Form factors of the $D_s \to \phi \ell \nu_\ell$ semileptonic decay with (2+1)-flavor lattice QCD

TL;DR

This paper performs a precise lattice QCD calculation of the form factors for the $D_s o \,phi \,\ell \,\nu_\ell$ decay, improving accuracy and extrapolating to physical pion mass and continuum limit.

Contribution

It provides the most precise lattice QCD results for the form factors of this decay, using multiple gauge ensembles to control systematic uncertainties.

Findings

Form factor ratios: r_V=1.614(19), r_2=0.741(31)

Achieved 1%-4% precision in form factors

Improved previous lattice QCD results significantly.

Abstract

We present a systematic lattice calculation of the vector and axial vector form factors $V$ and $A_i~(i=0,1,2)$ for the $D_s \to \phi \ell \nu_\ell$ semileptonic decay using (2+1)-flavor Wilson-clover fermion configurations generated by the CLQCD collaboration. Seven gauge ensembles with different lattice spacings, from $0.052~\text{fm}$ to $0.105~\text{fm}$, and different pion masses, from about $210~\text{MeV}$ to $320~\text{MeV}$ are utilized, enabling us to take both the continuum limit and physical pion mass extrapolation. The form factor ratios are obtained to be $r_V=1.614(19)$ and $r_2=0.741(31)$. Our results of form factors reach the precision of $1\%-4\%$, which greatly improves the previous lattice QCD results and obtains the most precise determination to date.