B_K in Staggered Chiral Perturbation Theory

We calculate the kaon B-parameter, B_K, to next-to-leading order in staggered chiral perturbation theory. We find expressions for partially quenched QCD with three sea quarks, quenched QCD, and full QCD with m_u = m_d but not equal to m_s. We extend the usual power counting to include the effects of using perturbative (rather than non-perturbative) matching factors. Taste breaking enters through the O(a^2) terms in the effective action, through O(a^2) terms from the discretization of operators, and through the truncation of matching factors. These effects cause mixing with several additional operators, complicating the chiral and continuum extrapolations. In addition to the staggered expressions, we present B_K at next-to-leading order in continuum partially quenched chiral perturbation theory for N_f=3 sea quarks with m_u = m_d but not equal to m_s.Comment: 56 pages, 3 figures (v3: Corrected normalization error in Eq.(4) and subsequent equations; physics results unchanged. Version accepted to Phys. Rev. D.

Taste violations in the scalar correlator in mixed action simulations

We study the behavior of the isovector scalar correlator, which is particularly sensitive to lattice artifacts, using domain-wall valence quarks on a staggered sea (generated by the MILC collaboration). We analyze this according to the prediction from chiral perturbation theory determined by Prelovsek, which indicates that the leading unitarity violations come from taste breaking effects. We show that our data behaves in the way predicted by Prelovsek, thus verifying that the largest contribution to the violations of unitarity which arise at finite lattice spacing can be described by the mixed-action chiral perturbation theory

The Kaon B-parameter in Mixed Action Chiral Perturbation Theory

We calculate the kaon B-parameter, B_K, in chiral perturbation theory for a partially quenched, mixed action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We find that the resulting expression is similar to that in the continuum, and in fact has only two additional unknown parameters. At one-loop order, taste-symmetry violations in the staggered sea sector only contribute to flavor-disconnected diagrams by generating an O(a^2) shift to the masses of taste-singlet sea-sea mesons. Lattice discretization errors also give rise to an analytic term which shifts the tree-level value of B_K by an amount of O(a^2). This term, however, is not strictly due to taste-breaking, and is therefore also present in the expression for B_K for pure G-W lattice fermions. We also present a numerical study of the mixed B_K expression in order to demonstrate that both discretization errors and finite volume effects are small and under control on the MILC improved staggered lattices.Comment: 29 pages, 4 figures; Expanded spurion discussion, other discussions clarified, version to appear in PR