Topics in Effective Field Theory for Lattice QCD

Abstract

In this work, we extend and apply effective field theory techniques to systematically understand a subset of lattice artifacts which pollute the lattice correlation functions for a few processes of physical interest. Where possible, we compare to existing lattice QCD calculations. In particular, we extend the heavy baryon Lagrangian to the next order in partially quenched chiral perturbation theory and use it to compute the masses of the lightest spin-1/2 and spin-3/2 baryons to next-to-next-to leading order. We then construct the twisted mass chiral Lagrangian for baryons and apply it to compute the lattice spacing corrections to the baryon masses simulated with twisted mass lattice QCD. We extend computations of the nucleon electromagnetic structure to account for finite volume effects, as these observables are particularly sensitive to the finite extent of the lattice. We resolve subtle peculiarities for lattice QCD simulations of polarizabilities and we show that using background field techniques, one can make predictions for the 4 spin-dependent nucleon polarizabilities, quantities which are difficult to access experimentally. We then discuss the two-pion system in finite volume, determining the exponentially small volume corrections necessary for lattice determinations of the scattering parameters. We also determine the lattice spacing artifacts that arise for a mixed-action lattice simulation of the two-pion system with Ginsparg-Wilson valence quarks and staggered sea quarks. We show that the isospin 2 scattering length has a near continuum like behavior, differing from the chiral perturbation theory calculation by a computable difference.

Ph.D. Thesis, 180 pages, 23 figures

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• Staggered Chiral Perturbation Theory at Next-to-Leading Order
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• Finite volume corrections to pi-pi scattering
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• B_K in Staggered Chiral Perturbation Theory
• Baryon Electromagnetic Properties in Partially Quenched Heavy Hadron Chiral Perturbation Theory
• Compton scattering from the proton at NLO in the chiral expansion
• Unphysical Operators in Partially Quenched QCD
• Numerical simulations with two flavours of twisted-mass Wilson quarks and DBW2 gauge action
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• The Gell-Mann -- Okubo mass relation among baryons from fully-dynamical mixed-action lattice QCD
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• Nucleon and Delta masses in twisted mass chiral perturbation theory
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