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

...+15
Dec 2022

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

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