Reworking the Tucson-Melbourne Three-Nucleon Potential

We introduce new values of the strength constants (i.e., $a$, $b$, $c$, and $d$ coefficients) of the Tucson-Melbourne (TM) 2$\pi$ exchange three nucleon potential. The new values come from contemporary dispersion relation analyses of meson factory $\pi$N scattering data. We make variational Monte Carlo calculations of the triton with the original and updated three-body forces to study the effects of this update. We remove a short-range -- $\pi$-range part of the potential due to the $c$ coefficient and discuss the effect on the triton binding energy.