P- and T-violating πNN 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, η, ρ and ω 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 πNN vertex. Using the mean square radius, we estimate the effect of the PTV πNN vertex on the neutron electric dipole moment, and find a very small correction. We also extract the renormalisation group β function and use it to discuss evolution of the PTV πNN coupling constant beyond the hadronic mass scale.