B-meson decay constants from improved lattice NRQCD and physical u, d, s and c sea quarks

Abstract

We present the first lattice QCD calculation of the decay constants fB and fB s with physical light quark masses. We use configurations generated by the MILC collaboration including the effect of u, d, s and c HISQ sea quarks at three lattice spacings and with three u/d quark mass values going down to the physical value. We use improved NRQCD for the valence b quarks. Our results are fB = 0.186(4) GeV, fB s = 0.224(5) GeV, fB s /fB = 1.205(7) and MB s − MB = 85(2) MeV, superseding earlier results with NRQCD b quarks. We discuss the implications of our results for the Standard Model rates for B (s) → µ + µ − and B → τ ν.

Hindered M1 radiative decay ofϒ(2S)from lattice NRQCD

“…We use a lattice NRQCD action correct through O(v 4 ), with additional spin-dependent O(v 6 ) terms 1 and include discretisation corrections. This lattice formalism has already been used successfully to study bottomonium S, P and D wave mass splittings [13,15], precise hyperfine splittings [16,17], B meson decay constants [18], Υ and Υ leptonic widths [19] and B, D meson mass splittings [17]. The Hamiltonian evolution equations can be written as…”

“…Each of these fields, as well as the covariant derivatives, must be tadpole-improved using the same improvement procedure as in the perturbative calculation of the matching coefficients [13,20] (thus removing unphysical tadpole diagrams from using the Lie group element rather than the Lie algebra element in the construction of the lattice field theory). We take the mean trace of the gluon field in Landau gauge, u 0L = 1 3 Tr U µ (x) , as the tadpole parameter, calculated in [13,18].…”

New physics contribution toBs→μ+μ−within R-parity violating supersymmetric models

“…where τ Bs is the average lifetime of the B s meson. We use during the numerical analysis τ Bs = 1.509 ps, [13], f Bs = 0.225 GeV [14], V ⋆ tb V ts = 0.0405 [15] (as mentioned above, we neglect the small phase of this CKM product), [16]. For the top quark mass we use m pole t = 173.2 GeV [17], which yields for the MS,QCD renormalized mass m t (m t ) = 163.2 GeV [1]; η Y = 1.012 for [18][19][20].…”

“…The expression for A µµ ∆Γ in terms of Wilson coefficients of the low-energy effective operators may be found in [2]. For the considered case of real NP couplings and under simplifying assumption (14), one can show after doing some algebra that A µµ ∆Γ = 1. Thus, the experimentally allowed (1σ) interval for the B(B s → µ + µ − ) (given by Eq.…”

“…If we give up the simplifying assumption(14), A ν (B s → µ + µ − ) will also contain a term with a scalar bispinor bilinear form. This term however won't interfere with the other terms of the transition amplitude, so it does not play any essential role in our analysis.…”