Determination of the temperature dependence of the up- down-quark mass in QCD

Abstract

The temperature dependence of the sum of the QCD up- and down-quark masses, $(m_u + m_d)$ and the pion decay constant, $f_\pi$, are determined from two thermal finite energy QCD sum rules for the pseudoscalar-current correlator. This quark-mass remains mostly constant for temperatures well below the critical temperature for deconfinement/chiral-symmetry restoration. As this critical temperature is approached, the quark-mass increases sharply with increasing temperature. This increase is far more pronounced if the temperature dependence of the pion mass (determined independently from other methods) is taken into account. The behavior of $f_\pi(T)$ is consistent with the expectation from chiral symmetry, i.e. that it should follow the thermal dependence of the quark condensate, independently of the quark mass.