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Statistical Assessment and Comparison of Truncation Error and Convergence Patterns in Modern Nucleon-Nucleon Potentials

Millican, Patrick James
http://orcid.org/0000-0003-1199-9457
http://rave.ohiolink.edu/etdc/view?acc_num=osu1722955231050488

Abstract Details

2024, Doctor of Philosophy, Ohio State University, 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, the cutoff is an upper bound in momentum of roughly 400–700 MeV that confines the theory to describing low-energy nuclear physics characteristic of interactions inside the nucleus. The contributions of interactions taking place at higher energies (and therefore shorter distances) are not ignored but rather absorbed into so-called low-energy constants that determine the strength of contact interactions in the χEFT Lagrangian. This theory was first pioneered by Weinberg, who used it to great effect in predicting the values of experimental observables for few-nucleon systems. Since then, many further instantiations of χEFT have emerged, all trained on experimental values of scattering experiments as inputs and all useful in predicting few-nucleon scattering observables with accuracy and precision. All their predictions, no matter their accuracy, also carry truncation error, and recent efforts have made admirable progress in quantifying that error so that it can be propagated correctly. In this thesis, one particular model for this truncation error—namely, the BUQEYE model, which is a statistical model employing a Gaussian process (GP) to describe nucleon-nucleon (NN) scattering data—is explained and its utility proven on an exemplary modern NN potential based on χEFT. That initial case accomplished, we broaden our inquiry to other modern NN interactions, showing the model’s continued utility. Importantly, given that ours is a statistical model, it makes a number of assumptions about how the underlying data ought to be characterized. Not only are these assumptions themselves (such as GP stationarity) tested and modified according to empirical facts, but the disproportionate richness of this admittedly rather simple model not only permits but in fact demands the assessment of features of the potentials, including the estimation using Bayesian statistics of the χEFT soft scale and breakdown scales and an evaluation of pathologies in the convergence patterns of the potentials themselves. This work sets the stage for future efforts that will employ a Bayesian statistical approach to calibrate and to mix χEFT potentials (and other potentials, including those that incorporate three-body forces and that resolve only nucleons) for far more accurate predictions of nuclear properties, and will generally advance the estimable goal of predicting nuclear observables with the truest uncertainty estimates possible.
Richard Furnstahl (Advisor)
Thomas Humanic (Committee Member)
Yuri Kovchegov (Committee Member)
Louis DiMauro (Committee Member)
217 p.
Nuclear Physics; Physics; Statistics
physics; nuclear physics; effective field theory; EFT; computational statistics; Bayesian statistics; Bayesian; theoretical nuclear physics; chiral EFT; chiral effective field theory; chiEFT; pions; pion physics; Weinberg power counting

Recommended Citations

Citations

  • Millican, P. J. (2024). Statistical Assessment and Comparison of Truncation Error and Convergence Patterns in Modern Nucleon-Nucleon Potentials [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1722955231050488

    APA Style (7th edition)

  • Millican, Patrick. Statistical Assessment and Comparison of Truncation Error and Convergence Patterns in Modern Nucleon-Nucleon Potentials. 2024. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1722955231050488.

    MLA Style (8th edition)

  • Millican, Patrick. "Statistical Assessment and Comparison of Truncation Error and Convergence Patterns in Modern Nucleon-Nucleon Potentials." Doctoral dissertation, Ohio State University, 2024. http://rave.ohiolink.edu/etdc/view?acc_num=osu1722955231050488

    Chicago Manual of Style (17th edition)

osu1722955231050488
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This open access ETD is published by The Ohio State University and OhioLINK.
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