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The large energy-scale behaviour of the parity and time-reversal violating(PTV) pion-nucleon coupling constant is analyzed in a model combiningrenormalization-group techniques and the dressing of the PTV vertex with a pionloop. With the strong $\pi N N$ vertex as a mixture of the pseudovector andpseudoscalar couplings, we show that depending on the admixture parameter, twoqualitatively distinct types of behaviour are obtained for the PTV couplingconstant at high energy scales: an asymptotic freedom or a fixed-point. We finda critical value of the admixture parameter which delineates these twoscenarios. Several examples of the high-energy scale behaviour of the PTV $\piN N$ constant are considered, corresponding to realistic hadronic models of thestrong pion-nucleon interaction.

Connection between the high energy-scale evolution of the P- and T-odd $\pi N N$ coupling constant and the strong $\pi N N$ interaction