$\mathbf{\gamma Z}$ Box at Low Energy

Abstract

We calculate the 1-loop $\gamma Z$ box-graph correction to electron-quark scattering at low energy and low momentum transfer. Both electron and quark masses are kept non-zero. From our result, we extract coupling constants for the low-energy effective Lagrangian with parity-violating 4-fermion interaction terms. We study the zero-mass limits and show that a non-zero electron mass is sufficient to obtain finite, well-defined couplings which are insensitive to a hadronic mass cutoff. We finally discuss the impact of our results on the determination of the weak charge of the proton from polarized electron-proton scattering.