Boyle, Peter

Del Debbio, Luigi

Arthur, Rudy

Science and Technology Facilities Council (STFC)

2013-09-24T10:12:07Z

2013-09-24T10:12:07Z

2012-11-28

This thesis presents an improved method to calculate renormalization constants in a regularization invariant momentum scheme using twisted boundary conditions. This enables us to simulate with momenta of arbitrary magnitude and a fixed direction. With this new technique, together with non-exceptional kinematics and volume sources, we are able to take a statistically and theoretically precise continuum limit. Thereafter, all the running of the operators with momentum scale is due to their anomalous dimension. We use this to develop a practical scheme for step scaling with off shell vertex functions. We develop the method on 16³ × 32 lattices to show the practicality of using small volume simulations to step scale to high momenta. We also use larger 24³×64 and 32³×64 lattices to compute renormalization constants very accurately. Combining these with previous analyses we are able to extract a precise value for the light and strange quark masses and the neutral kaon mixing parameter BK. We also analyse eigenvectors of the domain wall Dirac matrix. We develop a practical and cost effective way to compute eigenvectors using the implicitly restarted Lanczos method with Chebyshev acceleration. We show that calculating eigenvectors to accelerate propagator inversions is cost effective when as few as one or two propagators are required. We investigate the technique of low mode averaging (LMA) with eigenvectors of the domain wall matrix for the first time. We find that for low energy correlators, pions for example, LMA is very effective at reducing the statistical noise. We also calculated the η and η′ meson masses, which required evaluating disconnected correlation functions and combining stochastic sources with LMA.

http://hdl.handle.net/1842/7825

en

The University of Edinburgh

Step Scaling with off-shell renormalisation. Phys.Rev. D83 (2011) 114511

Step Scaling with off-shell renormalisation. PoS LATTICE2010 (2010) 244

Continuum Limit of BK from 2+1 Flavor Domain Wall QCD. Phys.Rev. D84 (2011) 014503

Continuum Limit Physics from 2+1 Flavor Domain Wall QCD. Phys.Rev. D83 (2011) 074508

Opening the Rome-Southampton window for operator mixing matrices. Phys.Rev. D85 (2012) 014501

Lattice Results for Low Moments of Light Meson Distribution Amplitudes. Phys.Rev. D83 (2011) 074505

Light Meson Distribution Amplitudes. PoS LATTICE2010 (2010) 154

lattice

QCD

non-perturbative renormalization

NPR

Eigenvectors

Non-perturbative renormalization and low mode averaging with domain wall fermions

Thesis or Dissertation

Doctoral

PhD Doctor of Philosophy