First calculation of [formula omitted] in lattice QCD

Abstract

We present the results of a calculation of the matrix elements of the quark weak current which are relevant for semileptonic decays of D-mesons into light pseudoscalar and vector mesons. The computations are performed by averaging the results over 15 gauge field configurations, generated in the quenched approximation by the Metropolis algorithm, at β = 6.0, on a 20 X 10 2 X 40 lattice, with Wilson fermions. From the study of the matrix elements 〈 K −| J μ | D 0〉 and 〈 K ∗0|J μD +〉 we find the partial rate for the semi-leptonic decay of the D + into K ∗0 e +ν e is given by Γ( D + → K ∗0 e +ν e ) = (5.2±1.9) X 10 10 s −1 , in good agreement with the experimental result (4.1 ± 0.7 ± 0.5) X 10 10 s −1, and that the ratio of the partial rates Γ( D + → K ∗0 e +ν e ) Γ( D ) → K − e +ν c ) is given by 1.1±1.3, which is larger than the experimental value 0.45 ± 0.09 ± 0.07. We also compute the ratio of the longitudinal to transverse polarization rates in K ∗0 decays and find 1.7 ± 0.6, to be compared to the experimental value 2.4 −0.9 +1.7 ± 0.2. We finally discuss future improvements in the accuracy of our theoretical predictions.