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Dissertation Defense - Noah Donald
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Noah Donald, "Physics beyond the standard model and Nature’s smallest length scales" Zoom link available upon request
Abstract: While the standard model has been extremely successful at predicting physics at energies comparable to that of modern collider experiments, this theory is expected to break down in higher energy regimes. Hence, it is interesting to study theories that are asymptotically safe, i.e., which remain valid at arbitrarily small distance scales. We begin by studying an extension of the standard model which gauges baryon number and includes an approximation to the nonperturbative gravitational corrections to the renormalization group equations for each of the couplings. By working within the asymptotic safety paradigm, we restrict the parameter space of the theory at the TeV scale. We analyze several different fixed-point scenarios, comment on the model's phenomenology, and show how a stable TeV scale dark matter candidate can be included.
In contrast to theories where there is no minimum length scale, many approaches to quantum gravity, such as causal set theory, view spacetime as discretized somewhere near the Planck scale. Given the remoteness of the Planck scale to modern experimental limits, signals of such a discretization are hard to come by. However, several discrete spacetime approaches generically give rise to spacetime defects whose number density may be characterized by a larger length scale. We propose several models of these defects and study their impact on the Feynman propagator of a two-dimensional free scalar quantum field defined on a causal set. We find that this leads to a multivalued position space Feynman propagator when plotted against the magnitude of the spacetime interval. Just as the usual propagator depends on initial and terminal points, these different branches correspond to whether these points are defects or generic spacetime points. Additionally, in a low-energy effective description of the propagator, we find that the average of these different branches leads to a Feynman propagator with a mass shift and a wavefunction renormalization that are due to defects in the discretization of the free theory rather than from loop effects due to interactions.
If there is new physics at very high energy scales, like the Planck scale, then it is a puzzle why the scale of electroweak symmetry breaking is so much smaller. It is well known that quantum corrections to the Higgs mass are quadratically divergent in the presence of a high energy scale where new physics will become important. While standard model extensions, such as supersymmetry, look to cancel such corrections, and thus eliminate a fine-tuning problem, others have elevated specific kinds of tunings to organizing principles. We study an extension of the standard model with a dark sector where strong dynamics triggers the condensation of dark quarks which leads to a linear term in an extended Higgs potential. By applying a paradigm where one tunes to the edge of the positivity domain of this potential, we obtain large separation between a light dark scale and the electroweak scale. We then show that the paradigm-restricted parameter space of the model can remain consistent with experimental restrictions on a dark matter candidate.
Bio: Noah Donald was born in Pittsburgh, Pennsylvania in 1998. He graduated from Mount Lebanon high school in 2016 and then went to study Mathematics and Physics at The Ohio State University in Columbus, Ohio. He graduated in 2020 with a B.S. in Physics and a B.S. in Mathematics. After a lengthy process of applying and perusing different graduate programs in Math and Physics, he settled on pursuing Physics at William & Mary. He started at William & Mary in the Fall of 2020 and began doing research with Prof. Chris Carone in the high energy theory group.
Sponsored by: Physics