3 Decipher
the
Quantum
Realm

Atoms are the building blocks of matter, but what are the building blocks of atoms? For more than a century we have known that each atom is composed of electrons surrounding a heavy nucleus, bound together by the electromagnetic force. The nucleus is composed of protons and neutrons, which are themselves composed of quarks, bound together by the strong force. The building blocks of atoms are particles, and the forces that bind the building blocks are also described by particles. All known subatomic phenomena can be described by particles and their interactions, an amazing new concept in modern science.

When we look deeper, we see that there is a rich landscape of quantum effects that rule the subatomic realm. The electron appears indivisible, yet its properties are affected by a quantum dance among all subatomic particles. The heaviest known subatomic particle is the top quark, which is surprisingly as massive as a gold atom. While the massless photons and gluons mediate the electromagnetic and strong force respectively, the mediators of the weak force, the W and Z bosons, are massive, blurring the distinction between “force” and “matter”. The Higgs boson, the particle associated with the Higgs field that permeates the universe, gives mass to other particles. The Standard Model provides a unified, elegant picture of the subatomic realm that has withstood the most rigorous tests at LHC and KEK. Beautiful as this picture is, it does not yet account for the masses of the mysterious and mutable neutrinos, which oscillate into one another as they travel through the universe.

Is the Standard Model the ultimate description of the quantum realm? Certainly not, which motivates the two science drivers under this theme for the next decade:

Elucidate the Mysteries of Neutrinos. Neutrinos come in three types, or flavors, which undergo quantum oscillations. While the Standard Model can be augmented to accommodate neutrino mass and oscillations, we do not know in which specific way to extend the model. Moreover, different extensions make vastly different predictions about the birth of the universe. We must further investigate the mysteries of neutrinos in order to explore the deep connections between their physics and the Standard Model.

Reveal the Secrets of the Higgs Boson. The discovery of the Higgs boson in 2012 was a major victory for the Standard Model. Subsequent investigations have revealed that the metastable vacuum in the Standard Model puts the universe on a knife-edge of cosmic collapse. Determining the ultimate fate of the universe and looking for physics beyond the Standard Model motivates further scrutiny of the Higgs sector.

3.1.1  –Science Overview

Neutrinos are the second most abundant known particles in the universe and yet remain an enigma within the framework of the Standard Model. The observation of neutrino oscillations, and the consequent realization that neutrinos have mass, is one of the revolutionary discoveries of recent decades. Despite being the lightest of matter particles, the tiny mass of neutrinos challenges the standard paradigm of particle physics and has opened a compelling new domain of exploration within the quantum realm.

Nature produces—and we observe—neutrinos in three different “flavors”: electron neutrino, muon neutrino, and tau neutrino. We understand each of these neutrino flavors to be a chimera, a mixture of states with different masses. According to quantum mechanics such a mixture will evolve, or oscillate, into another flavor as it travels. Neutrino oscillation processes have been extensively observed, and the admixture of neutrino mass states assigned to each flavor (mass mixing) and the differences between the neutrino masses have been measured. Yet the actual values of the neutrino masses remain unknown, and we are not yet sure how they are acquired. Various theoretical frameworks propose diverse methods for neutrino mass generation, often introducing novel particles and interactions. Certain theories even require that neutrinos must be their own antiparticles that will naturally but surprisingly lead to lepton number violation and provide a necessary condition for the matter dominant universe we observe now.

Likewise, we have not definitively measured the ordering of the neutrino masses, i.e. is the neutrino mass state that has the smallest overlap with the electron neutrino the heaviest or the lightest? We refer to the case where the lightest neutrino has the largest overlap with the electron neutrino as “normal” ordering, because the mass spectrum of the neutrinos in this case follows the familiar mass spectrum of the quarks and charged leptons.

The opposite, or inverted, ordering would be a consequential surprise. For instance, a new symmetry would likely be needed to account for why the two heavier neutrinos are so similar in mass. Neutrino mass ordering impacts efforts that seek to measure the neutrino masses and to understand how neutrinos acquire mass in the first place.

Precision studies of neutrino oscillations can resolve important questions beyond neutrino mass ordering. Is the lightest (or heaviest) neutrino state an equal combination of muon and tau neutrinos, which would hint at new symmetries? Is three-flavor mixing a complete description of all neutrino flavor transitions? Do antineutrinos oscillate differently than neutrinos, namely is the charge-parity inversion (CP) symmetry violated, and could this difference relate to the origins of matter-antimatter asymmetry in the universe?

