Kendall, Iain D.
Lattice QCD studies of Upsilon physics.
PhD thesis, University of Glasgow.
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Non-Relativistic QCD (henceforth NRQCD) is a non-relativistic effective theory that
models the strong interaction. We use this formulation to perform lattice simulations of
the bound states of b quarks, known as the Upsilon spectrum. These simulations are performed
on a range of gauge ensembles provided by the MILC collaboration that include three
flavours of quark content - one at the approximate mass of the strange quark, and two
degenerate flavours that range from about a half to a tenth of the mass of the strange
We implement a random wall algorithm in the creation of our b quark propagators,
and develop a technique to combine the random wall with smearing functions, which are
used to assist in picking out the relevant quantum numbers in the the resulting meson
correlator. This is the first time these techniques have been used in this manner.
We employ a Bayesian fitting procedure to extract energies and amplitudes from our
simulated correlators. By using the 2S−1S Upsilon splitting on each configuration, and matching
to experimental results, we are able to extract the lattice spacings for each ensemble
from which we determine the heavy quark potential scale parameter r1. In concert with
results from our collaborators, we outline the procedure for combining multiple determinations
of r1, and present the collaborative result. We then use this parameter in a
determination of the strong coupling constant αs in the MS scheme.
We investigate the dispersion relation of the NRQCD action, and note some undesirable
features that we are able to resolve with the precision attainable using the random
wall. We look at a number of ways to address these issues, including non-perturbative and
perturbative tuning of coefficients. Using the perturbative coefficients, we then proceed
to calculate heavy-heavy currents, which are perturbatively matched to the continuum,
and allow us to give results for the Upsilon leptonic width.
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