Valon-hadron crossover and phenomenology of quark-gluon plasma in the context of lattice calculations
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EMENTARY PARTICLES AND FIELDS Theory
Valon–Hadron Crossover and Phenomenology of Quark–Gluon Plasma in the Context of Lattice Calculations I. I. Royzen* Lebedev Institute of Physics, Russian Academy of Sciences, Leninski ˘ı pr. 53, Moscow, 117924 Russia Received July 5, 2006
Abstract—The phase crossover in the energy range ΔT 50−60 MeV as explicitly suggested by the results of lattice calculations at μ = 0 is interpreted here in terms of an evolving superposition of hadron and subhadron states of nuclear matter, the former being gradually displaced by the latter with increasing temperature. It is shown that the expected imperfectness of the quark–gluon gas even at temperatures substantially higher the chiral-transition temperature may be a direct consequence of a slow decrease [in proportion to 1/ln(T /Λ)] in the Coulomb part of the color particle interaction at short distances. PACS numbers: 12.38.Mh, 12.39.Ba, 25.75.Nq DOI: 10.1134/S1063778807060154
1. INTRODUCTION AND CURRENT STATUS OF THE PROBLEM In the present study, an attempt is made to correlate the hypothesis that dynamical (constituent) quarks (valons) play a significant role in the formation of subhadron states of nuclear matter [1–4] to the results of direct lattice calculations [5] that claim to provide an ab initio approximation of exact averaging within quantum statistical mechanics in the system of particles interacting according to the QCD Lagrangian. They unambiguously indicate that, upon heating an equilibrium system of zero baryon chemical potential, this system undergoes a transition from a hadron phase to quark–gluon plasma (chirally symmetric phase) via a crossover state (not at a fixed temperature as in a conventional phase transition) where the two phases coexist over a broad temperature range 140 ≤ T ≤ 200 MeV. At the upper end of this range, the plasma phase displaces completely the hadron phase. This means that the order parameter R0−1 , which characterizes the hadron phase (confinement radius, which takes a value of R0 1 fm in the hadron phase), does not vanish abruptly, but it decreases gradually as the temperature increases within the above range. As a result, the long-standing discussion [3–6] as to whether it *
is possible to discriminate two phase transitions— color deconfinement (hadronization) and restoration (breakdown) of chiral symmetry upon heating (cooling) nuclear matter—becomes virtually meaningless, since the above crossover range is on the same order of magnitude as the presumed temperature separation of the two transitions.1) A very slow transformation of the nascent quark–gluon gas into a perfect gas upon a further heating above the average chiral-transition temperature Tc 170 MeV (more precisely, for T ≥ 200 MeV) is yet another intriguing result of lattice calculations, which was the motivation for treating quark–gluon plasma as a state where the interaction between the particles is so strong that it is likely to be some kind of a perfect liquid rather than a gas [7]. At the same time, simple estimates show that i
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