The staggered chiral perturbation theory in the two-flavor case and SU(2) chiral analysis of the MILC data

Abstract

rt 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