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. 
Ruth S. Van de Water and Stephen R. Sharpe