Charmed and light pseudoscalar meson decay constants from HISQ simulations

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. We use the MILC highly improved staggered quark (HISQ) ensembles with four dynamical quark flavors. Our primary results are $f_{D^{+}}=212.6(0.4)({}_{-1.2}^{+1.0})\mathrm{MeV}$, $f_{D_s}=249.0(0.3)({}_{-1.5}^{+1.1})\mathrm{MeV}$, and $f_{D_s}/f_{D^{+}}=1.1712(10)({}_{-32}^{+29})$, where the errors are statistical and total systematic, respectively. We also obtain $f_{K^{+}}/f_{\ddot{I}{€}^{+}}=1.1956(10)({}_{-18}^{+26})$, updating our previous result, and determine the quark-mass ratios $m_s/m_l=27.35(5)({}_{-7}^{+10})$ and $m_c/m_s=11.747(19)({}_{-43}^{+59})$. When combined with experimental measurements of the decay rates, our results lead to precise determinations of the CKM 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.

7 pages, 1 figure. Proceedings of the 32nd International Symposium on Lattice Field Theory; 23-28 June, 2014, Columbia University, New York