inflation started the universe was much smaller than an atomic nucleus. Inflation rapidly turned energy into matter and expanded it to create the immense universe that exists today. Our current understanding is that this expansion must have resulted in an equal number of matter and antimatter particles. If it had stayed that way, however, all of the matter and antimatter particles would have annihilated each other, reverting back into pure energy.

Some physical process must have turned an extremely small fraction of the produced antimatter into matter, but the Standard Model does not explain this physical process. The model also lacks the quantum description of gravity consistent with the general theory of relativity developed by Albert Einstein early in the 20th Century. It is increasingly clear that discovery of new particles and the interactions among them is awaiting us and is likely to come from the exploration of the energy frontier.

The answers to the current mysteries about the universe are believed to be related to not-yet-discovered physics at the electroweak energy scale, a fundamental scale of nature at about 100 GeV. The apparently arbitrary size of this scale affects parameters as diverse as the dimensions of atoms and the half-lives of radioactive nuclei. The mechanism that sets this fundamental energy scale, or temperature, is unknown, and almost all theoretical explanations require new particles with masses of the same order of magnitude as this scale. Cooling through this temperature is known as the electroweak phase transition and results in many fundamental particles acquiring masses. The strength of this phase transition may have implications for the origin of matter, or baryogenesis. Understanding the origin of this energy scale and the impact that the associated physics has on our universe is a major quest of particle physics today.

The most direct way of answering these questions is by discovering new fundamental particles. If these are very massive they can only be produced directly in high-energy colliders, as the higher the collider energy the higher the mass that can be produced. Another possibility is that these particles are produced at lower energy but very rarely, for example in decays of known particles such as the Higgs boson. This requires accelerators that produce very high numbers of particles, including neutrino experiments with their high intensity beams and massive detectors.

These complementary approaches provide access to an extensive theoretical parameter space that covers both higher mass scales and new physics that is weakly coupled to the Standard Model. Overall, these searches can be broadly categorized into those that are guided by specific theoretical ideas, searches driven by questions resulting from experimental data (e.g. dark matter), and searches that are model-agnostic and perform a general exploration of the unknown. Together, these approaches provide comprehensive coverage of the Beyond the Standard Model (BSM) landscape and have the potential to yield groundbreaking insights into the universe.

A broad set of theoretical ideas guide BSM searches at colliders. This includes, for example, supersymmetry, a well-justified mathematical theory that predicts partner particles with a broad range of properties, and theories with composite particles or extra dimensions. A new experimental focus centers on maximizing the ability to identify exotic phenomena predicted by specific theories that are harder to find. Looking beyond specific models, experimental searches target exotic BSM states, including new gauge bosons or Higgs bosons, fermions, and other resonances that are a feature of many Standard Model extensions, including the ones motivated by the smallness of the neutrino masses.

Searches for dark matter are particularly well-motivated by many astrophysical and cosmological measurements which require BSM explanations. Weakly interacting massive particles (WIMPs) continue to be an important target for particle experiments, and high energy colliders are well-suited to search for them. In a widely studied and simple WIMP scenario, the dark matter particle is identified as a new heavy stable particle in the TeV(s) range. In many scenarios the dark matter is only a part of the dark (or hidden) sector. Some of the hidden sector particles may be directly observed through their tiny couplings to the Standard Model particles. Yet another class of candidates includes axion and axion-like particles. These typically couple very weakly to Standard Model particles and can be searched for at high-intensity beam-dump experiments, colliders, and dedicated experiments (see also section 4.1).

The Higgs boson is connected to most of the fundamental questions about the universe and is an integral part of the collider search program. The question of whether the Higgs boson is an elementary particle or a composite particle built of more fundamental constituents remains an important mystery. Current constraints from resonance searches suggest that if the Higgs is composite, the relevant energy scale is beyond the TeV scale. Future colliders that explore this energy scale could reveal this composite structure.

