D-meson semileptonic decays to pseudoscalars from four-flavor lattice QCD

TL;DR

This paper presents high-precision lattice QCD calculations of form factors for semileptonic D-meson decays, enabling precise determination of CKM matrix elements and testing the Standard Model with experimental data.

Contribution

The study provides the most precise lattice QCD calculations of D-meson semileptonic decay form factors and CKM matrix elements, including the first determination of |V_{cd}|^{D_s→K} from D_s decays.

Findings

Most precise |V_{cd}| to date, matching experimental error

First determination of |V_{cd}|^{D_s→K} from D_s decays

Results consistent with CKM unitarity within one standard deviation

Abstract

We present lattice-QCD calculations of the hadronic form factors for the semileptonic decays $D\to\pi\ell\nu$, $D\to K\ell\nu$, and $D_s\to K\ell\nu$. Our calculation uses the highly improved staggered quark (HISQ) action for all valence and sea quarks and includes $N_f=2+1+1$ MILC ensembles with lattice spacings ranging from $a\approx0.12$ fm down to $0.042$ fm. At most lattice spacings, an ensemble with physical-mass light quarks is included. The HISQ action allows all the quarks to be treated with the same relativistic light-quark action, allowing for nonperturbative renormalization using partial conservation of the vector current. We combine our results with experimental measurements of the differential decay rates to determine $|V_{cd}|^{D\to\pi}=0.2238(11)^{\rm Expt}(15)^{\rm QCD}(04)^{\rm EW}(02)^{\rm SIB}[22]^{\rm QED}$ and $|V_{cs}|^{D\to K}=0.9589(23)^{\rm Expt}(40)^{\rm QCD}(15)^{\rm EW}(05)^{\rm SIB}[95]^{\rm QED}$ This result for $|V_{cd}|$ is the most precise to date, with a lattice-QCD error that is, for the first time for the semileptonic extraction, at the same level as the experimental error. Using recent measurements from BES III, we also give the first-ever determination of $|V_{cd}|^{D_s\to K}=0.258(15)^{\rm Expt}(01)^{\rm QCD}[03]^{\rm QED}$ from $D_s\to K \ell\nu$. Our results also furnish new Standard Model calculations of the lepton flavor universality ratios $R^{D\to\pi}=0.98671(17)^{\rm QCD}[500]^{\rm QED}$, $R^{D\to K}=0.97606(16)^{\rm QCD}[500]^{\rm QED}$, and $R^{D_s\to K}=0.98099(10)^{\rm QCD}[500]^{\rm QED}$, which are consistent within $2\sigma$ with experimental measurements. Our extractions of $|V_{cd}|$ and $|V_{cs}|$, when combined with a value for $|V_{cb}|$, provide the most precise test of second-row CKM unitarity, finding agreement with unitarity at the level of one standard deviation.