Abstract
The QCD baryon number density can formally be expanded into a Laurent series in fugacity, which is a relativistic generalization of Mayer's cluster expansion. We determine properties of the cluster expansion in a model with a phase transition and a critical point at finite baryon density, in which the Fourier coefficients of the expansion can be determined explicitly and to arbitrary order. The asymptotic behavior of Fourier coefficients changes qualitatively as one traverses the critical temperature and it is connected to the branch points of a thermodynamic potential associated with the phase transition. The results are discussed in the context of lattice QCD simulations at imaginary chemical potential. We argue that the location of a branch point closest to the imaginary chemical potential axis can be extracted through an analysis of an exponential suppression of Fourier coefficients. This is illustrated using the four leading coefficients both in a toy model as well as by using recent lattice QCD data.
Highlights
Identification of the phases and structure of strongly interacting matter at finite baryon densities is one of the outstanding issues in modern nuclear physics
We have determined properties of the cluster expansion in fugacities that are associated with a presence of a phase transition and a critical point at finite baryon density
This has been achieved through the trivirial model (TVM)—a model which does contain a phase transition of a liquid-gas type and where one can evaluate the cluster expansion coefficients explicitly [Eq (22)]
Summary
Identification of the phases and structure of strongly interacting matter at finite baryon densities is one of the outstanding issues in modern nuclear physics. It has been established in the framework of lattice QCD that the quarkhadron transition at vanishing baryon density is a smooth crossover [1]. It is expected ( not proven) that a first-order quark-hadron transition takes place at sufficiently high baryon density, with the associated QCD critical point (CP) [2]. The search for a critical behavior at finite μB is performed using measurements of fluctuations in heavy-ion collisions [3–6] and using indirect lattice methods such as Taylor expansion around μB 1⁄4 0 [7–10] or analytic continuation from imaginary μB [11–13]. In the present work we will consider the above questions in the framework of an expansion p T4
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