𝐵 → 𝜌ℓ$\bar{v}$ Resonance Form Factors from 𝐵→ 𝜋𝜋ℓ$\bar{v}$ in Lattice QCD
The decay 𝐵 → 𝜌ℓ$\bar{v}$ is an attractive process for determining the magnitude of the smallest Cabibbo-Kobayashi-Maskawa matrix element, |𝑉 𝑢𝑏 |, 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, 𝐴 0 , 𝐴 1 , and 𝐴 12 . 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.