Author's School

Graduate School of Arts & Sciences

Author's Department/Program



English (en)

Date of Award

January 2010

Degree Type


Degree Name

Doctor of Philosophy (PhD)

Chair and Committee

Claude Bernard


As a part of the Standard Model: SM), Quantum Chromodynamics: QCD) is a widely accepted theory to describe the physics of quarks and gluons. Formulating QCD on finite discrete lattices in Euclidean space-time not only enables one to study the theory non-perturbatively, but also provides a framework analogous to statistical systems, in which numerical methods can be applied. In this work, we concentrate on one specific fermion formalism, staggered fermions. To interpret the data obtained from numerical simulations with staggered fermions, a particular version of chiral perturbation theory: χPT), rooted staggered χPT: rSχPT), is needed to incorporate the discretization effects, mainly taste-violations, and the fourth root procedure used for the staggered fermion formalism. In the light pseudoscalar sector, I study rSχPT in the two-flavor case. The pion mass and decay constant are calculated through NLO for a partially-quenched theory. In the limit where the strange quark mass is large compared to the light quark masses and the taste splittings, I show that the SU(2) staggered chiral theory emerges from the SU(3) staggered chiral theory, as expected. Explicit relations between SU(2) and SU(3) low energy constants and taste-violating parameters are given. The results are useful for SU(2) chiral fits to asqtad data and allow one to incorporate effects from varying strange quark masses. By using these formulae and continuum NNLO chiral logarithms, I then perform a systematic chiral analysis to the MILC lattice data in the light pseudoscalar sector. Superfine and ultrafine ensembles are used, where light sea quark masses and taste splittings are small compared to the simulated strange quark mass. Correlated fits with Bayesian analysis are done for both the pion mass and the pion decay constant. Physical quantities are obtained by extrapolating the results to the continuum and full QCD case where the light quarks masses are physical. I give results for the pion decay constant, SU(2) low-energy constants and the chiral condensate in the two-flavor chiral limit.



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