Another important question is whether there are additional Higgs bosons as predicted in supersymmetry models and elsewhere. The Higgs mechanism, as postulated in the Standard Model, is the most mathematically simple method to realize the electroweak symmetry breaking and give particles their masses. However, this simplicity causes serious problems when extrapolating the Standard Model to high energies; for example, a fantastical accident is required to accommodate the observed mass of the Higgs boson. These problems are alleviated if additional particles related to the Higgs are introduced, which is why it is important to search for those. The search must be very wide, since even the simplest extensions to the Higgs sector display a broad range of phenomenology and connections to fundamental physics questions like the origins of the electroweak phase transition and baryogenesis.

The mass and the small natural width of the Higgs boson present an opportunity for observing its decays into new particles even if the couplings between those particles and the Higgs are exceedingly small. Searches for exotic Higgs boson decays remain highly motivated even though the currently measured Higgs boson properties match the Standard Model expectations. Indeed, in many plausible scenarios these new particles could be our only direct window into physics beyond the Standard Model. These scenarios include decays into invisible particles, a mix of invisible and Standard Model particles, and complicated cascades with many-body final states. Long lifetimes are a generic feature of BSM particles in these cascades, yielding hard to detect but extremely low background signatures. The rate of such decays can be very small, so large samples of Higgs bosons are needed.

Specific examples of theoretical ideas and experimental searches that address some of the open questions in particle physics have been described above. However, the exploration of the energy frontier will allow us to observe exotic particles and interactions irrespective of whether or not they have been predicted by current theoretical understanding. High-energy colliders enable us to explore the unknown with the potential for discoveries beyond our current imagination.

5.1.2  –Ongoing Projects: ATLAS, CMS, LHCb, and HL-LHC

The ATLAS and CMS experiments at the LHC have explored an enormous amount of BSM parameter space and dramatically changed theoretical perspectives on the most pressing questions of high energy physics. The results from these studies have tightly constrained minimal models of supersymmetry, while dark matter searches have ruled out large chunks of the theoretical WIMP territory, setting strong constraints on the allowed values of the properties of both the dark matter and mediator particles. There have been major improvements in sensitivity to new, heavy gauge bosons and new fermions with the reach going beyond five times what was achieved prior to the LHC. Innovative experimental techniques, propelled by novel theoretical insights, have started to explore challenging signatures such as compressed spectra, boosted topologies, and long-lived particles.

In the immediate term, the HL-LHC will expand on this BSM program with a factor of 20 enhancement of the LHC Run 2 luminosity (Recommendation 1a). The reach for new, heavy particles will be extended significantly and the HL-LHC will produce approximately 180 million Higgs bosons in each of ATLAS and CMS, enabling a robust program of searches for exotic Higgs decays. Searches for dark matter will further scrutinize additional WIMP parameter space and target hidden sectors and particles interacting more feebly than WIMPs.

New detectors, such as pico-second-precision timing detectors, and forward tracking and extended trigger systems, will enable searches to better target new physics with challenging signatures. Alternative data-taking strategies and novel analysis techniques leveraging advances in AI/ML (e.g. anomaly detection) will provide access to parameter space that is currently unexplored.

The LHCb experiment, despite smaller luminosity and detector coverage, has a unique design that covers particles produced at small angles to the beam which allows it to be competitive with the general purpose detectors for some new particle searches. This is particularly true for Higgs decays into long-lived particles, where LHCb can leverage its advanced tracking and vertexing capabilities along with real-time data processing. Its upgrade for HL-LHC will allow for significant increase in instantaneous luminosity and sensitivity to the hidden sectors (Recommendation 3c).

