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Bottomonium Hyperfine Splitting on the Lattice and in the Continuum

  • Author / Creator
    Ahmed Ashraf Rayyan
  • In this thesis, based on the work of refs. [1, 2], we study the mass difference between the 1S spin-singlet and spin-triplet bottom quark-antiquark bound states within the effective theory of lattice non-relativistic quantum chromodynamics (NRQCD). The precise determination of this value, called the bottomonium hyperfine splitting, has been difficult to obtain due to disagreements between phenomenological, lattice, and experimental groups. In particular, the two latest independent lattice determinations’ central values differ beyond their quoted error bars even though they are based on the same bare lattice NRQCD simulation data. However, these two analyses differ in their “matching” methods, wherein the parameters of the effective theory are determined. The approach based on the expansion about the continuum limit was introduced in ref. [3] and differs from the standard perturbative matching employed by refs. [4–7]. Using a numerical and analytical solution of the lattice Schrödinger equation, we trace the discrepancy of the two results to a subtle problem regarding the Coulomb binding effects and their lattice artifacts, which leads to a breakdown in the standard perturbative matching unique to lattice regularization. We introduce a new consistent method named “Schrödinger matching,” which performs the matching using the solution of the full Schrödinger equation without an expansion in the Coulomb interaction. Our analysis resolves the discrepancy in favor of the result of ref. [3], which is 52.9 ± 5.5 MeV for the bottomonium hyperfine splitting; this reconciles the two lattice results, along with the perturbative QCD result and the most precise experimental measurements to date.

  • Subjects / Keywords
  • Graduation date
    Fall 2018
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3TB0ZB38
  • License
    Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.