B →ρℓ ν ¯ Resonance Form Factors from B →ππℓ ν ¯ in Lattice QCD

The decay B→ρℓν¯ is an attractive process for determining the magnitude of the smallest Cabibbo-Kobayashi-Maskawa matrix element, |Vub|, and can provide new insights into the origin of the long-standing exclusive-inclusive discrepancy in determinations of this standard-model parameter. This requires a nonperturbative QCD calculation of the B→ρ form factors V, A0, A1, and A12. The unstable nature of the ρ resonance has prevented precise lattice QCD calculations of these form factors to date. Here, we present the first lattice QCD calculation of the B→ρ form factors in which the ρ is treated properly as a resonance in P-wave ππ scattering. To this end, we use the Lellouch-Lüscher finite-volume formalism to compute the B→ππ form factors as a function of both momentum transfer and ππ invariant mass, and then analytically continue to the ρ resonance pole. This calculation is performed with 2+1 dynamical quark flavors at a pion mass of approximately 320 MeV, and demonstrates a clear path toward results at the physical point.