We review the progress on the determination of the CKM matrix elements |V_cs|, |V_cd|, |V_cb|, |V_ub| and heavy quark masses presented at the 6th International Workshop on the CKM Unitarity Triangle.
We study discretization effects in a mixed-action lattice theory with domain-wall valence quarks and Asqtad-improved staggered sea quarks. At the level of the chiral effective Lagrangian, discretization effects in the mixed-action theory give rise to
two new parameters as compared to the lowest order Lagrangian for staggered fermions -- the residual quark mass, m_res, and the mixed valence-sea meson mass-splitting, Delta_mix. We find that the size of m_res is approximately four times smaller than our lightest valence quark mass on our coarser lattice spacing, and comparable to that of simulations by RBC and UKQCD. We also find that the size of Delta_mix is comparable to the smallest of the staggered meson taste-splittings measured by MILC. Because lattice artifacts are different in the valence and sea sectors of the mixed-action theory, they give rise to unitarity-violating effects that disappear in the continuum limit. Such effects are expected to be mild for many quantities of interest, but are significant in the case of the isovector scalar (a_0) correlator. Specifically, once m_res, Delta_mix, and two other parameters that can be determined from the light pseudoscalar spectrum are known, the two-particle intermediate state bubble contribution to the scalar correlator is completely predicted within mixed-action chiral perturbation theory (MAChPT). We find that the behavior of the scalar meson correlator is quantitatively consistent with the MAChPT prediction; this supports the claim that MAChPT describes the dominant unitarity-violating effects in the mixed-action theory and can be used to remove lattice artifacts and recover physical quantities.
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 fro
m 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.
