Dirac-mode analysis for quark number density and its application for deconfinement transition

Takahiro M Doi,Kouji Kashiwa,M Della Morte,E Gámiz Sánchez,P Fritzsch,C Pena Ruano

doi:10.1051/epjconf/201817512003

Takahiro M Doi, Kouji Kashiwa + Show 4 more

Open Access

https://doi.org/10.1051/epjconf/201817512003

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Journal: EPJ Web of Conferences	Publication Date: Jan 1, 2018
Citations: 2	License type: CC BY 4.0

Affiliation: Kyoto University, RIKEN Nishina Center

Abstract

The quark number density at finite imaginary chemical potential is investigated in the lattice QCD using the Dirac-mode expansion. We find the analytical formula of the quark number density in terms of the Polyakov loop in the large quark mass regime. On the other hand, in the small quark mass region, the quark number density is investigated by using the quenched lattice QCD simulation. The quark number density is found to strongly depend on the low-lying Dirac modes while its sign does not change. This result leads to that the quark number holonomy is not sensitive to the low-lying Dirac modes. We discuss the confinement-deconfinement transition from the property of the quark number density and the quark number holonomy.

Highlights

One of the important task in nuclear and particle physics is the nonperturbative understanding of the phase structure of Quantum Chromodynamics (QCD) at finite temperature (T ) and real chemical potential
QCD data, the sign of the quark number density are insensitive to the low-lying Dirac-modes and this behavior is similar to the Polyakov loop
From the heavy quark mass expansion with the Dirac mode expansion, we found that low-lying Dirac modes do not dominantly contribute to the quark number density in all order of the heavy quark mass expansion

Summary

Introduction

One of the important task in nuclear and particle physics is the nonperturbative understanding of the phase structure of Quantum Chromodynamics (QCD) at finite temperature (T ) and real chemical potential (μR). The Polyakov loop, which respect the gauge-invariant holonomy, is the exact order-parameter of the confinement-deconfinement transition in the infinite quark mass limit. This argument is based on the analogy of the topological order discussed in Refs. Spatially closed loops which do not wind the temporal length are canceled out each other and have no contribution to the quark number density in total in each order n. In the heavy quark-mass expansion of the quark number density (6), there are higher order terms beyond the leading terms, which are the Polyakov loop and its conjugate.

Dirac-mode expansion of the quark number density

Large quark mass region

Small quark mass region

Summary and discussion