B¯s→K semileptonic decay from an Omnès improved constituent quark model

We study the f+ form factor for the semileptonic B¯s→K+ℓ−ν¯ℓ decay in a constituent quark model. The valence quark estimate is supplemented with the contribution from the B¯⁎ pole that dominates the high q2 region. We use a multiply-subtracted Omnès dispersion relation to extend the quark model predictions from its region of applicability near qmax2=(MBs−MK)2∼23.75GeV2 to all q2 values accessible in the physical decay. To better constrain the dependence of f+ on q2, we fit the subtraction constants to a combined input from previous light cone sum rule by Duplancic and Melic (2008) [11] and the present quark model results. From this analysis, we obtain Γ(B¯s→K+ℓ−ν¯ℓ)=(5.47−0.46+0.54)|Vub|2×10−9MeV, which is about 10% and 20% higher than the predictions based on Lattice QCD and QCD light cone sum rules respectively. The former predictions, for both the form factor f+(q2) and the differential decay width, lie within the 1σ band of our estimated uncertainties for all q2 values accessible in the physical decay, except for a quite small region very close to qmax2. Differences with the light cone sum results for the form factor f+ are larger than 20% in the region above q2=15GeV2.