5.1.3  –New Initiative: A Portfolio of Agile Projects to Search for Direct Evidence of New Particles

Another strategy to look for long-lived particles at colliders is to construct auxiliary experiments that are placed far away from the primary collision points. Proposed auxiliary experiments like CODEX-b and MATHUSLA can extend the sensitivity to BSM particle lifetimes in Higgs decays by several orders of magnitude. Experiments at the proposed Forward Physics Facility at CERN like FASER2 and FORMOSA would be sensitive to the hidden sectors through the Vector and Heavy Neutral Lepton portals. At Fermilab, PIP-II is expected to make many more protons than needed for DUNE, and we anticipate proposals for experiments using the excess protons. These experiments should compete in the portfolio for agile projects (see Recommendation 3a and Section 6.2).

5.1.4  –Major Initiative: Higgs Factory

Beyond HL-LHC, an electron-positron Higgs factory (Recommendation 2c) will provide a very large sample of Higgs bosons with small backgrounds, as well as unique access to exotic Higgs decays, which a hadron collider may find challenging to identify. Such a machine will provide access to new direct production processes below the Higgs mass and will have indirect sensitivity to higher energy scales, as described in Section 5.2. Results from searches related to extended Higgs sectors are expected to improve upon the HL-LHC results by an order of magnitude, covering a wide range of plausible parameter space where a strong electroweak phase transition enabling baryogenesis is allowed. Accumulation of large luminosities will enable the exploration of uncharted territories in direct searches for feebly coupled light states, such as heavy neutral leptons and axion-like particles. Since it will also produce very large numbers of Z bosons, new particles will also be searched for in Z-boson decays.

5.1.5  –20-Year Vision & Future Opportunities

The program described in this section consists of a combination of large and small projects and holds great promise for discovery. By the end of this 20-year period we will have ultimate LHC results from the general purpose experiments and a constellation of agile auxiliary experiments. We will also be in the final stages of construction of a Higgs factory, and will have made progress on the high-field magnets, multi-MW proton driver, wakefield accelerator technology, and muon cooling, including operation of several technology tests and demonstrators (see Secs 6.4 & 6.5). All of this progress will enable us to move forward with a 10 TeV pCM collider.

A 10 TeV pCM collider (muon collider, FCC-hh or possible wakefield collider) will provide the most comprehensive increase in BSM discovery potential (Recommendation 4a). Dramatic increases in sensitivity are expected for both model-dependent and model-independent searches. Such a collider will be able to reach the thermal WIMP target for minimal WIMP candidates and hence will play a critical role in providing a definitive test for this class of models.

In many cases, the sensitivity for new gauge bosons, fermions, or other resonances will be extended by an order of magnitude beyond the HL-LHC. For example, for a universal Z’ benchmark scenario, direct searches at a 100 TeV proton collider provide extensive coverage up to masses of about 45 TeV for a range of couplings. Furthermore, a 10 TeV muon collider can uniquely probe Z’ masses around 100 TeV using indirect effects.

A 10 TeV pCM collider will provide access to new hidden sectors by producing a substantially higher mediator mass or probing even smaller couplings. It will provide opportunities to produce new states with masses of order 10 TeV and directly address the open question related to the composite nature of the Higgs boson. It can also serve as a giga-Higgs factory and provide the ultimate reach for Higgs scalars. For example, direct searches for an extra scalar at a 10 TeV muon collider, taking advantage of vector boson production enhancement, could probe most of the parameter space corresponding to percent level deviations in Higgs couplings, and even explore regions with smaller deviations which will be difficult to observe in precision measurements.

Overall, 10 TeV colliders are a unique tool to directly produce and study new particles and their properties. Their comprehensive coverage of the BSM parameter space enables us to explore the unknown for potential discoveries that may address some of the most fundamental questions about the universe.

For example, a muon collider, if technologically achievable and affordable, presents a great opportunity to bring a new collider to US soil. A 10 TeV collider fits on the Fermilab site and is a good match with Fermilab’s strengths. Its development has synergies with the neutrino program beyond DUNE and the required upgrades to the accelerator complex would also enable fixed target and beam dump experiments to look for new particles directly or via their quantum imprints.