We do not fully understand why some fundamental forces respect the CP, while others violate it. For example, we have long had experimental evidence that interactions involving the weak force do not conserve CP. Conversely, our description of interactions involving the strong force could provide a mechanism for CP violation, yet all measurements so far are consistent with the relevant parameter being zero. Theories that describe particular patterns of CP violation and conservation can be connected to such questions as the nature of dark matter, or why a universe born with equal amounts of matter and antimatter developed into the overwhelmingly matter-dominated universe we observe today. It therefore makes sense to search for and measure CP violation in every context that we can.

Neutrinos have also opened a new view of astrophysical phenomena that can provide unique probes of neutrino physics. The neutrino signal from the core collapse of a massive star in the Milky Way galaxy provides a window into neutrino flavor transitions and transport in a turbulent environment with high neutrino density. Such an environment cannot be simulated on Earth.

Neutrinos have also opened a new view of astrophysical phenomena that can provide unique probes of neutrino physics. The neutrino signal from the core collapse of a massive star in the Milky Way galaxy provides a window into neutrino flavor transitions and transport in a turbulent environment with high neutrino density. Such an environment cannot be simulated on Earth.

3.1.2  –Ongoing Projects: NOvA, T2K, SBN, IceCube, DUNE Phase I, PIP-II

Ongoing accelerator-based experiments NOvA and T2K have pioneered electron neutrino and antineutrino appearance observations. They have introduced approaches to control systematic uncertainties as applied to combined measurements of mass ordering and CP violation and other mass mixing parameters. A joint T2K and NOvA analysis of the two datasets is ongoing, and results obtained with the complete datasets may provide early indication of future discovery. Ongoing experiments also conduct interesting searches for phenomena beyond the Standard Model.

Over the past decades neutrino oscillation searches at length/distance scales of 1 MeV/m have found a number of anomalous results: The liquid scintillator neutrino detector (LSND) anomaly, the reactor antineutrino anomaly, the MiniBooNE low-energy excess and the gallium anomaly. These anomalies have not been confirmed, and the reactor antineutrino anomaly has been recently resolved. The remaining phase space will be conclusively tested by the current short-baseline neutrino (SBN) program at Fermilab. The SBN program is also crucial in maturing the liquid argon (LAr) technology and analysis. SBN, T2K, NOvA, and other ongoing experiments also make measurements of neutrino interactions, which underpin our understanding of neutrino oscillation mixing (Recommendation 1c).

The DUNE experiment consists of three elements: a far detector complex at SURF, a near detector complex hosted at Fermilab, and a neutrino beam sent across the 1300 km distance between the two facilities. The program has achieved significant design and construction milestones, successfully scaling Liquid Argon Time Projection Chamber (LArTPC) technology and preparing the largest underground laboratory in the US (scheduled for completion by 2025).

For the first phase of DUNE, the far detector complex will comprise two 10 kt LArTPCs in an underground area designed to accommodate up to four modules. In this phase these detectors and a near detector facility will be illuminated by the world’s brightest neutrino beam, generated by the LBNF at Fermilab. The PIP-II accelerator upgrade currently under construction is central in enabling at least 1.2 MW proton beam operation during Phase I (Recommendation 1b).

DUNE’s comprehensive program of neutrino oscillation measurements sets the mass-ordering question as its first goal. Thanks to DUNE’s long baseline and broad energy range of neutrinos that result in a strong separation between normal and inverted mass ordering scenarios, DUNE Phase I is expected to achieve a definitive measurement of the mass ordering within its first decade of operation. This result, when combined with measurements made over shorter distances by experiments such as JUNO, probes nonstandard couplings to matter. These measurements, when combined with Hyper-Kamiokande and ongoing experiments, may clarify the nature of mixing or uncover where the three-flavor mixing model is incomplete.

DUNE’s large, underground LAr detectors also have a unique sensitivity to the electron neutrino component of a supernova neutrino burst. They will therefore complement measurements by other underground neutrino detectors, such as Hyper-Kamiokande, as well as all-flavor measurements by the Antarctic neutrino observatory IceCube and future direct dark matter detectors that constrain the overall burst energetics.

