Semileptonic Decays of $D$ Mesons in Three-Flavor Lattice QCD

We present the first three-flavor lattice QCD calculations for $D\to \pi l\nu$ and $D\to Kl\nu$ semileptonic decays. Simulations are carried out using ensembles of unquenched gauge fields generated by the MILC Collaboration. With an improved staggered action for light quarks, we are able to simulate at light quark masses down to $1/8$ of the strange mass. Consequently, the systematic error from the chiral extrapolation is much smaller than in previous calculations with Wilson-type light quarks. Our results for the form factors at $q^2=0$ are $f_{+}^{D\to \pi }(0)=0.64(3)(6)$ and $f_{+}^{D\to K}(0)=0.73(3)(7)$, where the first error is statistical and the second is systematic, added in quadrature. Combining our results with experimental branching ratios, we obtain the Cabibbo-Kobayashi-Maskawa matrix elements $|V_{cd}|=0.239(10)(24)(20)$ and $|V_{cs}|=0.969(39)(94)(24)$, where the last errors are from experimental uncertainties.

Figure 1

$a^{-1/2}{f}_{\perp }$ as a function of $(aE{)}^2$ for the $D\to \pi$ decay. Symbols are raw data and lines are fitting curves with the parametrization of Eq. (5). Results at $m_l=0.03$, 0.02, and 0.01 are shown.

Figure 2

$m_l$ dependence and chiral fits for $a^{-1/2}{f}_{\perp }^{D\to \pi }$ for several values of $(aE{)}^2$. The $\mathrm{S}\chi \mathrm{P}\mathrm{T}+\mathrm{\text{linear}}$ fit (solid line), $\mathrm{S}\chi \mathrm{P}\mathrm{T}+\mathrm{\text{quadratic}}$ fit (dotted line) and linear fit (dashed line).

Figure 3

$D\to \pi$ and $D\to K$ form factors. The experimental values are taken from Ref. [19].