Doctor of Philosophy, The Ohio State University, 2024, Physics

The practice of nuclear physics is divided into experiment and theory. Experimental nuclear physics makes observations of nuclear properties, such as radii and binding energies, while theoretical nuclear physics interprets the results, assimilates them into broader and more fundamental theories, and counsels the direction of future experimental efforts. In order to learn from experimental data, theoretical nuclear physicists make models to describe interactions between fields under the guidelines of quantum field theory even when there may be no closed mathematical form for those interactions. In cases where such a closed form is lacking (and, indeed, even in some cases where such a form is known) and the physics of interest is confined to a physical regime, the dominant paradigm is that of effective field theory (EFT). A cutoff or cutoffs in some physical variable(s) bound the regime where an EFT seeks to describe physical phenomena, which restricts the degrees of freedom, the constituent fields and interactions available for calculations. Additionally, an EFT preserves the symmetries of the underlying theory to create its own Lagrangian that is an infinite sum including all possible terms compliant with those symmetries. An EFT therefore needs a power-counting scheme that organizes the terms by like magnitude. With the calculation of physical observables from an infinite sum of terms being impossible under any circumstances (and putting to the side the fact that such sums are almost always asymptotic and will diverge given enough terms), EFTs truncate at some order and leave an infinite number of higher-order terms out of calculations; the contribution of these terms to theoretical predictions constitutes the truncation error. The specific instantiation of EFT on which this thesis focuses is chiral effective field theory (χEFT), which treats interactions between protons and neutrons (“nucleons,” collectively) as mediated by the exchange of pions. In χEFT, (open full item for complete abstract)

Committee: Richard Furnstahl (Advisor); Thomas Humanic (Committee Member); Yuri Kovchegov (Committee Member); Louis DiMauro (Committee Member) Subjects: Nuclear Physics; Physics; Statistics

Doctor of Philosophy (PhD), Ohio University, 2016, Physics and Astronomy (Arts and Sciences)

This dissertation discusses three topics in effective field theories (EFTs) for the strong interaction. We argue that the Bayesian method is ideal for estimating the low-energy constants (LECs) of EFT that encode physics of the underlying theory. We construct a Bayesian framework for obtaining a posterior probability density function (pdf) using pseudodata from a toy model in conjunction with a prior pdf that encodes naturalness. The central values of the parameters and their standard deviations are obtained from this posterior pdf. We also employ marginalization in our analysis to integrate out the nuisance parameters of the theory. The lowest-lying scalar-isoscalar resonance in the QCD spectrum is the sigma-meson. We add the sigma-meson to standard chiral perturbation theory (ChiPT) and treat it as an explicit degree of freedom in an extended version of SU(2) ChiPT, ChiPTS . We analyze the amplitudes for the various processes from threshold through the energies at which the sigma-resonance affects the physical observables. The 6He nucleus can be understood as a Borromean three-body system of a tight 4He core surrounded by a halo of two neutrons (n) forming a bound state. Because the valence neutrons are loosely bound to the 4He-core, a separation of scales exists between the sizes of the core and the whole halo nucleus. A “Halo EFT” can thus be used in this system. We perform a Halo EFT treatment of 6He up to next-to-leading order.

Committee: Daniel Phillips (Advisor); Charlotte Elster (Committee Member); Carl Brune (Committee Member); Douglas Green (Committee Member) Subjects: Nuclear Physics

Doctor of Ministry , Ashland University, 2023, Doctor of Ministry Program

The purpose of this project was to impact Christian couples from New Life Church in Colorado Springs through an eight-week workshop to practice prayer and risk taking to deepen their intra and interpersonal connection with each other and God. The post-test measures included qualitative measures of participants' awareness connecting their capacity to be aware of and participate with the work of the Holy Spirit. The quantitative post-test instrument showed that the participants' awareness regarding what interferes with their identity security with God was increased due to the study. The qualitative post-test instrument showed an increase in the participants' awareness regarding how their relationship with God impacted their intra and interpersonal relationships.

Committee: Shane Johnson Dr. (Advisor) Subjects: Counseling Psychology; Pastoral Counseling; Spirituality

Doctor of Philosophy (PhD), Ohio University, 2022, Physics and Astronomy (Arts and Sciences)