Strong software and computing development that includes AI/ML dedicated effort has been integral to the success of the ongoing and planned neutrino experiments. Therefore, it is essential that advances in software, computing and AI/ML keep up with demands of new neutrino projects, large data rates, and complexity of data analysis as irreplaceable tools for handling high statistics, rare and exotic particle searches.

3.1.3  –Major Initiatives: Early Implementation of ACE-MIRT & DUNE Phase II

Following Recommendation 2b, we envision that DUNE Phase II will include early implementation of an enhanced 2.1-MW beam using ACE-MIRT, third far detector, and upgraded near detector complex.

Early implementation of ACE-MIRT enables beam operations at 2.1 MW to start promptly, permitting DUNE to achieve Phase I design exposure of 120 kt*MW*yr by the mid-2030s, the original planned timescale. ACE-MIRT achieves higher beam power prior to a booster replacement by making several changes to the Fermilab accelerator complex. In particular, enhancements of the acceleration and magnet systems reduce the cycle time of the Main Injector and the LBNF target station components, thereby delivering a given beam intensity more frequently. Reliability of the Booster synchrotron becomes critical during this period and must be assessed and likely addressed through additional measures as described in section 6.6.2. The changes would enable a robust determination of the neutrino mass ordering by the middle of the next decade (Recommendation 2b).

Phase II completion leaves DUNE poised to deliver the most precise measurement of the CP phase across a range of possible CP phase space. It is the ultimate long baseline experiment based on a proton-derived, high-intensity neutrino beam. It is designed to cover a broad spectrum of neutrino energies, enabling an in-depth exploration of the quantum mechanics of neutrino oscillation throughout multiple oscillation cycles. Thus the experiment will comprehensively test the validity of the three-flavor neutrino oscillation framework with best-in-class precision and will search for signatures of unexpected neutrino interactions. In addition, DUNE’s long baseline and high neutrino energy provide unique sensitivity to matter effects and new neutrino interactions, and they allow us to study the direct appearance of tau neutrinos.

To fully achieve these goals, DUNE must collect an extremely large sample of neutrinos and gain exquisite control of the relevant systematic uncertainties. The requisite statistics depend on the ACE-MIRT upgrade and the expansion of the DUNE Far Detector. The increased detector volume provided by an additional far detector module (FD3) leverages international partnerships and benefits all aspects of the DUNE science program, including those, like supernova neutrino burst studies, that are independent of the neutrino beam. Together these upgrades more than quadruple the DUNE Phase I exposure to achieve 600 kt*MW*yr by the mid-2040s, the originally envisioned timescale. At this integrated exposure we expect statistical and systematic uncertainties to be roughly balanced, giving DUNE significant and unique discovery potential across the neutrino mixing landscape.

With higher statistics, control of systematic uncertainties (such as those arising from the interaction of neutrinos and nuclei) becomes increasingly crucial. A more capable near detector (MCND), a gas target combined with a magnetic field and electromagnetic calorimeter, is indispensable for this purpose. In addition, by being exposed to the world’s most intense neutrino beam, it will create a unique laboratory for the discovery of novel particles and interactions, many of which could shed light on the nature of dark matter and possible hidden sectors.

The opportunities opened by DUNE Phase II shine brightest when complemented by a strong theory effort. The interaction of neutrinos and nuclei represents a complex many-body quantum problem, and significant theoretical work is required to gain quantitative understanding at a subatomic or nuclear level. This work will further reduce systematic uncertainties. Similarly, theoretical models of new physics will help interpret any anomalies or surprises in DUNE data. In fact, new developments in theory can open up the science opportunities of new physics searches both at the near and far detectors, many of which are not directly related to neutrinos.

3.1.4  –Future Opportunities: DUNE FD4, the Module of Opportunity

The advent of ACE-MIRT will enable rapid acquisition of beam neutrino statistics, allowing DUNE to achieve 600 kt*MW*yr without deploying a fourth detector module (FD4). This paves the way for an expanded physics program, featuring an upgraded, more efficient detector with enhanced charge reconstruction capabilities. Such a detector would allow for full exploitation of the long baseline neutrino program. A more capable detector with significantly improved light collection, charge granularity, and high radiochemical purity would push the detector energy threshold down to MeV, or lower, while improving track and energy reconstruction.

