Properties of 2+1-flavor QCD in the imaginary chemical potential region: A model approach

2017/03/31 by Junpei Sugano, Hiroaki Kouno, Masanobu Yahiro
Mathematics · Physics and Astronomy · #Combinatorics #Dimensionless quantity #Function (biology) #High-Energy Particle Collisions Research #Mathematical physics #Mathematics #Order (exchange) #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Thermodynamics #hep-ph

paper · pdf · doi:10.1103/physrevd.96.014028

published as Phys. Rev. D 96, 014028 (2017) · 9 pages, 8 figures

arxiv created 2017/07/07 · openalex publication_date 2017/07/27 · arxiv updated 2017/08/02 · openalex created_date 2017/08/08 · openalex updated_date 2026/08/05

Abstract

We study properties of 2+1-flavor QCD in the imaginary chemical potential region by using two approaches. One is a theoretical approach based on the QCD partition function, and the other is a qualitative one based on the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. In the theoretical approach, we clarify conditions imposed on the imaginary chemical potentials \ensuremathμ_f=i\ensuremathθ_fT to realize the Roberge-Weiss (RW) periodicity. Here, T is the temperature, the index f denotes the flavor, and \ensuremathθ_f are dimensionless chemical potentials. We also show that the RW periodicity is broken if any one of \ensuremathθ_f is fixed to a constant value. In order to visualize the condition, we use the PNJL model as a model possessing the RW periodicity and draw the phase diagram as a function of \ensuremathθ_u=\ensuremathθ_d\ensuremath≡\ensuremathθ_l for two conditions of \ensuremathθ_s=\ensuremathθ_l and \ensuremathθ_s=0. We also consider two cases, (\ensuremathμ_u,\ensuremathμ_d,\ensuremathμ_s)=(i\ensuremathθ_uT,iC₁T,0) and (\ensuremathμ_u,\ensuremathμ_d,\ensuremathμ_s)=(iC₂T,iC₂T,i\ensuremathθ_sT); here, C₁ and C₂ are dimensionless constants, whereas \ensuremathθ_u and \ensuremathθ_s are treated as variables. For some choice of C₁ (C₂), the number density of the up (strange) quark becomes smooth in the entire region of \ensuremathθ_u (\ensuremathθ_s) even in the high T region. This property may be important for lattice QCD simulations in the imaginary chemical potential region, since it makes the analytic continuation more feasible.

Citations

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