P- and T-violating $\pi N N$ form factor

Abstract

The form factor of the parity and time-reversal violating (PTV) pion-nucleon interaction is calculated from one-loop vertex diagrams. The degrees of freedom included in the effective lagrangian are nucleons, pions, $\eta$, $\rho$ and $\omega$ mesons. We show that by studying the form factor one can constrain the PTV meson-nucleon coupling constants. We evaluate the mean square radius associated with the PTV $\pi N N$ vertex. Using the mean square radius, we estimate the effect of the PTV $\pi N N$ vertex on the neutron electric dipole moment, and find a very small correction. We also extract the renormalisation group $\beta$ function and use it to discuss evolution of the PTV $\pi N N$ coupling constant beyond the hadronic mass scale.