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Bayesian Methods for Effective Field Theories

Wesolowski, Sarah
http://orcid.org/0000-0001-8556-2421
http://rave.ohiolink.edu/etdc/view?acc_num=osu1500037172071861

Abstract Details

2017, Doctor of Philosophy, Ohio State University, Physics.
Microscopic predictions of the properties of atomic nuclei have reached a high level of precision in the past decade. This progress mandates improved uncertainty quantification (UQ) for a robust comparison of experiment with theory. With the uncertainty from many-body methods under control, calculations are now sensitive to the input inter-nucleon interactions. These interactions include parameters that must be fit to experiment, inducing both uncertainty from the fit and from missing physics in the operator structure of the Hamiltonian. Furthermore, the implementation of the inter-nucleon interactions is not unique, which presents the additional problem of assessing results using different interactions. Effective field theories (EFTs) take advantage of a separation of high- and low-energy scales in the problem to form a power-counting scheme that allows the organization of terms in the Hamiltonian based on their expected contribution to observable predictions. This scheme gives a natural framework for quantification of uncertainty due to missing physics. The free parameters of the EFT, called the low-energy constants (LECs), must be fit to data, but in a properly constructed EFT these constants will be natural-sized, i.e., of order unity. The constraints provided by the EFT, namely the size of the systematic uncertainty from truncation of the theory and the natural size of the LECs, are assumed information even before a calculation is performed or a fit is done. Bayesian statistical methods provide a framework for treating uncertainties that naturally incorporates prior information as well as putting stochastic and systematic uncertainties on an equal footing. For EFT UQ Bayesian methods allow the relevant EFT properties to be incorporated quantitatively as prior probability distribution functions (pdfs). Following the logic of probability theory, observable quantities and underlying physical parameters such as the EFT breakdown scale may be expressed as pdfs that incorporate the prior pdfs. Problems of model selection, such as distinguishing between competing EFT implementations, are also natural in a Bayesian framework. In this thesis we focus on two complementary topics for EFT UQ using Bayesian methods--- quantifying EFT truncation uncertainty and parameter estimation for LECs. Using the order-by-order calculations and underlying EFT constraints as prior information, we show how to estimate EFT truncation uncertainties. We then apply the result to calculating truncation uncertainties on predictions of nucleon-nucleon scattering in chiral effective field theory. We apply model-checking diagnostics to our calculations to ensure that the statistical model of truncation uncertainty produces consistent results. A framework for EFT parameter estimation based on EFT convergence properties and naturalness is developed which includes a series of diagnostics to ensure the extraction of the maximum amount of available information from data to estimate LECs with minimal bias. We develop this framework using model EFTs and apply it to the problem of extrapolating lattice quantum chromodynamics results for the nucleon mass. We then apply aspects of the parameter estimation framework to perform case studies in chiral EFT parameter estimation, investigating a possible operator redundancy at fourth order in the chiral expansion and the appropriate inclusion of truncation uncertainty in estimating LECs.
Richard Furnstahl (Advisor)
Robert Perry (Committee Member)
Annika Peter (Committee Member)
Michael Lisa (Committee Member)
299 p.
Nuclear Physics
bayesian; nuclear physics; effective field theory; nucleon-nucleon scattering

Recommended Citations

Citations

  • Wesolowski, S. (2017). Bayesian Methods for Effective Field Theories [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1500037172071861

    APA Style (7th edition)

  • Wesolowski, Sarah. Bayesian Methods for Effective Field Theories. 2017. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1500037172071861.

    MLA Style (8th edition)

  • Wesolowski, Sarah. "Bayesian Methods for Effective Field Theories." Doctoral dissertation, Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1500037172071861

    Chicago Manual of Style (17th edition)

osu1500037172071861
345
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This open access ETD is published by The Ohio State University and OhioLINK.