## Current Research: In More Detail

*Early universe quantum field theory*

Explaining the origin of the cosmic matter-antimatter asymmetry remains one of the key unsolved problems in fundamental physics. Assuming both that the inflationary paradigm is correct and that inflation wiped out any preexisting asymmetry, the particle physics of the subsequent universe must have generated the observed asymmetry — a process called baryogenesis. Without this asymmetry, we would not exist.

Nobel laureate Andrei Sakharov identified three ingredients for successful baryogenesis: (1) non-conservation of total baryon number (B); (2) breaking of charge conjugation (C) symmetry and its combination with parity (P) invariance, otherwise known as CP-violation; and (3) either out-of-equilibrium processes in the early universe or breaking of the combination of CP and time-reversal (T) symmetry, or CPT-invariance. The Standard Model has the needed B non-conservation, but it fails to satisfy Sakharov’s remaining criteria.

Our research focuses on the possibility that successful baryogenesis occurred in conjunction with electroweak symmetry-breaking, an event that occurred when the universe was ~ 10 picoseconds old and when the Higgs mechanism induced non-zero masses for most if not all elementary particles. This paradigm is called “electroweak baryogenesis” (EWBG).

Successful EWBG requires two main elements:

- A different thermal history of the Higgs field (electroweak symmetry-breaking) than is found in the Standard Model (needed for Sakharov 3)
- Sources of CP-violation beyond those known to exist in the Standard Model (Sakharov 2)

We explore the possibilities for new physics beyond the Standard Model (BSM) by

- Building and/or studying existing BSM scenarios that can accommodate these two elements:
- Computing the implications for the thermal history of the Higgs field and the generation of CP-violating particle number asymmetries in the early universe. This work requires us to develop and exploit quantum field theory tools for
- Thermal field theory, including the use of effective field theory and non-perturbative (lattice) methods
- Non-equilibrium field theory for quantum transport, vacuum transitions, and electroweak sphaleron dynamics

- Analyzing the implications for experimental tests of BSM EWBG models using
- High-energy collider searches for new particles at the Large Hadron Collider and prospective future colliders
- High-precision studies of the Higgs boson properties
- Low-energy searches for permanent electric dipole moments of the electron, neutron, atoms, and molecules
- Searches for a stochastic gravitational wave background in probes such as LISA, Taiji, and Tianqin

*Tests of fundamental symmetries and studies of neutrino properties*

The electroweak sector of the Standard Model does not respect either P or CP symmetry, but it does satisfy others: conservation of total lepton (L) and B (at the classical but not quantum level) and preservation of the flavors of different charged leptons (apart from unobservable small effects of neutrino mass). Answers to the key questions posed above can require BSM scenarios that break CP and P in ways that differ from the Standard Model, break the conservation of B and L at the classical (Lagrangian) level, and imply the non-preservation of charged lepton flavor.

My team presently focuses on BSM-breaking of two fundamental symmetries, CP and L, with the latter having deep connections to the nature of neutrinos.

*CP-violation:* Searches for electric dipole moments (EDMs) are among the most powerful probes of CP-violation. Our research analyzes the connections between EDMs and

- CP-violation needed for successful EWBG
- High-energy collider searches for BSM particles and interactions

We also work on improving the reliability of EDM computations. While computing the EDM of charged leptons is a relatively straightforward exercise in quantum field theory, doing so for the neutron, atoms, and molecules is complicated by the presence of strong interactions, many-body atomic physics, and nuclear structure. Our research addresses some aspects of these Standard Model physics challenges.

*Lepton number violation (LNV): *One of the most elegant and widely considered paradigms for explaining non-zero neutrino masses requires LNV. This scenario may also generate the cosmic matter-antimatter asymmetry though a process known as leptogenesis. In contrast to EWBG, most successful leptogenesis scenarios would have taken place much earlier than ten picoseconds and involve very heavy partners of the light neutrinos. The masses of the heavy neutrinos generally must be so heavy that it is not possible to produce them directly in today’s laboratory experiments. Thus, we must look for indirect evidence of both their existence and their LNV interactions.

On the experimental side, the most powerful way to look for LNV is to search for the neutrinoless double beta decay (NLDBD) of atomic nuclei. In NLDBD, a nucleus decays to a different one by changing two neutrons into two protons while emitting two electrons and no neutrinos. To date, NLDBD has not been observed. Instead, experiments have obtained very stringent upper limits on the rates at which NLDBD can occur. New, much more sensitive “ton-scale” experiments are being planned to increase the sensitivity to the rate by two orders of magnitude.

On the theoretical side, we would like to understand the implications of present and prospective NLDBD experiments for LNV BSM scenarios. Our present work focuses on the possibility that in addition to very high-scale LNV, there may be LNV interactions involving BSM particles at the TeV scale or lower. In particular, we seek to explore

- Implications of TeV-scale and below-LNV models for NLDBD, using the methods of effective field theory (EFT)
- Complementarity between NLDBD searches and new particle searches at the LHC and prospective future colliders
- Implications of TeV-scale LNV for leptogenesis scenarios
- The relationships between NLDBD and other probes, including searches for charged lepton flavor violation and astrophysical probes of neutrino properties

In doing so, we work with a combination of “complete” BSM models, such as the Left-Right Symmetric Model, and simplified models that incorporate key elements of complete BSM theories. This work is highly interdisciplinary, involving ideas and methods in particle physics, nuclear physics, and cosmology.

*Precision calculations*

Many experiments seek evidence for BSM physics through exquisitely precise measurements of processes that also occur in the Standard Model. Such measurements span a range in energy scales. Low-energy studies include those of the anomalous magnetic moment of the muon, beta-decays of atomic nuclei and the neutron, and parity-violating asymmetries in fixed-target polarized electron scattering. High-energy processes include measurements of the W-boson mass in proton-proton collisions at the LHC and — looking to the future — precision measurements of Higgs boson properties and electroweak observables using e+e- annihilation in proposed future colliders, such as the CERN Future Collider (FCC-ee) or China Circular Electron Positron Collider (CEPC).

In all cases, one must have sufficiently reliably Standard Model predictions in order to interpret experimental results in terms of possible BSM contributions. The experimental state-of-the-art now challenges theorists to push the frontier of our ability to perform reliable computations using quantum field theory methods. The challenges are twofold:

- In perturbation theory, theorists must go beyond the leading order (LO) and next-to-leading order (NLO) to next-to-next-to-leading order (NNLO). Doing so typically requires working at the level of two (or more) quantum loops. A particular challenge entails computing these loops when they contain particles of widely differing masses.
- We must also reliably incorporate the effects of low-energy strong interactions, whose effects cannot be obtained in perturbation theory. In the case of nuclear beta-decay, reliably incorporating the effects of nuclear structure remains an ongoing challenge.

My team is part of a small but growing worldwide network of theorists who are tackling these Standard Model challenges. The research is highly technical and has high impact, making it well-suited for computationally minded, ambitious theorists.