Susceptibilities of rotating quark matter in Fourier-Bessel basis

TL;DR

This paper develops a method to analyze susceptibility functions in rotating quark matter using Fourier-Bessel basis, revealing rotational effects on various susceptibilities and providing benchmarks for lattice QCD simulations.

Contribution

It introduces a Fourier-Bessel basis approach for susceptibility analysis in rotating finite-size systems, addressing noninvariance issues and deriving resummation formulas.

Findings

Rotational effects significantly influence meson, baryon number, and topological susceptibilities.

The Fourier-Bessel basis effectively captures noninvariant radial translation properties.

Results provide benchmarks for future lattice QCD studies in rotating frames.

Abstract

We analyze various two-point correlation functions of fermionic bilinears in a rotating finite-size cylinder at finite temperatures, with a focus on susceptibility functions. Due to the noninvariance of radial translation, the susceptibility functions are constructed using the Dirac propagator in the Fourier-Bessel basis instead of the plane-wave basis. As a specific model to demonstrate the susceptibility functions in an interacting theory, we employ the two-flavor Nambu-Jona-Lasinio model. We show that the incompatibility between the mean-field analysis and the Fourier-Bessel basis is evaded under the local density approximation, and derive the resummation formulas of susceptibilities with the help of a Ward-Takahashi identity. The resulting formulation reveals the rotational effects on meson, baryon number, and topological susceptibilities, as well as the moment of inertia. Our results may serve a useful benchmark for future lattice QCD simulations in rotating frames.