B̄s → K semileptonic decay from an Omnès improved nonrelativistic quark model

Abstract

We study the f+ form factor for the B̄s → K+ℓ−v̄ℓ semileptonic decay in a nonrelativistic quark model. The valence quark contribution is supplemented with a B̄*-pole term that dominates the high q2 region. To extend the quark model predictions from its region of applicability near q2max = (MBs – MK)2 we use a multiply-subtracted Omnès dispersion relation. We fit the subtraction constants to a combined input from previous light cone sum rule results in the low q2 region and the quark model results (valence plus B̄*-pole) in the high q2 region. From this analysis, we obtain Γ(B̄s → K+ℓ−v̄ℓ) = (5.47+5.54−0.46)|Vub|2 × 10−9 MeV, which is about 10% and 20% higher than predictions based on Lattice QCD and QCD light cone sum rules respectively.