Relations among correlation functions in the high temperature phase of QCD with broken SU(3)

Abstract

Group-theoretic arguments are used to determine the dependence of twopoint correlators of quark bilinears on the current quark masses. The leading difference between π and δ correlators is found to be of order m s times a U(1) Aviolating correlator. These general arguments are consistent with Schaefer's observation that if U(1) A violation persists to high enough temperatures then the strange η can be lighter than the non-strange one.At high temperatures the SU(N f ) L ×SU(N f ) R chiral symmetry of QCD (with N f flavors of light quark) is believed to be broken only by the nonzero current quark masses. The nature of this phase is of considerable interest, in particular because of its relevance to ultrarelativistic heavy-ion collisions and the early universe. One aspect of this phase that has received recent interest [1][2][3][4][5][6][7] is the role of the anomalously broken U(1) A symmetry at high temperatures. Because of this anomaly, topological features of the QCD vacuum split the η ′ from the pion in the low-temperature phase [8]. This question, currently being studied using lattice-gauge simulations of two-flavor QCD by a number of groups [9][10][11][12], is whether these topological features persist above the QCD phase transition.

LATTICE QCD AT FINITE TEMPERATURE

“…Alternatively, the anomalous U A (1) could become restored effectively through the disappearance of topologically non-trivial zero modes of the Dirac matrix at or even below the critical temperature rendering the transition first order [10]. This case would be reflected in a degeneracy [16] between the pion and the scalar isovector meson (δ/a 0 ), which does not seem to be realized [17].…”

Chiral multiplets of hadron currents

“…The up and down quark masses are presumably light enough for such a procedure to make sense. Moreover, the nature of the chiral symmetry of the underlying theory allows one to deduce certain relations between correlators which hold to order m 2 q rather than m q , thereby enhancing the range of validity of the chiral expansion [7]. Treating the strange quark mass as small is clearly far more problematic.…”