Two-loop renormalization of fermion bilinear operators on the lattice

Understand

We compute the renormalization functions on the lattice, in the RI' scheme, of local bilinear quark operators $\bar{\psi}\Gamma\psi$, where $\Gamma= 1, \gamma_5, \gamma_\mu, \gamma_5\gamma_\mu, \gamma_5\sigma_{\mu\nu}$.

• This calculation is carried out to two loops for the first time.
• We consider both the flavor non-singlet and singlet operators.
• As a prerequisite for the above, we compute the quark field renormalization, $Z_\psi$, up to two loops.