Domain-Wall Fermion with R5 R_5 Symmetry

We present the domain-wall fermion operator which is reflection symmetric in the fifth dimension, with the approximate sign function $S(H)$ of the effective 4-dimensional Dirac operator satisfying the bound $|1-S(\lambda)| \le 2 d_Z$ for $\lambda^2 \in [\lambda_{min}^2, \lambda_{max}^2]$, where $d_Z$ is the maximum deviation $| 1- \sqrt{x} R_Z(x) |_{\rm max}$ of the Zolotarev optimal rational polynomial $R_Z(x)$ of $1/\sqrt{x}$ for $x \in [1, \lambda_{max}^2/\lambda_{min}^2]$, with degrees $(n-1,n)$ for $N_s = 2n$, and $(n,n)$ for $N_s = 2 n + 1$.Comment: This work is dedicated to late Professor James S. Bal

Mass Spectra of DsD_s and Ωc\Omega_c in Lattice QCD with Nf=2+1+1N_f= 2+1+1 Domain-Wall Quarks

We perform hybrid Monte Carlo simulation of lattice QCD with $N_f=2+1+1$ optimal domain-wall quarks on the $32^3 \times 64$ lattice with lattice spacing $a \sim 0.06$ fm, and generate a gauge ensemble with physical $s$ and $c$ quarks, and pion mass $\sim 280$ MeV. Using 2-quark (meson) and 3-quark (baryon) interpolating operators, the mass spectra of the lowest-lying states containing $s$ and $c$ quarks ($D_s$ and $\Omega_c$) are extracted \cite{Chen:2017kxr}, which turn out in good agreement with the high energy experimental values, together with the predictions of the charmed baryons which have not been observed in experiments. For the five new narrow $\Omega_c$ states observed by the LHCb Collaboration \cite{Aaij:2017nav}, the lowest-lying $\Omega_c(3000)$ agrees with our predicted mass $3015(29)(34)$ MeV of the lowest-lying $\Omega_c$ with $J^P = 1/2^{-}$. This implies that the $J^P$ of $\Omega_c(3000)$ is $1/2^-$.Comment: 8 pages, 3 figures, talk presented at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spai