Illustration by Abigail Malate for U.S. Particle Physics

5.2Pursue Quantum Imprints of New Phenomena

5.2.1  –Science Overview

The direct search for new phenomena in particle physics has been often accomplished by going to higher energies with accelerators. This is simply because of Einstein’s famous equation E=mc², which allows for producing heavier particles (large m) once there is higher energy (higher E). Here, c is the speed of light, a constant of nature that converts the unit of mass to energy. This is how new heavy particles have been discovered, clearly demonstrating new phenomena that lead to new theories, and eventually, new paradigms.

However, in the quantum world, another window for discovery is available. Even when new particles are beyond the reach of accelerators, their quantum imprints can be searched for. The quantum effects are fuzzy, and just like quantum bits can be 0 and 1 at the same time, particles can exist and not exist at the same time. They are called “virtual” particles. But they can leave clear imprints on the behavior of particles we observe.

There is a long history in particle physics of unexpected discoveries through quantum imprints and their theoretical interpretation. The study of radioactive beta decay led to the prediction of the neutrino and the properties of the W boson; the explanation of matter-antimatter asymmetry in kaons led to the prediction of the third quark family; the observation of Neutral Current Weak Interaction events in neutrino scattering resulted in the indirect discovery of the Z boson; measurements of B meson mixing predicted the high mass of the top quark. The characteristics of the observed quantum imprints often led to the definition of the accelerators required to directly produce the relevant new particles successfully.

Before the LHC discovered the Higgs particle, its mass had been constrained around the actual measured value from precision measurements of the top quark and the W boson. Measurements of the decays of the Higgs boson already rule out the existence of a fourth generation of particles that follow the same template as the known three.

The physics of flavor is particularly sensitive to quantum imprints of particles that are not present in either the initial or the final state of interactions. The existence of three families of elementary particles of matter and their mass and mixing patterns are a key feature, and a puzzle, in the Standard Model. Rare quark flavor transitions have unparalleled sensitivity to the existence of new physics many orders of magnitude beyond the reach of direct searches in current and planned energy frontier accelerators.

For electrons, muons, and tau leptons, Standard Model mixing is so rare that any observation of a flavor-changing signal called Charged Lepton Flavor Violation in any current or planned experiment would be an important discovery and an unambiguous signature of new physics. Collider experiments can search for subtle effects that would be caused by particles with masses much too heavy to be produced directly.

A discovery made by any current or planned experiments would indicate specific directions in which to focus subsequent experiments to directly observe the underlying new physics, and potentially suggest the new energy scale to be probed. Progress necessitates clean theoretical predictions and high precision experiments with huge data samples and excellent control of systematic uncertainties. Theoretical and experimental progress go hand in hand, with advances in one side motivating further activity and progress in the other side, in a continuous synergistic interplay.

Currently a number of intriguing experimental deviations from theoretical Standard Model predictions have been observed. The most significant of these anomalies are related to g-2, the magnetic moment of the muon, which appears larger than anticipated; decays of the bottom quark to a strange quark and a pair of charged leptons, which may be less frequent than expected; and a possibility that bottom quark decays to tau leptons and muons do not have the same strength, pointing to possible Lepton Flavor Universality Violation. All of these anomalies might be resolved by improved experimental precision or theoretical predictions. They also might be the first signs of new discoveries.

5.2.2  –Ongoing Projects: Mu2e, Belle II, LHCb, ATLAS, CMS

The largest experimental efforts of the US dedicated to indirect probes of new physics currently are the Mu2e charged Lepton Flavor Violation experiment, hosted by Fermilab, and the Belle II and LHCb programs, hosted by KEK in Japan and CERN, respectively. These programs will continue over the time frame of this report with alternating periods of data taking and upgrades (Recommendation 1). The other HL-LHC experiments also present many opportunities for indirect searches, as will experiments at future colliders.

