B → D^* vector, axial-vector and tensor form factors for the full q^2 range from lattice QCD

We compute the complete set of SM and tensor B_(s)→ D_(s)^*ℓν̅ semileptonic form factors across the full kinematic range of the decay using second generation MILC n_f=2+1+1 HISQ gluon field configurations and HISQ valence quarks, with the heavy-HISQ method. Lattice spacings range from 0.09fm to 0.044fm with pion masses from ≈ 300MeV down to the physical value and heavy quark masses ranging between ≈ 1.5 m_c and 4.1 m_c ≈ 0.9 m_b; currents are normalised nonperturbatively. Using the recent B_(s)→ D^*_(s)ℓν̅_ℓ data from Belle and LHCb together with our form factors we determine a model independent value of V_cb=39.03(56)_exp(67)_latt× 10^-3, in agreement with previous exclusive determinations and in tension with the inclusive result at the level of 3.6σ. We observe a ≈ 1σ tension between the shape of the differential decay rates computed using our form factors and those measured by Belle. We compute a lattice-only SM value for the ratio of semitauonic and semimuonic decay rates, R(D^*)=0.273(15), which we find to be closer to the recent Belle measurement and HFLAV average than theory predictions using fits to experimental differential rate data for B→ D^*ℓν̅_ℓ. Determining V_cb using the total rate for B→ D^*ℓν gives a value in agreement with inclusive results. We compute the longitudinal polarisation fraction for the semitauonic mode, F_L^D^*=0.395(24), which is in tension at the level of 2.2σ with the recent Belle measurement. Our calculation combines B→ D^* and B_s→ D_s^* lattice results, and we provide an update which supersedes our previous lattice computation of the B_s→ D_s^* form factors. We also give the chiral perturbation theory needed to analyse the tensor form factors.