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

TL;DR

This paper reports progress in calculating the $V_{ub}$ matrix element via a novel $B o ho o\pi\pi\ellar{ u}$ transition using lattice QCD, aiming to improve understanding of CKM matrix elements.

Contribution

It introduces a lattice QCD approach to determine $V_{ub}$ from the $B o ho o\pi\pi\ellar{ u}$ process, incorporating the $ ho$ resonance in the $ ho o\pi\pi$ scattering.

Findings

Preliminary results on lattice calculations of the transition.

Use of $N_f=2+1$ isotropic clover fermions.

Analysis of the $ ho$ resonance effects in the decay.

Abstract

$V_{ub}$ is the smallest and least known of all CKM matrix elements; the community currently determines its magnitude primarily through the exclusive process $B\to\pi\ell\bar{\nu}$. Here we present our progress toward a lattice QCD determination of the $V_{ub}$ matrix element from a novel transition -- $B\to\pi\pi\ell\bar{\nu}$ 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.