Susceptibilities of rotating quark matter in Fourier-Bessel basis

TL;DR

This work develops a rotating-frame formalism for quark matter in a finite cylinder by employing a Dirac propagator in the Fourier-Bessel basis and analyzes fermionic two-point correlators within a two-flavor NJL model. It derives resummed meson susceptibilities via $\chi_\alpha(r;M(r)) = \chi_\alpha^{(1\text{-loop})}/(1 - G_\alpha \chi_\alpha^{(1\text{-loop})})$ and computes topological, baryon-number, and angular-momentum (moment of inertia) susceptibilities, all with a radial dependence $M(r)$ arising from the local density approximation. Ward-Takahashi identities are shown to constrain these susceptibilities, ensuring consistency with chiral and axial symmetries despite the radial inhomogeneity. Numerically, rotation amplifies thermal suppression for light mesons, induces pronounced radial structure near the boundary, and leaves the moment of inertia as a clear probe of chiral restoration and rotational effects. The results offer useful benchmarks for lattice QCD in rotating frames and illuminate how rotation reshapes QCD-like fluctuations in finite geometries.

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.

Figures (8)

• Figure 1: The rotational effect on the dynamical quark mass normalized by its vacuum value $M_{\rm vac}$: (a) the $r$-dependence of the dynamical quark mass at fixed temperatures, and (b) the numerical validation of the local density approximation.
• Figure 2: The temperature dependence of the dynamical quark mass at fixed $r$. The temperature is normalized by the pseudocritical temperature evaluated in the absence of rotation and boundary effects.
• Figure 3: The rotational effect on the meson susceptibilities normalized by the square of the pion decay constant ($f_\pi=92.4\,{\rm MeV}$). (a): the $r$-dependence of meson susceptibilities at fixed temperature and (b): the temperature dependence of meson susceptibilities at fixed $r$.
• Figure 4: The rotational effect on the topological susceptibility normalized by its vacuum value $\chi^{\rm vac}_{\rm top}$. (a): the $r$-dependence of $\chi_{\rm top}$ and (b): the temperature dependence of $\chi_{\rm top}$.
• Figure 5: The rotational effect on the baryon number susceptibility normalized by the square of the pion decay constant. (a): the $r$-dependence of $\chi_{\rm B}$ and (b): the temperature dependence of $\chi_{\rm B}$.