A range of alternative targets, including low radioactivity argon, xenon-doped argon, and novel organic or water-based liquid scintillators, should be considered to maximize the science reach, particularly in the low-energy regime. Increased radiochemical purity would enhance detection sensitivity to low-energy supernova burst neutrinos, and in some cases even to coherent elastic neutrino-nucleus scattering (CEvNS) interactions triggered by a nearby core-collapse supernova. An upgraded detector module will provide excellent prospects for underground physics, including direct dark matter detection, exotic dark matter searches, and expanded sensitivity to solar neutrinos. R&D for advanced detector concepts should be supported.

The plethora of science opportunities has already sparked wide international interest and has been discussed in DUNE-organized workshops featuring presentations of novel technologies and detection approaches to improve DUNE’s capabilities. Maximizing the physics potential will require input from all stakeholders: DUNE collaboration, US funding agencies, and the international community. A decision-making process led by DOE, inclusive of the entire community and driven by all stakeholders, will ensure that the full potential of the FD4 is realized. The timeline should be driven by the most promising scientific opportunities and must be inclusive of the long baseline science program (Recommendation 4d).

3.1.5  –Interplay with Other Measurements of Neutrino Properties

Understanding the origins of neutrino mass is one of the big questions in physics. However, neutrino masses have not yet been directly measured. There are three approaches to measuring the neutrino mass: direct kinematic mass searches in nuclear beta decay, neutrinoless double beta decay, and cosmology. The first two approaches are under the stewardship of the DOE nuclear science program. Similarly, the question of whether neutrinos are their own antiparticles—Majorana particles—is one of the top science topics highlighted in the recent Nuclear Science Advisory Committee (NSAC) long-range plan via the pursuit of ton-scale neutrinoless double beta decay experiments. Measurements of the mass ordering by the particle physics program set the expected scale for these experiments. The outcome of these experiments is one of the most eagerly anticipated pieces to the puzzle of neutrino mass.

Neutrino mass also affects structure formation in the universe. Hence, careful measurements of the distribution of mass in the universe are sensitive to neutrino masses in the range of values indicated by neutrino oscillation. Cosmological surveys DESI and CMB-S4 can probe the sum of neutrino masses and that information can be directly confronted with the mass ordering measured by DUNE. IceCube and its upgrades test neutrino mixing at high energies and cosmic distances. Any disparities between these two realms would constitute a discovery with profound implications for our understanding of the universe’s fundamental properties.

Many models of neutrino mass generation require the neutrino to have heavy partners. In some cases, those partners can be tested in beam dump experiments like the more capable near detector of DUNE. For other mass ranges, those partners can be searched for at the LHC or future 10 TeV colliders.

3.1.6  –New Initiative: A Portfolio of Agile Projects for Neutrinos

A healthy portfolio of agile experiments focused on neutrino physics and capable of delivering transformative insights and technological advancements is essential to the future of the field. To advance the understanding of neutrinos, a multifaceted approach must support a versatile and dynamic portfolio of ASTAE experiments, as described in section 6.2.

Key breakthroughs in neutrino physics have been achieved through experiments shedding light on hidden facets of neutrino interactions and resolving outstanding neutrino anomalies. These experiments highlight the potential for discovery science in agile neutrino projects. Accurate measurements are also important for a deeper understanding of neutrinos, their interactions, energy spectra, flux and their roles in astrophysical phenomena and long-baseline neutrino oscillation experiments. The adaptability and deployment flexibility of agile experiments, whether near beams or reactors, offer promise for synergistic explorations of hidden sector particles and other phenomena in the evolving BSM field. Technology development, such as innovative materials and unique sensors, is critical to shaping the future of neutrino experiments.

The ASTAE portfolio for neutrinos should encompass precise measurements of neutrino interactions, comprehensive neutrino flux assessments, and searches for neutrino BSM physics, coupled with development of cutting-edge technologies for future detectors (Recommendation 3a).

3.1.7  –20-Year Vision

In the context of three-flavor neutrino oscillations, the collaborative efforts of DUNE, Hyper-K, and the global oscillation program could definitively validate this framework. The experimental outcomes of the first several years of operating will guide the future vision of DUNE, honing in on the complete picture of neutrino oscillations and even the physics of tau neutrinos, the least explored elementary particle of the Standard Model. Should there emerge indications of a paradigm shift such as CPT violation or of neutrino non-standard interactions, DUNE’s long baseline with large matter effects and Hyper-K’s shorter baseline with small matter effects will be critical in discerning this exciting new physics.

