THE PION AT FINITE TEMPERATURE AND DENSITY

We review the low-temperature variation in the pion mass with temperature. This dependence follows from explicit chiral symmetry breaking and can be calculated in terms of pionic interactions. We then show that the standard calculation of the density dependence of the pion mass gives only a small increase in this mass with increasing density. Explicit chiral symmetry breaking, which produces the bare quark masses, arises at a much higher mass scale than that of QCD. The bare quark masses are then magnified by the quark condensate to produce the much larger pion mass. This magnification disappears as the quark condensate "melts", bringing the pion mass essentially to zero at a density less-than-or-equal-to 2-rho-0, where rho-0 is the nuclear matter density. In the region of nuclear matter density rho-0, m-pi*/m-pi may even be somewhat smaller than m(N)*/m(N). Arguments are given that the nucleon mass, and masses of mesons made up out of up-and-down quarks should change much more rapidly with density than with temperature, at least for moderate changes in each. We suggest that the decreasing pion mass, while not effective in pion-nuclear processes at zero temperature, should play an important role in heavy-ion collisions.