Physics at a High Energy Muon Collider

Since the Fall of 2020, I have been involved in building the physics case for a high-energy muon collider, which could succeed the LHC in pushing the energy frontier, study the Higgs boson and the Standard Model in more detail, and hopefully unveil a more fundamental theory of nature that addresses some of the shortcomings of the Standard Model. You can read about some of this physics case in The Muon Smasher’s Guide, or in some of the reports from the 2021 Snowmass process ^{1 2}. Read on for a brief introduction to why muon colliders are such an exciting possibility, or scroll down for other links to more detailed references and to see my relevant publications.

The most direct and historically important way that physicists learn about nature at the most fundamental level is to collide particles at high energies. This has traditionally been done with electrons (and positrons) or protons (and anti-protons), with remarkable success: the experiments at the Large Electron-Positron Collider (LEP) studied $e^+ e^-$ collisions with center of mass energies both at the $Z$ pole (91 GeV), and up to about 209 GeV. These measurements still provide some of our best understanding of the electroweak sector. The Tevatron at Fermilab collided protons and anti-protons at a TeV, which enabled the discovery of the top quark. Since 2009, the Large Hadron Collider (LHC) has collided protons at energies from 7 to over 13 TeV. These led to the discovery of the Higgs boson in 2012, and continue to push the energy frontier, both studying the Standard Model at the highest energies ever achieved in terrestrial experiments, and setting limits on potential new particles.

While colliding protons and electrons has been enormously fruitful, it is clear that there are limits of pushing this program to higher energies. When charged particles are accelerated in circular rings, they emit synchrotron radiation with a power inverseley proportional to the fourth power of the charged particle mass. This makes it extremely challenging to accelerate electrons to high energies in circular colliders. Linear colliders are an intriguing alternative, but require extremely strong fields to accelerate the electrons quickly over a relatively short distance, or a very long collider. Protons, in contrast, are heavy enough that synchrotron radiation isn’t an issue, but unlike electrons, they are composite particles: they are really made up of strongly interacting quarks and gluons. As a result, the “effective” collision energies are much lower than the center of mass energies of the colliding protons, and most collisions are totally uninteresting for exploring short-distance physics.

Muons offer a fortuitous compromise: they are two hundred times heavier than the electron, so they can be readily accelerated in circular rings, but unlike the proton, they are fundamental particles, so the full center of mass energy is available in their collisions. Moreover, as muons do not participate in strong interactions, the electroweak processes of interest typically have much lower background rates in muon collisions than at proton colliders.

The cost of these advantages is that, unlike protons and electrons, muons are unstable: they decay with a lifetime of approximately 2 microseconds. This presents a number of experimental and accelerator design challenges, particularly in producing a high-luminosity beam suitable for collisions. There are also challenges in mitigating neutrino radiation and the beam-induced background. Recent advances have demonstrated that these challenges may be overcome, however, and that an operational muon collider on a 20-30 year timescale is technically achievable, with collisions at energies of 3 to 10 TeV. It is therefore crucial to understand the physics that could be explored at such a machine.

Muon Colliders and the Higgs Boson

A highlight of a high-energy muon collider program would be the ability to study the Higgs boson and its interactions at high-energy in great detail. This is because high-energy muons have a significant probability to radiate the electroweak gauge bosons, as shown in the figure below.

The $W$ and $Z$ bosons have significant couplings to the Higgs, allowing for the possibility of Higgs production via a process known as “Vector-boson fusion” (VBF). Unlike the $ZH$ production mode, which is the linchpin of “Higgs factory” colliders, which operate at center of mass energies $\sim 240 - 250$ GeV, the rate for the VBF process grows logarithmically with the center of mass energy.

As a result, a high-energy muon collider would have large rates of Higgs production, so its couplings to other Standard Model particles can be studied in detail. We provided the first estimate of these sensitivities in The Muon Smasher’s Guide, but a more detailed analysis can be found in the papers by my colleagues at Stony Brook.^{3 4}

Muon Colliders and New Physics at the TeV Scale

As mentioned above, another strength of muon colliders is that they have the reach to produce new, electroweak charged particles in processes utilizing the full center of mass energy of the collisions. This, along with the lower background rates, makes it possible to extend the reach for new particles by up to an order of magnitude compared to the LHC bounds, depending on the model considered. One focus of my research is on the complementarity between these direct searches and indirect searches for new physics in low-energy laboratory experiments, such as searches for an electric dipole moment (EDM) of the electron, or for lepton-flavor violating (LFV) processes like $\mu \to e\gamma$.

As an example, supersymmetric extensions of the Standard Model include sleptons which generically mix, leading to LFV processes and electron EDMs at one loop. These signals may be observed at forthcoming upgrades such as the Mu2e or ACME III experiments, which will dramatically improve the current sensitivity. If such a signal were to be observed, it would point to sleptons with masses of a few TeV, which could be directly produced at a high-energy muon collider. But a muon collider would not only be able to produce these new particles, it would also be able to study the directly related lepton-flavor violating decay processes directly at high energies. The constraints are illustrated in the figure below, and more details can be found in the corresponding paper.⁵ In this way, a muon collider would not only enable the discovery of new physics, but would allow the new physics to be precisely characterized and studied.