More information about some of my past and current research directions.
The Higgs field plays a central role in the Standard Model: its potential has a shape such that the Higgs field acquires a vacuum expectation value which spontaneously breaks the electroweak gauge symmetry of the Standard Model, leading to the disparate nature of the fundamental forces we see at low energies. In parallel, this vacuum expectation value gives masses to the Standard Model fermions via its Yukawa couplings. The values of the Higgs couplings are thus responsible for a great deal of the structure we see in the Universe, and testing the consistency of this theory is of paramount importance in particle physics.
Moreover, there are deep, theoretical reasons to believe that the Higgs is related to physics beyond the Standard Model that would appear at or around the TeV scale. These reasons make up the (Electroweak) Hierarchy Problem: according to our best notions of effective field theory, we should not expect scalar fields to appear with masses parametrically smaller than the cutoff of the theory (where new, microsopic physics would come into play). This is exemplified in all concrete models that predict the Higgs mass: if the new physics is much heavier than the electroweak scale, a significant amount of “fine-tuning” of the parameters of the theory is required to reproduce the observed Standard Model.
For all these reasons, it is crucial to test the Higgs sector of the Standard Model at the Large Hadron Collider (LHC) and future machines. A significant portion of my research is in this direction: both in constructing models of BSM physics related to the Higgs and understanding their signatures at collider experiments, and in performing detailed calculations necessary to interpret experimental measurements as constraints on BSM couplings of the Higgs.
Since 2020 I have been heavily involved in studying the unique physics case of a high-energy muon collider. As a heavier cousin of the electron, muons can be more readily accelerated to high energies without the barrier of synchrotron radiation, and while still being elementary particles whose full energy is available in the collision. There are significant challenges in accelerating muon beams, but these advantages offer a potentially much more efficient route to very high energy scales beyond the horizon of the LHC. A muon collider inscribed roughly inside the Fermilab campus, for instance, could reach center of mass energies of 8 – 10 TeV, providing a direct reach comparable to an 80 TeV proton collider.
My research has focussed on some of the unique signatures that are possible with high-energy muon collisions. At these energies, there are large cross sections for vector-boson-scattering processes. These provide unprecedented sensitivity to the electroweak-Higgs interactions, the mechanism of electroweak symmetry breaking, and even to new sources of CP-violation1. My collaborators and I have also shown that a high-energy muon collider would have incomparable sensitivity to new sources of lepton flavor violation as well 2 3. There is a great deal more work needed in realizing a Muon Collider; more details and information on getting involved in the broader effort can be found on the U.S. Muon Collider Collaboration (USMCC) website.
Most of the parameters of the Standard Model live in the masses and mixing angles of the fermions, which come from their Yukawa couplings to the Higgs. While the symmetries of the theory itself view all these couplings equivalently, they display enormous numerical hierarchies: the mass of the top quark is $\sim 10^5$ the mass of the up quark, and the quark mixing matrix is similarly described by mixing angles of 13, 2, and 0.2 degrees—far from the random mixing naively predicted by effective theory.
A part of my research program seeks to find dynamical explanations for this observed pattern, such as new symmetries, extra dimensions, or dynamics of new, strongly-coupled sectors coupled to the fermions. I’m particularly interested in how such a model might interact with other physics beyond the Standard Model, which is paradoxically often most constrained by precision measurements of the flavor sector of the SM. Some of my past work has focused on new ansätze for how BSM physics could couple to SM fermions, and I am also involved in understanding how future flavor physics experiments could test a variety of BSM physics models.
The Standard Model (excluding neutrino masses) contains two complex phases, which lead to CP violation: one in the quark mixing matrix, and another describing the misalignment between the topological structure of the strong interactions and the phase of the quark Yukawas couplings. As with the flavor puzzle above, there are no further distinctions between these angles on symmetry grounds in the SM, and yet, the first is measured to be ~ 70 degrees, while the second is unobserved and constructed to be < $10^{-10}$. Another prong of my research program is to understand possible explanations for this strong CP problem.
There are essentially two possible resolutions to this puzzle, both of which have exciting implications. The first is that there exists a new particle known as the axion, which has a topological coupling to the gauge fields and acquires a vacuum expectation value that cancels the misalignment angle to very good approximation. The axion hypothesis is particularly interesting because it is also a candidate for dark matter. I am particularly interested in understanding how the axion can fit into other models of physics beyond the Standard Model, perhaps giving us a window into physics in regimes where gravitational effects are important.
The second explanation is that parity or CP are actually fundamental symmetries of nature at short distances—forbidding the misalignment angle—and the CP-violating phase in the quark mixing matrix is a result of spontaneous symmetry breaking analogous to the Higgs mechanism in some new sector coupled to the quark fields. This resolution also has interesting connections to models of flavor as described above, and one focus of my research program is to better understand these connections. This resolution is also connected to early universe cosmology: the simplest implementations of this idea predict that in the early universe there was a phase transition where the universe went from CP-conserving to CP-violating. I am interested in understanding the nature of this phase transition and its implications for models of baryogenesis, which explain the observed excess of matter over antimatter in the universe, and rely crucially on a source of CP-violation beyond the Standard Model.
More soon…
“Barr–Zee Diagrams at a High-Energy Muon Collider”,
SDH, J. Lodman, A. Parikh and M. Reece,
JHEP 12 (2024) 134, arXiv:2410.01873 ↩
“Lepton Flavor Violation: From Muon Decays to Muon Colliders”,
P. Asadi, H. Bagherian, K. Fraser, SDH and Q. Lu,
Phys. Rev. D 113 (2026), arXiv:2509.22771. ↩
“Complementary Signals of Lepton Flavor Violation at a High-Energy Muon Collider”,
SDH, Q. Lu and M. Reece,
JHEP 07 (2022) 036, arXiv:2203.08825. ↩