Particle physics has expanded its scope to include a wide range of topics from very low to very high energies. Its core questions, though, remain the same: to identify the fundamental interactions that govern the universe, and to demonstrate that these are described by well-motivated equations of motion. Today, we know that these equations include the Standard Model, either as a fundamental or an effective low-energy description. The Standard Model is tested to a remarkable level. If one includes neutrino Yukawa couplings (an oversight of the founders), there are arguably no deviations seen in our measurements of the strong, weak, and electromagnetic interactions. But conceptually the Standard Model is far from perfect. It contains a large number of free parameters whose values it does not—and cannot—explain. And, it provides a shaky and unstable foundation for the pursuit of additional laws of nature required to solve the mysteries it leaves open.

The foundations of the Standard Model divide neatly into two parts, with very different status. On one side, there is the principle of local gauge invariance. This is a very beautiful concept that completely determines the structure of the couplings of fermions and gauge bosons in terms of three fundamental coupling constants, corresponding to the three Standard Model gauge groups SU(3) × SU(2) × U(1). The structure is highly constrained, and its validity has been dramatically confirmed by experiment, from low-energy tests of QED through the muon and electron (g−2) and the spectra of hydrogen and positronium [2], through the direct and highly redundant measurements of the gauge couplings at the Z resonance [3], to the measurements of W and Z boson production and multiple gluon radiation at the LHC [4]. All of the experimental successes of the Standard Model are tests of the consequences of the gauge principle

On the other side, there is the Higgs field and its associated couplings. Here one might hope that there would be a “Higgs principle” that explains the values and patterns of these couplings. Today, we have no principles at all. The Standard Model Higgs couplings are unrestricted—and, because they are parameter inputs of a renormalizable quantum field theory, they are uncalculable. Apparent predictions, such as the statement that CP violation is largest in the 3rd generation, are consequences of the gauge structure. The most central question is that of why electroweak symmetry is spontaneously broken at all. In the Standard Model, this is an arbitrary choice, with a particular parameter (µ 2 ) being chosen to be negative without explanation.

These considerations put a premium on improving our knowledge of the Higgs field. At the moment, we know only one Higgs boson. But models that give a dynamical explanation for the Higgs spontaneous symmetry breaking predict additional particles. These include additional scalars—an extended Higgs sector—and other particles whose interaction with the scalar field(s) generate the Higgs potential. These particles have consequences at currently accessible energies, both in flavor physics and in the couplings of the Higgs boson. We must take the opportunities we have now to discover concrete deviations from the Standard Model at current energies. It will be our task in the future to explore energies beyond LHC for new fundamental interactions connected to the Higgs field, and for this we must now to develop the new accelerator technologies that will get us there.

Many other questions are often cited as key mysteries of particle physics. But most of these are also, ultimately, questions about the Higgs boson and Higgs fields more generally.

The most obvious question about the Standard Model, one which has been with us since the discovery of the muon, is the origin of the mass spectrum of quarks and leptons. We now have direct experimental evidence from the LHC, at least for t, b, and τ , that the masses of Standard Model fermions are mainly due to their couplings to the 125 GeV Higgs boson [5]. This does not explain the masses of these particles; it only pushes the mystery back one level. Similarly, weak interaction mixing and CP violation in heavy quark decays can be complete accounted for by the more fundamental matrix of Higgs boson couplings [6]. There is a long history of attempts to give a dynamical explanation of this data, beginning with Harold Fritzsch’s 1977 paper [7]. However, despite many original ideas, the origin of the fermion masses and couplings has only gotten murkier as our knowledge of the masses and mixings has become more precise. The emphasis in flavor physics has now shifted to the search for flavor anomalies such as lepton non-universality. These are specifically outside the framework of the Standard Model and so would provide evidence for new fundamental interactions. The search for these effects has high importance. On the other hand, such anomalies must be due to new interactions at the TeV scale that play into the question of the determination of the Higgs Yukawa couplings. At best, we will only get some clues from the presence of anomalies. We will need to go to high energies with colliders to learn the underlying story

The generation of the cosmic baryon-antibaryon asymmetry requires a new source of CP violation beyond that in the Standard Model. Phases (aside from the strongly constrained θ parameter of QCD) enter a fundamental Lagrangian only in fermionscalar couplings. So this question is again a question about the Higgs boson, or about an extended Higgs sector. In the leptogenesis model, the new Higgs bosons are those that give masses and mixings to the heavy neutrinos of seesaw models; it will be a long time before we test such models. But in other models, the new Higgs interactions could be at a mass scale accessible to colliders. These provide another important goal for colliders at LHC and higher energies.

Many questions are asked about neutrinos, but these more reflect our still-imperfect knowledge of neutrinos rather than opportunities to go beyond the Standard Model. We do need to clarify the neutrino mass ordering and demonstrate CP violation in the neutrino mass matrix. To ask more fundamental questions, we need to know how the neutrino masses are generated. By the gauge principle for the electroweak interactions, neutrino masses must come from the Higgs field. The crucial question is whether the neutrino masses are Dirac, with a very small value of the Yukawa coupling, or Majorana, from a seesaw with a heavy right-handed neutrino. This question is not addressed by long-baseline neutrino experiments, but it lends importance to searches for neutrinoless double beta decay. Other commonly asked questions seem to have small importance. There is no evidence for low-mass sterile neutrinos, given the uncertainties on cross sections from low-energy QCD, and the motivation for additional searches is ad hoc. Other beyond-Standard-Model effects, such as flavorchanging higher dimension interactions, will remain more strongly constrained from measurements on charged leptons, which by gauge symmetry must appear in these operators, than from neutrino interactions.

