Heavy flavor meson decay constants with Wilson fermions at β = 6.4

Abstract

We present an extensive lattice study of the physical properties of mesons, composed of a heavy, H , and a light, q , quark, at β = 6.4 on a 24 3 × 60 lattice, using the Wilson action in the quenched approximation. We have studied the mass spectrum and the decay constants of vector and pseudoscalar mesons. We find significant violations of the mass scaling law f P √ M P = const. ( ∼ 50% for D-mesons and ∼ 20% for B-mesons). The results using quenched but propagating quarks are remarkably consistent with the static results when the scale is taken from the pion decay constant. Combining the results obtained by several calculations of the pseudoscalar decay constants as a function of the meson mass, at different values of the lattice spacing, we obtain by extrapolation f B √ B B = (220 ± 40) MeV ( f B = (205 ± 40) MeV and B B = 1.16 ± 0.07), where B B is the renormalization group invariant B-parameter relevant for B d - B d mixing. We also find f B s 2 B B , f B d 2 B B d = 1.19 ± 0.10 . This last result is relevant in experimental studies of B 3 - B 3 mixing. The vector-pseudoscalar mass splittings do not follow the predicted behaviour, M V 2 - M P 2 ∼ const., which is expected (and found experimentally) in the limit of large heavy quark masses (i.e. when m Q ⪢ Λ QCD ).