Lattice QCD inputs to the CKM unitarity triangle analysis

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Abstract

We perform a global fit to the Cabibbo-Kobayashi-Maskawa unitarity triangle using the latest experimental and theoretical constraints. Our emphasis is on the hadronic weak matrix elements that enter the analysis, which must be computed using lattice QCD or other nonperturbative methods. Realistic lattice QCD calculations which include the effects of the dynamical up, down, and strange quarks are now available for all of the standard inputs to the global fit. We therefore present lattice averages for all of the necessary hadronic weak matrix elements. We attempt to account for correlations between lattice QCD results in a reasonable but conservative manner: whenever there are reasons to believe that an error is correlated between two lattice calculations, we take the degree of correlation to be 100%. These averages are suitable for use as inputs both in the global Cabibbo-Kobayashi-Maskawa unitarity triangle fit and other phenomenological analyses. In order to illustrate the impact of the lattice averages, we make standard model predictions for the parameters ${\stackrel{^}{B}}_{K}$, $|{V}_{cb}|$, and $|{V}_{ub}|/|{V}_{cb}|$. We find a $(2--3)\ensuremath{\sigma}$ tension in the unitarity triangle, depending upon whether we use the inclusive or exclusive determination of $|{V}_{cb}|$. If we interpret the tension as a sign of new physics in either neutral kaon or $B$ mixing, we find that the scenario with new physics in kaon mixing is preferred by present data.

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