D-meson decay constants and a check of factorization in non-leptonic B-decays

Abstract

Abstract We compute the vector meson decay constants $ {f_{{D_{{(s)}}^{ * }}}} $ from the simulation of twisted mass QCD on the lattice with N f = 2 dynamical quarks. When combining these values with the pseudoscalar D (s)-meson decay constants, we were able (i) to show that the heavy quark spin symmetry breaking effects with the charm quark are large, $ {f_{{D_s^{ * }}}}/{f_{{{D_s}}}} = 1.26(3) $ , and (ii) to check the factorization approximation in a few specific B-meson non-leptonic decay modes. Besides our main results, $ {f_{{{D^{ * }}}}} = 278\pm 13\pm 10\,{\text{MeV}} $ , and $ {f_{{D_s^{ * }}}} = 311\pm 9\,{\text{MeV}} $ , other phenomenologically interesting results of this paper are: $ {f_{{D_s^{ * }}}}/{f_{{{D^{ * }}}}} = 1.16\pm 0.02\pm 0.06 $ , $ {f_{{D_s^{ * }}}}/{f_{{{D^{ * }}}}} = 1.46\pm 0.05\pm 0.06 $ , and $ {f_{{{D_s}}}}/{f_{{{D^{ * }}}}} = 0.89\pm 0.02\pm 0.03 $ . Finally, we correct the value for B(B 0 → D + π −) quoted by PDG, and find B(B 0 → D + π −) = (7.8 ± 1.4) × 10−7. Alternatively, by using the ratios discussed in this paper, we obtain B(B 0 → D + π −) = (8.3 ± 1.0 ± 0.8) × 10−7.