If there are hints of a need for heightened precision, muon-decay based neutrino beams emerge as the logical choice to enhance measurement accuracy. Depending on the nature of the departure from three-flavor oscillations, this could entail the deployment of a low-energy muon storage ring, as exemplified by the Neutrinos from Stored Muons (nuSTORM) experiment. This is certainly the case if novel neutrino types or interactions mediated by light new particles come into play. A facility like nuSTORM also has the potential to significantly refine our understanding of neutrino-nucleus interaction cross sections.

In cases where subtler signs of new particles or interactions surface, a muon storage ring with stored muon energies in the tens of GeV or higher range, commonly known as a neutrino factory, emerges as the most suitable source of neutrinos. Regardless of the specific approach, all muon-decay based neutrino sources offer unparalleled precision, well-characterized beams, and potent synergies with muon collider research and development efforts.

3.2.1  –Science Overview

The Higgs boson is an extraordinary and unique particle that is connected to the most puzzling questions of particle physics, including the origin of flavor, the matter-antimatter asymmetry, dark matter and dark energy, and inflation. The Higgs boson differs from other particles in that it is “frozen” in the universe. And once frozen, it is called the Higgs field because it permeates the universe. The field disturbs and slows down the motion of every elementary particle. The Higgs boson slows electrons in atoms so that they stay within the atom instead of flying off into space. Without the Higgs boson, or field, every electron in every atom would move at the speed of light and everything, including us, would evaporate in a nanosecond.

The Higgs boson is the only known fundamental particle that has no spin angular momentum, which permits it to have unique behavior: it can interact with all known matter particles and give them mass, depending on the strength of the interaction. The Higgs boson also provides a novel and distinct gateway to as yet unknown particles, such as dark matter.

Given the unique nature of the Higgs boson and its crucial role in holding together the atoms of the universe, the hunt for it was intense and extensive, beginning in 1964 with both theoretical and experimental efforts. To great fanfare, the Higgs boson was discovered in 2012 by an international effort at the LHC at CERN in Switzerland, with crucial contributions from the US community.

Major questions remain about the nature of the Higgs boson. We do not know if the Higgs field is a fundamental field, or if it is actually a composite field made from other constituents. We do not know if there is only one Higgs boson, or if there is a richer sector containing related particles with new dynamics. We do not know why the Higgs mass should be as low as it is in the absence of additional particles with similar masses that would stabilize it, or why the mass is not zero in the first place. We do not know if the Higgs boson can decay to non-Standard Model particles. The interactions of the Higgs boson with the matter particles—the generation of fermion masses and mixings—involve the largest number of experimentally measured Standard Model parameters whose values and pattern are not predicted by any theory. Understanding this pattern may shed light on important questions such as the matter-antimatter asymmetry and the origin of neutrino masses.

The properties of the Higgs field play a fundamental role in the evolution of the universe and the attributes of the other Standard Model particles. The Higgs field is unique in that it is the only known fundamental field that has a non-zero value in the vacuum state. In the early universe, all the Standard Model particles were massless and the fundamental forces behaved differently than they do today. As the universe cooled, the Higgs field acquired its current non-zero value. This “electroweak” phase transition, in turn, led to a universe in which the Standard Model particles acquired their current masses and the fundamental forces assumed their current form.

The characteristics of the electroweak phase transition are determined by the interactions of the Higgs field with itself (“Higgs self-coupling”) which determines the potential energy of the Higgs field (“Higgs potential”). How this transition happened and which of the puzzling phenomena in our understanding of the universe are related to this phase transition remain central questions in particle physics. Modifications to the potential and related phase transition, beyond the Standard Model predictions, could provide explanations for the dominance of matter over antimatter in the universe.

The fate of the universe depends on the properties of the Higgs sector. Extrapolations of the currently understood Higgs potential to extremely high energy, using the Standard Model, indicate that the current vacuum state of the Higgs field is not only “metastable”—not eternally stable—but that the universe is very close to the crossover point between stability and metastability. Further information about the potential will help interpret the meaning of this result. The Higgs boson may even be related to the field that drove the cosmological inflation, called the inflaton field, or to the mysterious dark energy that drives the current accelerated expansion of the universe, both of which require fields of zero spin.