The nature of dark matter is a major question whose solution is necessarily outside the Standard Model, and which need not be connected to the Higgs. It is very important to find direct evidence for the particle nature of dark matter and, through this discovery, to gain insight into its nature. The idea that dark matter is a particle with mass at the Higgs boson mass scale is now strongly challenged by experiment. This has motivated new searches for dark matter particles in a lower-mass region that is accessible at current accelerators or even benchtop experiments. Current discussions, though, leave out the possibility of dark matter particles in the TeV mass range that have higher annihilation rates by being more strongly coupled to the Higgs sector than previously emphasized candidates such as neutrinos or sleptons. Such heavier WIMPs—together with axions, which are also particles of the Higgs sector—are the best-motivated dark matter candidates today.

Models of flavor, baryogenesis, and neutrino mass all are built on hypotheses for the Higgs sector. Because we do not yet have a Higgs principle, these models cannot be predictive. These models rely on specific but arbitrary choices for the unconstrained scalar couplings. Until we have a more fundamental understanding of the nature of the Higgs sector, it will be difficult to make real progress on any of these issues. To gain that understanding, we need experiments that directly address the nature of the Higgs field.

This statement applies also to our ultimate goal, the unification of all interactions. Both dark matter and the mysteries of the Higgs imply that there are further fundamental forces beyond those of the Standard Model. Einstein tried to form a unified theory of nature using only gravity and electromagnetism, and we now know that that quest was doomed. We are in a similar situation today. We know that there are additional interactions that are needed to make a global theory of nature. We need experiments that will give us knowledge of them.

This experimental program is a major focus of the Energy Frontier report for Snowmass 2021 [8], and the conclusions of that report especially merit attention. This program must proceed in three phases.

First, we must continue the search at the LHC for new particles that could give evidence of a Higgs sector broader than that of the Standard Model. Though there is no such evidence yet, the capabilities of the LHC are hardly exhausted. These capabilities will be extended in the high-luminosity stage of the LHC [9].

Second, we need to search for evidence of a broader Higgs sector from detailed studies of the known Higgs boson. This is the most obvious place to learn about the Higgs sector, but current experiments have not yet reached the required level of precision. It is well documented that e⁺e⁻ Higgs factories have the capability of measuring the Higgs boson couplings at the sub-percent level, and that such measurements constitute broad searches for new physics that complement the LHC results [10]. We have the technology today to construct an e⁺e⁻ Higgs factory, one that is affordable with global collaboration. If no other region will step forward, the US should take the lead.

Third, we need to develop technologies for robust and cost-effective exploration of physics at energies of 10 TeV and above in parton-parton collisions. Today, approaches are proposed with proton, muon, electron, and photon colliders. We need to bring at least a subset of these to maturity.

The vision for the future of particle physics must acknowledge the central role of the Higgs field. The Higgs field is a crucial part of the Standard Model. It is our ignorance about this field that keeps us from solving the remaining mysteries that the Standard Model cannot address. To make progress, we must remedy this. We need to make clear (with apologies to Red Sanders and Vince Lombardi): “Higgs isn’t everything; it’s the only thing.” A vision for particle physics that is not built on this idea cannot address the most profound questions for our field or realize its greatest opportunities.

References

[1] https://www.nationalacademies.org/our-work/ elementary-particle-physics-progress-and-promise.

[2] T. Kinoshita, ed. Quantum Electrodynamics. (World Scientific Press, 1990.)

[3] S. Schael et al. [ALEPH, DELPHI, L3, OPAL, SLD, LEP Electroweak Working Group, SLD Electroweak Group and SLD Heavy Flavour Group], “Precision electroweak measurements on the Z resonance,” Phys. Rept. 427, 257-454 (2006) [arXiv:hep-ex/0509008 [hep-ex]].

[4] T. Gehrmann and B. Malescu, “Precision QCD Physics at the LHC”, Ann. Rev. Nucl. Part. Sci. 72, 233 (2022).

[5] C. Palmer [ATLAS and CMS], “Higgs boson experimental overview for ICHEP 2020,” PoS ICHEP2020, 034 (2021)

[6] A. J. Bevan et al. [BaBar and Belle], Eur. Phys. J. C 74, 3026 (2014) [arXiv:1406.6311 [hep-ex]].

[7] H. Fritzsch, “Calculating the Cabibbo Angle,” Phys. Lett. B 70, 436-440 (1977)

[8] M. Narain, L. Reina, A. Tricoli, et al. “The Future of US Particle Physics - The Snowmass 2021 Energy Frontier Report,” [arXiv:2211.11084 [hep-ex]]. See especially Section 7.

[9] X. Cid Vidal, et al. “Report from Working Group 3: Beyond the Standard Model physics at the HL-LHC and HE-LHC,” CERN Yellow Rep. Monogr. 7, 585 (2019) [arXiv:1812.07831 [hep-ph]].

[10] A. Aryshev et al. [ILC International Development Team], “The International Linear Collider: Report to Snowmass 2021,” [arXiv:2203.07622 [physics.acc-ph]]. See especially Chapters 12-14.

Note: In the fall of 2022, the decadal survey committee on Elementary Particle Physics of the US National Academies requested 2000 word Vision Papers, giving personal interpretations of the results of the Snowmass 2021 study and the future of the field. This article is Michael Peskin's contribution reflecting his viewpoint.