$B \rightarrow \pi \ell \nu$ with M\"{o}bius Domain Wall Fermions

Abstract

We report on the status of our calculation of the exclusive semileptonic decay, $B\rightarrow \pi \ell \nu$; a key process in the determination of the CKM matrix element $|V_{ub}|$. The M\"{o}bius domain wall action is used for both light and heavy quarks on gauge ensembles that include the effects of $2+1$ flavours of quarks in the sea at three values of the lattice spacing: $a\approx 0.08~\mathrm{fm}$, $a\approx0.055~\mathrm{fm}$, and $a\approx0.044~\mathrm{fm}$. Pion masses go down to $300~\mathrm{MeV}$ while heavy quarks masses are as large as $2.44m_c$. We present preliminary results of form factors from this process, showing dependence on momentum transfer, lattice spacing, and the heavy quark mass.