Form factors of the $D_s \to φ\ell ν_\ell$ semileptonic decay with (2+1)-flavor lattice QCD
Gaofeng Fan, Yu Meng, Chuan Liu, Zhaofeng Liu, Tinghong Shen, Ting-Xiao Wang, Ke-Long Zhang, Lei Zhang
TL;DR
The paper addresses the $D_s \to \phi \ell \nu_\ell$ semileptonic decay by computing the vector and axial-vector form factors $V$ and $A_i$ from lattice QCD. The authors use seven $(2+1)$-flavor Wilson-clover ensembles to perform controlled continuum and physical-pion extrapolations, applying the scalar-function method and a $z$-expansion to parametrize the $q^2$ dependence as $F(q^2,a,m_\pi)=\frac{1}{1-q^2/m_{\text{pole}}^2}\sum_{i=0}^2 (c_i+d_i a^2) [1+f_i(m_\pi^2-m_{\pi,\text{phys}}^{2})] z^{i}$ to extract $V$, $A_i$ and the ratios $r_V=V(0)/A_1(0)$ and $r_2=A_2(0)/A_1(0)$. They report $r_V=1.614(19)$ and $r_2=0.741(31)$, achieving $1-4\%$ precision, the most precise to date. The results enable precise determinations of branching fractions and the CKM element $|V_{cs}|$, and the methodology is readily extensible to other pseudoscalar-to-vector decays such as $D\to K^*$.
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 $D_s \to φ\ell ν_\ell$ 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.