## The application of automated perturbation theory to lattice QCD

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##### Authors

Monahan, Christopher John

##### Advisors

Horgan, Ron R.

##### Date

2011-11-08##### Awarding Institution

University of Cambridge

##### Author Affiliation

Department of Applied Mathematics and Theoretical Physics

Trinity College

##### Qualification

Doctor of Philosophy (PhD)

##### Language

English

##### Type

Thesis

##### Metadata

Show full item record##### Citation

Monahan, C. J. (2011). The application of automated perturbation theory to lattice QCD (Doctoral thesis). https://doi.org/10.17863/CAM.16107

##### Abstract

Predictions of heavy quark parameters are an integral component of precision
tests of the Standard Model of particle physics. Experimental measurements
of electroweak processes involving heavy hadrons provide stringent tests of
Cabibbo-Kobayashi-Maskawa (CKM) matrix unitarity and serve as a probe
of new physics. Hadronic matrix elements parameterise the strong dynamics
of these interactions and these matrix elements must be calculated nonperturbatively.
Lattice quantum chromodynamics (QCD) provides the framework for
nonperturbative calculations of QCD processes. Current lattices are too coarse
to directly simulate b quarks. Therefore an effective theory, nonrelativistic
QCD (NRQCD), is used to discretise the heavy quarks. High precision simulations
are required so systematic uncertainties are removed by improving the
NRQCD action. Precise simulations also require improved sea quark actions,
such as the highly-improved staggered quark (HISQ) action. The renormalisation
parameters of these actions cannot be feasibly determined by hand
and thus automated procedures have been developed. In this dissertation I
apply automated lattice pertubartion theory to a number of heavy quark
calculations.
I first review the fundamentals of lattice QCD and the construction of
lattice NRQCD. I then motivate and discuss lattice perturbation theory in
detail, focussing on the tools and techniques that I use in this dissertation.
I calculate the two-loop tadpole improvement factors for improved gluons
with improved light quarks. I then compute the renormalisation parameters
of NRQCD. I use a mix of analytic and numerical methods to extract the
one-loop radiative corrections to the higher order kinetic operators in the
NRQCD action. I then employ a fully automated procedure to calculate
the heavy quark energy shift at two-loops. I use this result to extract a
new prediction of the mass of the b quark from lattice NRQCD simulations
by the HPQCD collaboration. I also review the calculation of the radiative
corrections to the chromo-magnetic operator in the NRQCD action. This
computation is the first outcome of our implementation of background field
gauge for automated lattice perturbation theory.
Finally, I calculate the heavy-light currents for highly-improved NRQCD
heavy quarks with massless HISQ light quarks and discuss the application of
these results to nonperturbative studies by the HPQCD collaboration.

##### Keywords

Lattice QCD, NRQCD, Perturbation theory

##### Rights

Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales

Licence URL: http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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