Two perspectives for the thermal behavior of an effective hadronic coupling constant

The pion nucleon vertex function at finite temperature is studied in two fr ameworks: (a) the thermal (linear) sigma model to leading (one-loop) order, and (b) a thermal QCD-Finite Energy Sum Rule. Both approaches indicate tha t the strength of the pion-nucleon coupling decreases with increasing T, va nishing at a critical temperature. The associated mean-square radius is a m onotonically increasing function of T, diverging at the critical temperatur e. We interpret this fact as (analytical) evidence for deconfinement.