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T-dependence of pseudoscalar and scalar correlations

Inhomogeneous pseudoscalar and scalar Bethe-Salpeter equations solved using a renormalisation-group-improved rainbow-ladder truncation exhibit bound state poles below and above T_c, the critical temperature for chiral symmetry restoration. Above T_c the bound state amplitudes are identical, as are the positions and residues of the pseudoscalar and scalar poles in the vertices. In the chiral limit the pi^0 -> gamma gamma coupling vanishes at T_c, as do f_pi, m_sigma, g_{sigma pi pi}. For light current-quark masses the 2-pi decay channel of the isoscalar-scalar meson remains open until very near T_c, and the widths of the dominant pion decay modes remain significant in the vicinity of the crossover.