$B to rho ell bar{nu}$ resonance form factors from $B to pi pi ell bar{nu}$ in lattice QCD

The decay $B to rho ell bar{nu}$ 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 longstanding exclusive-inclusive discrepancy in determinations of this standard-model parameter. This requires a nonperturbative QCD calculation of the $B to rho$ form factors $V$, $A_0$, $A_1$, and $A_{12}$. The unstable nature of the $rho$ resonance has prevented precise lattice QCD calculations of these form factors to date. Here, we present the first lattice QCD calculation of the $B to rho$ form factors in which the $rho$ is treated properly as a resonance in $P$-wave $pi pi$ scattering. To this end, we use the Lellouch-Lüscher finite-volume formalism to compute the $B to pi pi$ form factors as a function of both momentum transfer and $pi pi$ invariant mass, and then analytically continue to the $rho$ 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.