The Vector Manifestation and Effective Degrees of Freedom At Chiral Restoration

The role of effective degrees of freedom on the vector and axial-vector susceptibilities and the pion velocity at chiral restoration is analyzed. We consider two possible scenarios, one in which pions are considered to be the only low-lying degrees of freedom – that we shall refer to as “standard” – and the other in which pions, vector mesons and constituent quarks (or quasiquarks in short) are the relevant low-lying degrees of freedom – that we shall refer to as “vector manifestation (VM).” We show at one-loop order in chiral perturbation theory with hidden local symmetry Lagrangian that while in the standard scenario, the pion velocity vanishes at the chiral transition, it instead approaches unity in the VM scenario. If the VM is realized in nature, the chiral phase structure of hadronic matter can be much richer than that in the standard one and the phase transition will be a smooth crossover: Sharp vector and scalar excitations are expected in the vicinity of the critical point. Some indirect indications that lend support to the VM scenario, and in consequence to BR scaling, are discussed. ∗Based on talks given at the YITP-RCNP Workshop on “Chiral Restoration in Nuclear Medium” at Yukawa Institute of Theoretical Physics, Kyoto, Japan, 7-9 October 2002 and the 2002 International Workshop “Strong Coupling Gauge Theories and Effective Field Theories (SCGT02)” at Nagoya University, Nagoya, Japan, 10-13 December 2002.