Form factors of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>π</mml:mi><mml:mo>ℓ</mml:mo><mml:mi>ν</mml:mi></mml:math> and a determination of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo stretchy="false">|</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">|</mml:mo></mml:math> with Möbius domain-wall fermions
Brian Colquhoun, S. Hashimoto, T. Kaneko, J. Koponen
Abstract
Using a fully relativistic lattice fermion action, we compute the form factors of the semileptonic decay $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}\ensuremath{\nu}$, which is required for the determination of the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{ub}|$. We employ the M\"obius domain-wall fermion formalism for the generation of lattice ensembles with $2+1$ sea quark flavors as well as for the valence heavy and light quarks. We compute the form factors at various values of the lattice spacing and multiple light and heavy quark masses, and extrapolate the results to the physical point. We combine our lattice results with the available experimental data to obtain $|{V}_{ub}|=(3.93\ifmmode\pm\else\textpm\fi{}0.41)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$.