The work and results discussed in this dissertation are presented in two parts. In the first part, the low energy 3He-alpha elastic scattering has been treated in a halo effective field theory (halo EFT) that exploits the separation of scales in this reaction. The amplitude up to next-to-next-to-leading order has been computed, developing a hierarchy of the effective-range parameters (ERPs) that contribute at various orders of the EFT. The resulting formalism has been used to analyze data for recent measurements at center-of-mass (CM) energies between 0.38 and 3.12 MeV using the scattering of nuclei in inverse kinematics (SONIK) gas target at TRIUMF as well as older data in this energy regime. A likelihood function that incorporates the theoretical uncertainty due to truncation of the EFT at a certain order has been employed in a Bayesian analysis of the posterior probability distribution of the ERPs. The posterior distributions of the ERPs and other relevant parameters have been obtained using Markov Chain Monte Carlo sampling. It is found here that the inclusion of a small amount of data on the analyzing power Ay is crucial to determine the sign of the p-wave splitting. The combination of Ay and SONIK data constrains all ERPs up to O(p^4) in both s- and p-waves quite well. The asymptotic normalization coefficients and s-wave scattering length are found consistent with a recent EFT analysis of the capture reaction 3He(alpha, gamma)7Be. In the second part, an additional contribution to the amplitude due to the vacuum polarization (VP) effect has been considered. The formalism to include this effect in all partial wave channels has been developed in terms of a VP phase shift, which is only tiny fraction of the sum of nuclear and coulomb phase shift. Exactly the same Bayesian modeling and sampling method used in the first part has been used to extract the ERPs when the effect of VP has been included. The change in chi-square, $\Delta \chi^2 = +0.19$ when the VP eff (open full item for complete abstract)

Committee: Daniel Phillips (Advisor); Rida Benhaddou (Committee Member); Carl Brune (Committee Member); Charlotte Elster (Committee Member) Subjects: Physics

Doctor of Philosophy (PhD), Ohio University, 2022, Physics and Astronomy (Arts and Sciences)

We extend an Effective Field Theory (EFT) developed to describe rotational bands in even-even nuclei to the odd-mass case. This organizes Bohr & Mottelson's treatment of a particle coupled to a rotor as a model-independent expansion in powers of the angular velocity of the overall system. We carry out this expansion up to fourth order in the angular velocity and present results for 99Tc, 159Dy, 167,169Er, 167,169Tm, 183W, 235U and 239Pu. In each case, we get clear systematic improvement, as we go to higher orders in our EFT, starting form simple low energy degrees of freedom. We clearly show the main benefit of this EFT by using a Bayesian analysis framework to properly and rigorously account for theoretical uncertainty. We make use of the EFT expansion to perform a Bayesian analysis of data on the rotational energy levels of the nuclei above and in 155Gd and 157Gd. The error model in our Bayesian analysis includes both experimental and EFT truncation uncertainties. It also accounts for the fact that low-energy constants (LECs) at even and odd orders are expected to have different sizes. We use Markov Chain Monte Carlo (MCMC) sampling to explore the joint posterior of the EFT and error-model parameters and show both the LECs and the breakdown scale can be reliably determined. We extract the LECs up to fourth order in the EFT and find that, provided we correctly account for EFT truncation errors in our likelihood, results for lower-order LECs are stable as we go to higher orders. LEC results are also stable with respect to the addition of higher-energy data. We extract the expansion parameter for all the nuclei listed above and find a clear correlation between the extracted and the expected value of the inverse breakdown scale, W, based on the single-particle and vibrational energy scales. However, the W that actually determines the convergence of the EFT expansion is markedly smaller than would be naively expected based on those scales.

Committee: Daniel Phillips (Advisor); Savas Kaya (Committee Member); Carl Brune (Committee Member); Charlotte Elster (Committee Member) Subjects: Nuclear Physics; Physics

Bachelor of Science (BS), Ohio University, 2021, Physics

I test methods for extrapolating from limited data through Bayesian modeling on a simplified model of Effective Field Theory, or "Toy." I fit finite polynomial models not only based on data, but on the Bayesian prior understanding of the parameters in this polynomial having "naturalness," or being of order 1. These polynomials are represented by probability distributions conditional on the degree of the polynomial and the naturalness hyperparameter. After generating a set of polynomial models, I perform Bayesian Model Averaging to create a "mixed model," which is a weighted summation of the individual models where the weights are the evidence that each model fits the data and prior. I test how these mixed models extrapolate when compared to each individual non-mixed model. Given a set of models that are useful for extrapolating, the mixed model performs better than a naively-selected non-mixed model.

Committee: Daniel Phillips (Advisor) Subjects: Nuclear Physics; Statistics

Doctor of Philosophy, The Ohio State University, 2019, Physics

The particle nature of dark matter is a compelling mystery in physics. Weakly interacting massive particles (WIMPs) are a well motivated hypothesis for the dark matter particle, and supersymmetric (SUSY) theories contain natural candidates. WIMP annihilation into Standard Model particles provides key constraints on properties of the dark matter and therefore on the large SUSY parameter space. Resonances associated with bound states of WIMPs can be important, because annihilation of WIMPs in bound states can increase the overall annihilation rate, thus possibly strengthening existing constraints on dark matter models. Orders-of-magnitude "Sommerfeld enhancements" to annihilation rates can arise near a sequence of TeV-scale critical values of the WIMP mass where there is a zero-energy S-wave resonance at the WIMP-pair scattering threshold. Close to these critical values, the low-energy behavior of the WIMPs can be described by a zero-range effective field theory (ZREFT) in which they interact nonperturbatively through contact interactions and through Coulomb interactions. In this thesis, we develop the ZREFT for a specific dark matter model: the weak-isospin triplet, hypercharge singlet 'wino' from supersymmetry. We first develop the framework of ZREFT for the simple case where the winos only have short-range weak interactions and do not pair-annihilate. The parameters of ZREFT are determined by matching the analytic wino-wino scattering amplitudes of ZREFT with scattering amplitudes calculated numerically by solving the Schrodinger equation for winos interacting through a potential due to the exchange of weak gauge bosons. ZREFT at leading order in the power counting gives a good description of the two-body observables, and the description can be systematically improved by going to next-to-leading order. The power of ZREFT is illustrated by computing the bound-state formation rate in the S-wave collision of two winos with two soft photons emitted. We next introduc (open full item for complete abstract)

