Confining but chirally symmetric dense and cold matter
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ELEMENTARY PARTICLES AND FIELDS Theory
Confining but Chirally Symmetric Dense and Cold Matter* L. Ya. Glozman** Institute for Physics, Theoretical Physics Branch, University of Graz, Austria Received March 31, 2011
Abstract—The possibility for existence of cold, dense chirally symmetric matter with confinement is reviewed. The answer to this question crucially depends on the mechanism of mass generation in QCD and interconnection of confinement and chiral symmetry breaking. This question can be clarified from spectroscopy of hadrons and their axial properties. Almost systematical parity doubling of highly excited hadrons suggests that their mass is not related to chiral symmetry breaking in the vacuum and is approximately chirally symmetric. Then there is a possibility for existence of confining but chirally symmetric matter. We clarify a possible mechanism underlying such a phase at low temperatures and large density. Namely, at large density the Pauli blocking prevents the gap equation to generate a solution with broken chiral symmetry. However, the chirally symmetric part of the quark Green function as well as all color non-singlet quantities are still infrared divergent, meaning that the system is with confinement. A possible phase transition to such a matter is most probably of the first order. This is because there are no chiral partners to the lowest lying hadrons. DOI: 10.1134/S1063778812050092
1. INTRODUCTION A key question to QCD at high temperatures and densities is whether and how deconfinement and chiral restoration transitions (crossovers) are connected to each other. In order to answer this question we need understanding of hadron mass generation in QCD, how both confinement and chiral symmetry breaking influence the origin of mass. We know from the trace anomaly in QCD that the hadron mass (we discuss here only the light quark sector) almost entirely consists of the energy of quantized gluonic field. However, this tells us nothing about the effect of chiral symmetry breaking on hadron mass. The chiral symmetry is dynamically broken in the QCD vacuum and this phenomenon is crucially important for the mass origin of the lowest-lying hadrons, such as pion, nucleon or rho-meson. Phenomenologically it follows from the well established (pseudo) Nambu– Goldstone nature of pion as well as from the absence of chiral partners to the lowest-lying hadrons. Their mass is determined to large degree by the quark condensate of the vacuum, which can be seen from the SVZ sum rules [1, 2], as well as from many different microscopical models. At the same time almost systematical parity doubling in both highly excited baryons [3] and mesons [4] suggests that chiral symmetry breaking ∗ **
The text was submitted by the author in English. E-mail: [email protected]
in the vacuum is almost irrelevant to the mass generation of these hadrons, i.e. the chiral (and U (1)A ) symmetry gets effectively restored, for a review see [5]. This conjecture is strongly supported by the pattern of strong decays of excited hadrons [6]. Experim
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