Charm quark system on the physical point in 2+1 flavor lattice QCD

Abstract

We investigate the charm quark system using the relativistic heavy quark action on 2+1 flavor PACS-CS configurations previously generated on 32 3 × 64 lattice. The dynamical up-down and strange quark masses are set to the physical values by using the technique of reweighting to shift the quark hopping parameters from the values employed in the configuration generation. At the physical point, the lattice spacing equals a −1 = 2.194(10) GeV and the spatial extent L = 2.88(1) fm. The charm quark mass is determined by the spin-averaged mass of the 1S charmonium state, from which we obtain m MS charm (µ = m MS charm ) = 1.260(1)(6)(35) GeV, where the errors are due to our statistics, scale determination and renormalization factor. An additional systematic error from the heavy quark is of order α 2 s f (m Q a)(aΛ QCD ), which is estimated to be a percent level if the factor f (m Q a) analytic in m Q a is of order unity. Our results for the charmed and charmed-strange meson decay constants are f D = 226(6)(1)(5) MeV, f Ds = 257(2)(1)(5) MeV, again up to the heavy quark errors of order α 2 s f (m Q a)(aΛ QCD ). Combined with the CLEO values for the leptonic decay widths, these values yield |V cd | = 0.205(6)(1)(5)(9), |V cs | = 1.00 (1)(1)(3)(3), where the last error is on account of the experimental uncertainty of the decay widths.1 |V cs | is hard to be estimated from neutrino and anti-neutrino experiments, |V cs | = 0.94 +0.32 −0.26 ± 0.13 [1].

Review of lattice results concerning low-energy particle physics

“…Truncation errors in HQET have been studied by comparing simulations of the effective field theory with corresponding quenched simulations using a non-perturbatively improved Wilson action with heavy quark masses in the charm-mass region in large volumes [390] and up to the b-quark mass in small volumes [391]. Moreover, the consistency between independent determinations of the bottom [73,336,365,370,[392][393][394] and charm [60,72,73,85,333,395,396] quark masses using NRQCD, HQET, Tsukuba, HISQ, twisted-mass Wilson, and other O(a) improved Wilson heavy quarks, as well as their agreement with non-lattice determinations [74] further validate lattice heavy-quark methods.…”

“…The PACS-CS Collaboration published in 2011 a computation of the D and D s decay constants with 2 + 1 flavours of non-perturbatively O(a) improved Wilson fermions and the Iwasaki gauge action [333]. For the charm quark the Tsukuba heavy quark action is used.…”

“…In practice, the contribution to the clover coefficient in the massless limit is computed non-perturbatively [665], while the mass-dependent contributions, which differ for c B and c E , are calculated at one loop in mean-field improved lattice perturbation theory [666]. The hopping parameter is fixed non-perturbatively to reproduce the experimentally measured spin-averaged 1S charmonium mass [333]. One of the anisotropy parameters (r t in Ref.…”

“…One of the anisotropy parameters (r t in Ref. [333]) is also set to its one-loop perturbative value, while the other (ν in Ref. [333]) is fixed non-perturbatively to obtain the continuum dispersion relation for the spin-averaged charmonium 1S states (such that M 1 = M 2 ).…”

“…[333]) is also set to its one-loop perturbative value, while the other (ν in Ref. [333]) is fixed non-perturbatively to obtain the continuum dispersion relation for the spin-averaged charmonium 1S states (such that M 1 = M 2 ). For the renormalisation and improvement coefficients of weak current operators, the contributions in the chiral limit are obtained nonperturbatively [21,667], while the mass-dependent contributions are estimated using one-loop lattice perturbation theory [668].…”