Committee: Eric Braaten (Advisor); Stuart Raby (Committee Member); Yuri Kovchegov (Committee Member); Richard Kass (Committee Member) Subjects: Physics

Bachelor of Science (BS), Ohio University, 0, Physics

In a variety of scientific disciplines, fitting data to curves is a crucial part of error analysis. The most popular means of doing this is a simple chi-squared minimization. However, this method comes with limitations, namely that it can produce a physically unrealizable fit to the data, i.e. a fit that doesn't make sense when considering other, more qualitative data. We attempt to remedy this by applying Bayesian methods to simulated data in toy models. We show that these methods are effective for extracting parameters from data. We also assess the presence of missing terms from residual data, and seek to find the order of those terms. Through a series of examples we demonstrate the power and limitations of our methods. All methods developed are available in the form of code for the Mathematica® software from Wolfram.

Committee: Daniel Phillips (Advisor) Subjects: Nuclear Physics; Physics; Statistics

Psy. D., Antioch University, 2018, Antioch Seattle: Clinical Psychology

The purpose of this dissertation is to explore how a mainstream theory of psychological practice might inadvertently conceal and ignore contemporary values and ideologies and their pathological consequences. Through a hermeneutic approach, I interpreted Leslie Greenberg's Emotion-focused therapy: Coaching clients to work through their feelings (2nd ed), a popular and widely used theory in psychotherapy. As a practitioner with humanistic foundations, this was also an opportunity for the author to understand his own unexamined values as a therapist. Specific EFT constructs and concepts that reflected Enlightenment assumptions and values were examined. EFT was situated within Enlightenment philosophy, particularly it's alignment with European movements for increasing individual freedoms and resisting church and other perceived arbitrary authority. An argument of how Enlightenment perceptions were disguised within EFT's scientific and objectivist frameworks was formed based on this contextualization. One way that Enlightenment philosophy contributed to increasing individual freedom was by relocating moral sources within the individual, which led to a configuration of the self that is reflected in theories like EFT. Broadly, the assumptions that were surfaced reflected philosophical ideas promulgated by Descartes, Locke, Kant and Rousseau, as well as essential ideas from Expressivist and Romantic philosophies in general. Several themes were identified through the interpretation: The Reduction and Reification of Emotion as a Basic Building Block, The Emotional Brain and Interiorized Emotion, Emotion Scheme and the World Inside Our Brain, Immunity from Cultural Influence, Emotion Transformation as a Return to Grace, Internal Guide and the Voice of Nature, and Uniting of the Expressivist and Instrumental Stance. Examining the assumptions of EFT revealed how moral assumptions can become concealed within a mainstream psychotherapy theory, which in turn helped to expl (open full item for complete abstract)

Committee: Mary Wieneke Ph.D. (Committee Chair); Phil Cushman Ph.D. (Committee Member); Sarah Peregrine Lord Psy.D. (Committee Member) Subjects: Clinical Psychology; Mental Health; Philosophy; Psychology; Psychotherapy; Social Psychology; Therapy

Bachelor of Science (BS), Ohio University, 2015, Physics

This thesis is focused on the rigorous calculations of effective field theories made possible through the application of Bayesian inference. We begin with a complete Bayesian extraction of low-energy constants from a blind toy function. Logically following is the presentation of an extended discussion on the formulation of statistically significant confidence intervals on the predictions of such a theory. Finally, we return to the extraction procedure to gain insights into the indications of a dysfunctional relationship between the prior of a Bayesian analysis and the data.

Committee: Daniel Phillips (Advisor); David Drabold (Other) Subjects: Physics

Doctor of Philosophy (PhD), Ohio University, 2010, Physics and Astronomy (Arts and Sciences)

We develop a subtractive renormalization scheme to evaluate the NN scattering phase shifts using chiral effective theory potentials. This allows us to consider arbitrarily high cutoffs in the Lippmann-Schwinger equation. We employ NN potentials computed up to next-to-next-to-leading order (NNLO) in chiral effective theory, using both dimensional regularization and spectral-function regularization. We evaluate the cutoff-dependence and the renormalization point dependence of our results, and apply them to the calculation of the process of deuteron electro-disintegration.

Committee: Daniel Phillips PhD (Committee Chair); Charlotte Elster PhD (Committee Member); Carl Brune PhD (Committee Member); Todd Young PhD (Committee Member) Subjects: Physics