A lattice QCD study of the $B\to \pi \pi \mathrm{\ell }\bar{\nu }$ transition

$V_{ub}$ is the smallest and least known of all CKM matrix elements; the community currently determines its magnitude primarily through the exclusive process $B\to \pi \mathrm{\ell }\bar{\nu }$. Here we present our progress toward a lattice QCD determination of the $V_{ub}$ matrix element from a novel transition – $B\to \pi \pi \mathrm{\ell }\bar{\nu }$ process, where the $\pi \pi$ system is in a $P$ wave and scattering features the $\rho (770)$ resonance as an enhancement. We perform our calculation on $N_f=2+1$ isotropic clover fermions on a lattice of $L\approx 3.6$ fm and a pion mass of $\approx 320$ MeV; for the $b$-quark we use the anisotropic clover action. After a brief overview of the theoretical framework, we will discuss some preliminary results.