Pseudoscalar decay constants of kaon and D-mesons from Nf=2 twisted mass Lattice QCD

Abstract

We present the results of a lattice QCD calculation of the pseudoscalar meson decay constants fpi, fK, fD and fDs, performed with Nf=2 dynamical fermions. The simulation is carried out with the tree-level improved Symanzik gauge action and with the twisted mass fermionic action at maximal twist. We have considered for the final analysis three values of the lattice spacing, a~0.10 fm, 0.09 fm and 0.07 fm, with pion masses down to mpi~270 MeV. Our results for the light meson decay constants are fK=158.1(2.4) MeV and fK/fpi=1.210(18). From the latter ratio, by using the experimental determination of Gamma(K-->mu nu_mu (gamma))/ Gamma(pi--> mu nu_mu (gamma)) and the average value of |Vud| from nuclear beta decays, we obtain |Vus|=0.2222(34), in good agreement with the determination from semileptonic Kl3 decays and the unitarity constraint. For the D and Ds meson decay constants we obtain fD=197(9) MeV, fDs=244(8) MeV and fDs/fD=1.24(3). Our result for fD is in good agreement with the CLEO experimental measurement. For fDs our determination is smaller than the PDG 2008 experimental average but in agreement with a recent improved measurement by CLEO at the 1.4 sigma level.

Figures (6)

• Figure 1: Effective pseudoscalar meson masses $m_{PS}^{eff} (a\,\mu_{sea}, a\,\mu_{val}^{(1)}, a\,\mu_{val}^{(2)})$ as a function of time, in lattice units, with $\mu_{sea}$ and $\mu_{val}^{(1,2)}$ denoting generically the sea and valence quark masses respectively. For illustrative purposes the following choices of quark mass combinations are displayed: $m_{PS}(0.0040,0.0040,0.0040)$ (pion), $m_{PS}(0.0040,0.0040,0.0220)$ (kaon), $m_{PS}(0.0040,0.0040,0.2500)$ ($D$-meson), $m_{PS}(0.0040,0.0220,0.2500)$ ($D_s$-meson). In each plot we compare the effective masses as obtained from the two ensembles $B_1$ and $B_6$, which correspond to different lattice sizes. Dashed and solid lines represent the 1-$\sigma$ ranges of the corresponding masses as obtained from the fit of the two-point correlation functions.
• Figure 2: Lattice results for $r_0 f_{\pi}\equiv r_0 f_{PS}(\mu_l,\mu_l,\mu_l)$ and $r_0 f_{K}\equiv r_0 f_{PS}(\mu_l,\mu_l,\mu_s)$ as a function of the pion mass square $(r_0 m_\pi)^2 \equiv (r_0 m_{PS}(\mu_l,\mu_l,\mu_l))^2$. For the kaon, we display data with $\mu_s$ fixed to the simulated mass that corresponds to a reference meson mass $r_0 m_{PS}(\mu_l,\mu_s,\mu_s)\simeq 1.63$. The SU(2)- (SU(3)-) ChPT extrapolation to the physical pion mass is represented at fixed lattice spacing by the dashed (dotted) curves, and in the continuum limit by the solid (dashed-dotted) curve. Our results for the physical values of the pion and kaon decay constants, obtained from SU(2)-ChPT, are illustrated by diamonds in the plot. In the kaon case an interpolation to the physical strange quark mass is performed.
• Figure 3: Lattice QCD determinations of the ratio $f_K/f_\pi$ obtained from simulations with $N_f=2$Aoki:2004ht and $N_f=2+1$Allton:2008pnLellouch:2009fg, Aoki:2004ht-Aubin:2008ie dynamical quarks. A star in the legend denotes preliminary results. The results are also compared with the experimental average of $f_K/f_\pi$ obtained by using for $V_{us}$ the determination from $K_{\ell 3}$ decays Antonelli:2008jg.
• Figure 4: From top-left to bottom-right: lattice results for $f_{D_s} \sqrt{m_{D_s}}$, $R_1=f_{D_s} \sqrt{m_{D_s}}/f_K$, $R=f_{D_s}\sqrt{m_{D_s}}/(f_D \sqrt{m_D})$ and $R_2=(f_{D_s} \sqrt{m_{D_s}}/f_K)/(f_D \sqrt{m_D}/f_{\pi})$ as a function of the pion mass square $m_\pi^2 \equiv m_{PS}(\mu_l,\mu_l,\mu_l)^2$, in units of $r_0$. We display data with $\mu_s$ and $\mu_c$ fixed to the simulated masses that correspond to reference strange and charmed meson masses $r_0 m_{PS}(\mu_l,\mu_s,\mu_s)=1.63$ and $r_0 m_{PS}(\mu_l,\mu_s,\mu_c)=4.41$. The SU(2)- (SU(3)-) ChPT extrapolation to the physical pion mass is represented at fixed lattice spacing by the dashed (dotted) curves, and in the continuum limit by the solid (dashed-dotted) curve. The physical results, illustrated by diamonds in the plots, are obtained from SU(2)-ChPT after interpolating to the physical strange and charm quark masses.
• Figure 5: Lattice QCD determinations of the $D$-mesons decay constants $f_{D_s}$ (top) and $f_D$ (bottom) obtained from simulations with $N_f=2$AliKhan:2001jgBernard:2002pc and $N_f=2+1$Follana:2007uvBernard:2009wr dynamical fermions. A star in the legend denotes preliminary results. The lattice results for $f_{D_s}$ are also compared with the PDG 2008 experimental average PDG and with the recent improved measurement by CLEO Alexander:2009ux. For $f_D$ we compare with the CLEO determination :2008sq.