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Chiral Phase Transition in the scaled O(4)-Model

By O. Bohr, B. -j. Schaefer and J. Wambach


Due to the non-Abelian character of QCD gluons selfinteract and form bound states, so-called glueballs. Such glueballs have been seen in recent lattice simulations and are actively searched for in experiment. Glueballs can be used to construct effective models of QCD which respect the symmetries and anomaly structure of the theory. At the classical level and in the limit of vanishing quark masses QCD for n flavors exhibits a global chiral U(n)L × U(n)R symmetry and is in addition invariant under scale transformations. Due to anomalies not all of the associated currents are conserved and the symmetry is broken down to SU(n)L × SU(n)R which, in the case of two flavors, is isomorphic to O(4). This symmetry is spontaneously broken to SU(n)L+R. The divergence of the anomalous scale current is given by the trace of the energy-momentum tensor which, in the limit of massless quarks, is given by 〈θ µ µ 〉 = 〈β(g) 2g Ga µν(x)Gaµν(x) 〉 , (1) where G a µν(x) denotes the gluonic field-strength tensor and β(g) is the usual QCD beta function. An effective realization of the scale anomaly can be achieved by adding to the classical Lagrangian a scalar color singlet dilaton field χ with an interaction potential of the form ( ) 4 ( χ V (χ) = h ln χ

Year: 2011
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