The fact that the properties of the Higgs field are connected to so many of the fundamental questions in particle physics highlights the central role of the Higgs boson and the importance of understanding all aspects of the Higgs field. The quest to reveal the true nature of the Higgs sector is multi-faceted, requiring dedicated experimental and theoretical programs, and it necessitates pushing the frontiers of both precision and energy. In the near term, the LHC and its successor the HL-LHC are crucial for studying the Higgs field. In the longer term, future colliders will be essential for precision measurements of the Higgs sector and for a definitive measurement of the Higgs potential.

3.2.2  –Ongoing Projects: ATLAS, CMS, HL-LHC

The 2012 discovery of the Higgs boson by the ATLAS and CMS experiments at the LHC was a watershed moment in particle physics; it completed the Standard Model and provided the first observation of a fundamental particle with zero spin. The dataset collected since then has provided a wealth of new measurements related to the Higgs sector. ATLAS and CMS have measured the Higgs boson mass to better than 0.2%, have established that it has zero spin, and have made initial measurements of its lifetime using quantum interference effects. The interactions, or couplings, of the Higgs boson with some of the Standard Model particles (W and Z bosons and third-generation charged fermions) have been measured to 5–10% precision.

All the major production modes of the Higgs boson have been observed, with the experimental sensitivity of some modes nearing the precision of state-of-the-art theory predictions, which are at a few percent-level accuracy. This level of precision constrains the scale of new BSM physics to be above a few hundred GeV to a TeV, depending on the model (see section 5 for further discussion). However, the LHC is still far from probing the detailed shape of the Higgs potential to the degree needed to probe the electroweak phase transition described above. Specifically, more precise measurements of the Higgs self-coupling are needed.

The next phase of the LHC, the HL-LHC, will commence in 2029 and dramatically increase the rate of particle collisions that can occur (Recommendation 1a). This challenge will be handled with new, upgraded detectors that build upon innovations in instrumentation and state-of-the-art technology. Advances in software and computing (including AI/ML) will enable experiments to gather more data and detect rare events at a greater rate. About 180 million Higgs bosons are expected to be produced during the HL-LHC run in each experiment, a factor of 10 more than what is projected for the current LHC run. This large dataset is expected to improve our understanding of the Higgs boson in a major way.

Many of the Higgs boson couplings to other Standard Model particles will be measured to a precision within a few percent or lower. Increasing the precision of these measurements to sub-percent level will provide sensitivity to BSM physics above a TeV in mass. The HL-LHC will enable measurements of the rare decay of the Higgs to muon pairs and thus show that the Higgs boson also generates mass of second generation fermions. The Higgs couplings will also be tested at the 2% level if the Higgs boson decays to undetected particles lighter than half its mass, such as, for example, dark matter.

For the first time, the Higgs potential will be tested experimentally; the HL-LHC will be able to say if and how strongly the Higgs boson couples to itself, and whether the Higgs field’s potential energy has the form predicted by the Standard Model, with precision of around 50%. Deviations of the Higgs potential from the Standard Model predictions can have important implications related to the matter-antimatter asymmetry, as well as the ultimate fate of the universe.

Higgs boson physics can only be studied at high-energy collider experiments, which are currently limited to the LHC and HL-LHC. Longer term, future colliders, described below, will further our understanding of the Higgs boson by testing its couplings to lighter quarks, by improving the precision of the Higgs couplings, and by measuring the Higgs potential. Advances in theoretical calculations of Higgs properties will be required to fully understand the experimental results.

3.2.3  –Major Initiative: Higgs Factory

Beyond the HL-LHC, a Higgs factory will produce large numbers of Higgs bosons with small backgrounds and enable more detailed studies of Higgs boson properties and interactions (Recommendation 2c). Defined as an electron-positron collider that can cover the center-of-momentum energy range of 90 GeV to 350 GeV, a Higgs factory can measure couplings with smaller uncertainties than the HL-LHC due to a combination of more precise knowledge of the momentum of the incoming particles, smaller background environments, and better detector resolutions. Higgs factories offer significant advantages to measuring the production of the Higgs boson. For example, e⁺e^– colliders allow us to identify the presence of a Higgs boson independent of how it decays, and hence provide an unbiased sample for a model-independent and high precision measurement of its properties. This unique feature will also allow a Higgs factory to improve searches for Higgs boson decay to unknown invisible particles, such as dark matter, by an order of magnitude over the HL-LHC, and to improve the sensitivity for unexpected decays into detected particles by up to four orders of magnitude in some cases. Further discussion of these capabilities can be found in section 5.1.

