## Date Awarded

2024

## Document Type

Dissertation

## Degree Name

Doctor of Philosophy (Ph.D.)

## Department

Physics

## Advisor

Christopher Carone

## Committee Member

Joshua Erlich

## Committee Member

Justin Stevens

## Committee Member

Andrew Jackura

## Committee Member

Jose Goity

## Abstract

Although general relativity and the standard model have proved incredibly consistent at all scales accessible to tests, they are not expected to accurately describe nature at all scales; we know there is new physics to be discovered at higher energy scales (shorter distances). The nonrenormalizability of gravity prohibits a predictive quantum field theory description, unless the infinite parameter space needed to absorb divergences can be constrained. An asymptotically safe theory is one in which all of the couplings in the theory run to either zero or a nonzero ultraviolet fixed point. Requiring that a coupling reach an ultraviolet fixed point constrains it to live on an ultraviolet critical surface that is of smaller dimension than the original parameter space. We study a theory with gauged baryon number, and require that it is asymptotically safe by introducing gravitational corrections above the Planck scale. This constrains the parameter space of the theory, giving a relationship between the baryon number gauge coupling and a coupling that gives the kinetic mixing between baryon number and hypercharge, effectively removing a free parameter. We then introduce a TeV-scale, fermionic dark matter candidate into the theory, with the baryon number gauge boson acting as a portal between the visible and dark sectors. The dark matter relic density for our candidate is determined and compared to direct detection bounds. We then examine the problem of the enormous fine-tuning required to keep the Higgs boson mass light despite contributions from large quadratic divergences, called the hierarchy problem. Higher derivative theories are one class of theories that offer a solution to this problem. Infinite-derivative nonlocal theories and finite-derivative Lee-Wick theories each have strengths in this regard, but they also each have weaknesses (for instance, Lee-Wick particles cancel quadratic divergences, but we would have ideally expected to detect them by now at current collider sensitivities). Asymptotically nonlocal theories interpolate between the two and behave differently from either, although they appear nonlocal in the low-energy limit. In asymptotic nonlocality, an emergent nonlocal scale arises that regulates quadratic divergences and that is hierarchically smaller than the mass of the lightest new particle, suggesting a solution to the hierarchy problem. We examine the center-of-mass energy dependence of the cross section in an asymptotically nonlocal theory and demonstrate that the behavior is different from either a nonlocal or Lee-Wick theory. We then derive the Feynman rules in an asymptotically nonlocal extension of QCD, which are needed for the study of strong interaction processes at hadron colliders. We examine the basic process of dijet production from two-into-two parton scattering, calculating the relevant parton-level cross sections. An experimental bound on the nonlocal scale is determined by comparing the predicted dijet invariant mass spectrum in our model with data from the Large Hadron Collider.

## DOI

https://dx.doi.org/10.21220/s2-nm7y-ey59

## Rights

© The Author

## Recommended Citation

Anderson, Mikayla, "Extensions Of The Standard Model With Improved Ultraviolet Behavior" (2024). *Dissertations, Theses, and Masters Projects.* William & Mary. Paper 1727787939.

https://dx.doi.org/10.21220/s2-nm7y-ey59