Mu2e, which searches for the conversion of a muon captured by a nucleus into an electron with no emitted neutrinos, will extend our sensitivity to charged lepton flavor violation in this sector by a remarkable four orders of magnitude. Our access to new muon-electron-quark interactions will increase by an order of magnitude in energy scale, up to 104 TeV. Any observed signal at Mu2e would indicate new physics, and should be followed up by further experiments for its full characterization.

The Belle II and LHCb programs focus on decays of bottom and charm quarks, and of tau leptons. The clean, controlled environment of electron-positron collisions (for Belle II) and the extremely high rates and broad-spectrum production in proton-proton collisions (for LHCb) make the two experiments complementary in many ways. These experiments will further probe, with unprecedented precision, Standard Model predictions for quark behavior and lepton physics including leptoquark searches, flavor changing neutral currents, as well as conducting wide hidden sector searches. They will reduce the experimental uncertainties in the measurements in tension with the Standard Model by an order of magnitude or more, and introduce qualitatively new tests made possible by the extremely large number of particle decays available for study. The experiments will continue the established program of searches for potential new signs of unexpected matter-antimatter differences, and of performing measurements which overconstrain and challenge Standard Model parameters to search for inconsistencies between different processes.

The quantum imprints of particles too heavy to be produced in significant rates at the LHC can still result in observable departures from the predictions of the Standard Model. ATLAS and CMS at LHC currently have the unique capability of studying the interactions of directly produced top quarks, Higgs bosons, and W and Z bosons. The data from the ATLAS and CMS experiments, in conjunction with other results, are being used to assemble a comprehensive picture of potential deviations from the Standard Model caused by massive new particles in a largely model-independent manner. The sensitivity of HL-LHC for certain new physics models can reach scales as high as 20 TeV. These measurements complement those at lower energies to provide a comprehensive view of the possible existence of new particles.

5.2.3  –New Initiatives: Belle II and LHCb upgrades

The upgraded Belle II experiment will record 25 times more data of electron-positron collisions by 2035 at the SuperKEKB accelerator at KEK in Japan. The facility produces world record luminosity using the most advanced nano-size beams. The unique environment of the SuperKEKB offers access to decays with multiple undetected particles in the final state, such as hadron and tau decays producing more than one neutrino. The experiment will also further constrain hadronic vacuum polarization which is important for the precise comparison of theoretical and experimental results on the muon g-2. Quark mixing parameters will be measured with ultimate precision (Recommendation 3c).

The US community has extensive experience with this science at the BaBar experiment at the SLAC National Accelerator Laboratory in the early 2000s, and has a lot to contribute to the operation of the detector and analyses of data.

To achieve such an unprecedentedly powerful beam, there are many challenges in the accelerator. A major technological challenge is producing a nanobeam, namely the ability to focus the beam down to the nanometer scale just before collisions. Another is to maintain a very high degree of vacuum in the beam pipe, as a small amount of residue gas can interact with the beam and cause problems. Finally the intense beams can also cause a high level of background at the collision point that needs to be mitigated. These technologies are important for all future electron-positron colliders and therefore it is crucial that the US is involved in their development for the future of the field.

LHCb after its second upgrade will produce huge B hadron samples and will reach unprecedented precision in a large number of observables in the 2035 to 2043 time period. The scientists in the LHCb collaboration will explore extremely rare flavor processes, including matter-antimatter asymmetries in the charm sector, and will also search for and study pentaquarks, hidden sector particles, anomalous B meson decays, and more. LHCb upgrade II will be a major project that opens a new era of precision in the rare phenomena explored by the experiment (Recommendation 3c).

The LHCb experiment, together with BaBar, Belle, and Belle II, have also produced a new type of matter composed of quarks. It has been known that most matter around us is either made of three quarks, such as protons and neutrons (collectively called baryons), or of a quark and an antiquark, such as pions and kaons (called mesons). However these experiments discovered a type of matter made of two quarks and two antiquarks (tetraquarks) or four quarks and an antiquark (pentaquarks). The study of these exotic particles helps us understand the forces that bind quarks together. Such novel states of matter are of strong interest not only in particle physics but also in nuclear physics, and might also exist at the interior of very dense stars such as neutron stars.

