We present renormalization constants of overlap quark bilinear operators on $2+1$-flavor domain wall fermion configurations. This setup is being used by the $\chi \mathrm{QCD}$ Collaboration in calculations of physical quantities such as strangeness in the nucleon and the strange and charm quark masses. The scale-independent renormalization constant for the axial-vector current is computed using the Ward identity. The renormalization constants for scalar, pseudoscalar, and vector currents are calculated in the RI-MOM scheme. Results in the $\overline{\mathrm{MS}}$ scheme are also given. The step scaling function of quark masses in the RI-MOM scheme is computed as well. The analysis uses, in total, six different ensembles of three sea quarks, each on two lattices with sizes ${24}^3\times 64$ and ${32}^3\times 64$ at spacings $a=(1.73\mathrm{GeV}{)}^{-1}$ and $(2.28\mathrm{GeV}{)}^{-1}$, respectively.

• Received 9 January 2014

DOI:https://doi.org/10.1103/PhysRevD.90.034505