We report a quark spin calculation from the anomalous Ward identity with overlap fermions on 2+1 flavor dynamical fermion configurations with light sea quark masses. Such a formulation decomposes the divergence of the flavor-singlet axial-vector current into a quark pseudoscalar term and a triangle anomaly term, flavor by flavor. A large negative contribution from the anomaly term is observed and it is canceled within errors by the contribution from the pseudoscalar term in the disconnected insertion in the heavy quark region. On the other hand, net negative contributions are obtained for the light and strange quarks in the disconnected insertion, since their quark pseudoscalar terms are smaller than that of the heavy quark. Our results are obtained from the 2+1 flavor domain wall fermion configurations on the 24^3*64 lattice with a-1 = 1.78(5) GeV and the light sea quark at m_{pi} = 330 MeV. We use the overlap fermion for the valence and the quark loop so that the renormalization constants Z_m and Z_P cancel in the pseudoscalar operator 2mP. In addition, the overlap Dirac operator is used to calculate the local topological charge in the anomaly so that there is no renormalization for the anomaly term either. In this study, we find the total quark spin to be small mainlyly due to the large negative anomaly term which could be the source for the proton spin crisis.
We use overlap fermions as valence quarks to calculate meson masses in a wide quark mass range on the $2+1$-flavor domain-wall fermion gauge configurations generated by the RBC and UKQCD Collaborations. The well-defined quark masses in the overlap fermion formalism and the clear valence quark mass dependence of meson masses observed from the calculation facilitate a direct derivation of physical current quark masses through a global fit to the lattice data, which incorporates $O(a^2)$ and $O(m_c^4a^4)$ corrections, chiral extrapolation, and quark mass interpolation. Using the physical masses of $D_s$, $D_s^*$ and $J/psi$ as inputs, Sommers scale parameter $r_0$ and the masses of charm quark and strange quark in the $overline{rm MS}$ scheme are determined to be $r_0=0.465(4)(9)$ fm, $m_c^{overline{rm MS}}(2,{rm GeV})=1.118(6)(24)$ GeV (or $m_c^{overline{rm MS}}(m_c)=1.304(5)(20)$ GeV), and $m_s^{overline{rm MS}}(2,{rm GeV})=0.101(3)(6),{rm GeV}$, respectively. Furthermore, we observe that the mass difference of the vector meson and the pseudoscalar meson with the same valence quark content is proportional to the reciprocal of the square root of the valence quark masses. The hyperfine splitting of charmonium, $M_{J/psi}-M_{eta_c}$, is determined to be 119(2)(7) MeV, which is in good agreement with the experimental value. We also predict the decay constant of $D_s$ to be $f_{D_s}=254(2)(4)$ MeV. The masses of charmonium $P$-wave states $chi_{c0}, chi_{c1}$ and $h_c$ are also in good agreement with experiments.
We present renormalization constants of overlap quark bilinear operators on 2+1-flavor domain wall fermion configurations. Both overlap and domain wall fermions have chiral symmetry on the lattice. The scale independent renormalization constant for the local axial vector current is computed using a Ward Identity. The renormalization constants for the scalar, pseudoscalar and vector current are calculated in the RI-MOM scheme. Results in the MS-bar scheme are obtained by using perturbative conversion ratios. The analysis uses in total six ensembles with lattice sizes 24^3x64 and 32^3x64.
The charmless bottom meson decays are systematically investigated based on an approximate six quark operator effective Hamiltonian from perturbative QCD. It is shown that within this framework the naive QCD factorization method provides a simple way to evaluate the hadronic matrix elements of two body mesonic decays. The singularities caused by on mass-shell quark propagator and gluon exchanging interaction are appropriately treated. Such a simple framework allows us to make theoretical predictions for the decay amplitudes with reasonable input parameters. The resulting theoretical predictions for all the branching ratios and CP asymmetries in the charmless $B^0, B^+, B_sto pipi, pi K, KK$ decays are found to be consistent with the current experimental data except for a few decay modes. The observed large branching ratio in $Bto pi^0pi^0$ decay remains a puzzle though the predicted branching ratio may be significantly improved by considering the large vertex corrections in the effective Wilson coefficients. More precise measurements of charmless bottom meson decays, especially on CP-violations in $Bto K K$ and $B_sto pipi, pi K, KK$ decay modes, will provide a useful test and guide us to a better understanding on perturbative and nonperturbative QCD.