Furthermore, such a collider will enable very strong consistency checks within the electroweak sector of the theory by testing it through quantum loops that relate the masses of the heaviest Standard Model particles: the W and Z bosons, the top quark, and the Higgs boson. The precision on the masses, the Higgs boson width, and its interactions with other particles will be improved by up to a factor of 10 compared to the HL-LHC. For example, a precision of 0.1–0.2% will be achieved on its coupling to the Z, which will extend the reach for new BSM physics by tens of TeV, well-beyond the HL-LHC reach (section 5.2). A Higgs factory will also significantly improve the knowledge of the coupling to the charm quark, and potentially also the coupling to the strange quark.

3.2.4  –Future Opportunities: 10 TeV Parton Center-of-Momentum Colliders

On a longer timescale, a 10 TeV pCM collider—for example, a 10 TeV muon collider, FCC-hh, or possibly a wakefield-based e⁺e^– collider—will enable a comprehensive physics portfolio that includes ultimate measurements in the Higgs sector and also a broad search program (Recommendation 4a). A precise measurement of the coupling of the Higgs boson to itself will tell us about the shape of the Higgs potential, which feeds into the behavior of the electroweak phase transition, and has consequences related to the matter-antimatter asymmetry and the ultimate fate of the universe. At the HL-LHC a measurement of the Higgs self-coupling with a precision of 50% should be possible. However, a precision of 5%—an order of magnitude improvement—will dramatically enhance our knowledge of the potential and be sufficient to discover or rule out many models which could explain the matter-antimatter asymmetry. This can only be achieved with a collider with 10 TeV or greater pCM, due to the greatly enhanced rate of production of events with multiple Higgs bosons that are needed for measuring the Higgs selfcoupling.

At 10 TeV pCM energies, an extremely large number of Higgs bosons will be produced. As a result, these facilities will be able to further improve measurements of Higgs boson couplings, especially for rarer decays such as muon pairs or a Z boson and a photon, which furthers the mass reach to new particles well beyond that of the HL-LHC. 10 TeV colliders will also be the first opportunity to improve the measurement of the strength of the top quark-Higgs boson coupling after the HL-LHC, due to the high collision energy required. Overall, the precision on the Higgs couplings increases by an order of magnitude or more at a 10 TeV pCM collider compared to the HL-LHC achieving sub-percent level precision.

A unique aspect of a 10 TeV pCM collider is its potential to directly probe the causes of possible deviations in Higgs boson properties. At a Higgs factory, a deviation in the measured Higgs couplings would generally point to new physics outside the direct discovery reach of that collider. A 10 TeV pCM collider, on the other hand, would enable both precision measurements that illustrate indirect effects of new physics on Higgs properties and also direct discovery of the particles responsible.

Overall, 10 TeV pCM colliders have a broad search program with a high potential for observing additional Higgs bosons if they exist. They can also directly probe hidden sector physics through Higgs exotic decays. This and the broader science case for a 10 TeV pCM collider is discussed further in section 5.1.

3.2.5  –20-Year Vision

In 20 years the HL-LHC program will be completed, a Higgs factory will be preparing to take data, and a vigorous R&D program will be paving the path to a 10 TeV pCM collider. Each of these projects will fill in the map of the Higgs boson’s behavior in complementary ways: The HL-LHC will deliver the first draft, the Higgs factory will provide incredible detail in key areas of the landscape, and the 10 TeV pCM collider will reveal the challenging heights of the Higgs boson’s interaction with itself.

Every refinement will provide an opportunity to test whether the Higgs boson does in fact give masses to other particles as expected, to determine if it is a fundamental object or in fact composed of other particles, to see if it has unexpected interactions, and to verify that it bootstraps its own mass as predicted by the Standard Model. These studies, propelled by advances in theory, and software and computing, will enable us to obtain a much clearer picture of the Higgs boson and a better understanding of how it has shaped our universe.

This roadmap relies on the design and construction of accelerators and detectors at the forefront of particle physics. The technology choices for achieving the Higgs factory and 10 TeV pCM collider goals need to be determined based on technical feasibility, cost-effectiveness, host site capacity, sustainability, and synergies with the demands of other science topics. The European Strategy for Particle Physics Update, which typically includes scientists and funding agency representatives from the US, is planned for later this decade and will be a milestone in the decision process. In this context, a separate panel (Recommendation 6) is recommended to provide additional guidance to the accelerator program.