Charmed and light pseudoscalar meson decay constants from four-flavor lattice QCD with physical light quarks

Abstract

We compute the leptonic decay constants ${f}_{{D}^{+}}$, ${f}_{{D}_{s}}$, and ${f}_{{K}^{+}}$ and the quark-mass ratios ${m}_{c}/{m}_{s}$ and ${m}_{s}/{m}_{l}$ in unquenched lattice QCD using the experimentally determined value of ${f}_{{\ensuremath{\pi}}^{+}}$ for normalization. We use the MILC highly improved staggered quark ensembles with four dynamical quark flavors---up, down, strange, and charm---and with both physical and unphysical values of the light sea-quark masses. The use of physical pions removes the need for a chiral extrapolation, thereby eliminating a significant source of uncertainty in previous calculations. Four different lattice spacings ranging from $a\ensuremath{\approx}0.06$ to 0.15 fm are included in the analysis to control the extrapolation to the continuum limit. Our primary results are ${f}_{{D}^{+}}=212.6(0.4)(\genfrac{}{}{0}{}{+1.0}{\ensuremath{-}1.2})\text{ }\text{ }\mathrm{MeV}$, ${f}_{{D}_{s}}=249.0(0.3)(\genfrac{}{}{0}{}{+1.1}{\ensuremath{-}1.5})\text{ }\text{ }\mathrm{MeV}$, and ${f}_{{D}_{s}}/{f}_{{D}^{+}}=1.1712(10)(\genfrac{}{}{0}{}{+29}{\ensuremath{-}32})$, where the errors are statistical and total systematic, respectively. The errors on our results for the charm decay constants and their ratio are approximately 2--4 times smaller than those of the most precise previous lattice calculations. We also obtain ${f}_{{K}^{+}}/{f}_{{\ensuremath{\pi}}^{+}}=1.1956(10)(\genfrac{}{}{0}{}{+26}{\ensuremath{-}18})$, updating our previous result, and determine the quark-mass ratios ${m}_{s}/{m}_{l}=27.35(5)(\genfrac{}{}{0}{}{+10}{\ensuremath{-}7})$ and ${m}_{c}/{m}_{s}=11.747(19)(\genfrac{}{}{0}{}{+59}{\ensuremath{-}43})$. When combined with experimental measurements of the decay rates, our results lead to precise determinations of the Cabibbo-Kobayashi-Maskawa matrix elements $|{V}_{us}|=0.22487(51)(29)(20)(5)$, $|{V}_{cd}|=0.217(1)(5)(1)$ and $|{V}_{cs}|=1.010(5)(18)(6)$, where the errors are from this calculation of the decay constants, the uncertainty in the experimental decay rates, structure-dependent electromagnetic corrections, and, in the case of $|{V}_{us}|$, the uncertainty in $|{V}_{ud}|$, respectively.