These experiments also produce large samples of tau particles. In addition to charged lepton flavor violation searches at Mu2e from muon decays, they can search for the same violation in tau decays, a complementary probe to quantum imprints of particles well beyond the reach of current collider experiments.

All experiments mentioned here are major international projects with small but important US contributions and demonstrate the good investment value of international engagements.

5.2.4  –Major Initiative: Higgs Factory

One of our recommendations for major initiatives is the US involvement in a Higgs factory. The main purpose of the factory is to reveal the secrets of the Higgs boson (section 3.2). However, the Higgs boson is also a sensitive probe of the quantum imprints of new phenomena. For instance, it is possible that there are more than one type of Higgs boson, and the discovered particle is only the first one in a new family. Even when the additional Higgs bosons are well beyond the reach of HL-LHC, their existence affects the interaction of the first one with various particles and can be inferred from the precise measurements of the Higgs couplings. Another possibility is that the Higgs boson is not an elementary particle but is composite consisting of smaller constituents, and then the resulting finite size of the Higgs boson can be inferred from the precise measurements of the Higgs couplings.

The Higgs factory we recommend can be run at the Z pole. Its high luminosity could produce of the order of 10⁹–10¹² Z bosons and a large sample of WW events. These abilities would enable an exceptional program of precision studies of electroweak interactions, extending the probed energy scale by a factor of 3–10 beyond the HL-LHC. In fact, a similar program was conducted at the Large Electron Positron Collider (LEP) in the 1990s that resulted in the prediction of masses of the top quark and the Higgs boson, the exclusion of fourth family of quarks and leptons, and other important results without ever reaching the relevant energy scales. With a much bigger sample of Z and W bosons, we will obtain an unprecedented reach to quantum imprints of new phenomena. A successful Z pole program will involve challenging, high collision rate environments that will necessitate advances in accelerator and detector design, as well as imposing computing requirements an order of magnitude beyond those of the HL-LHC.

In addition, the Z bosons would then produce large samples of bottom and charm hadrons, and tau leptons in their decays, and at the 10¹² Z boson scale will become extremely useful in that regard.

For example, the FCC-ee circular collider is expected to produce a sample of bottom mesons twenty times larger than that of Belle II, enabling a strong indirect search program which will complement its Higgs boson and electroweak parameter measurements. That search program is unfeasible at LHCb-II or Belle II. Precision measurement of the top quark mass is an indirect measure of its interaction with the Higgs boson, which controls the quantum mechanical evolution of the Standard Model at high energies; a 350 GeV Higgs Factory stage will reduce the uncertainty in this crucial parameter by a factor of ten. Proposed 10 TeV-scale machines will probe even higher scales.

Comparing the direct measurements of the top quark and Higgs boson masses at a Higgs factory to the precision measurements of Z and W boson properties can reveal hidden quantum imprints of new particles and phenomena at 10 TeV energy scale.

5.2.5  –20-Year Vision & Future Opportunities

The intense proton beams provided by the Fermilab accelerator complex have the potential to further extend searches for quantum imprints of new phenomena. There is ongoing discussion of an Advanced Muon Facility using the beams of the PIP-II accelerator currently under construction. We encourage further development of this concept, which would increase sensitivity to multiple possible charged lepton flavor violation processes by about a factor of 100 (Recommendation 4a).

The possible future replacement of the Fermilab booster with a new accelerator producing higher intensity proton beams can support a comprehensive facility for experiments on flavor physics, searches for extremely rare phenomena, and CP violation. With careful planning the new accelerator can also become a key enabler for future neutrino experiments and/or a muon collider, in line with the longterm vision of our report.