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Using the MILC 2+1 flavor asqtad quark action ensembles, we are calculating the form factors f 0 and f + for the semileptonic B s → Kℓν decay. A total of six ensembles with lattice spacing from ≈ 0.12 to 0.06 fm are being used. At the coarsest and finest lattice spacings, the light quark mass m ′ l is one-tenth the strange quark mass m ′ s . At the intermediate lattice spacing, the ratio m ′ l /m ′ s ranges from 0.05 to 0.2. The valence b quark is treated using the Sheikholeslami-Wohlert Wilson-clover action with the Fermilab interpretation. The other valence quarks use the asqtad action. When combined with (future) measurements from the LHCb and Belle II experiments, these calculations will provide an alternate determination of the CKM matrix element |V

We present preliminary blinded results from our analysis of the form factors for B → D * ν decay at non-zero recoil. Our analysis includes 15 MILC asqtad ensembles with N f = 2 + 1 flavors of sea quarks and lattice spacings ranging from a ≈ 0.15 fm down to 0.045 fm. The valence light quarks employ the asqtad action, whereas the b and c quarks are treated using the Fermilab action. We discuss the impact that our results will have on |V cb | and R(D *).