Banghui Hua | Searcharxiv

arXiv2026

Confinement and Chiral Phase Transitions: The Role of Polyakov Loop Kinetics Terms

We studied a crucial but often oversimplified ingredient in predicting gravitational-wave signals from QCD-type phase transitions: the kinetic term of the Polyakov loop. For the first time, we derive this term from first principles in finite-temperature pure SU(3) Yang-Mills theory, incorporating a field-dependent renormalization factor--a calculation we also extend to theories with more colors. Employing this derived kinetic term alongside three commonly-used effective potentials (the Haar-measure, polynomial, and quasi-particle models), we demonstrate that it substantially modifies the predicted GW energy spectrum from confinement transitions by 1-2 orders of magnitude. Based on this, we provide the first complete analysis of the chiral transition within the Polyakov-Nambu-Jona-Lasinio (PNJL) framework, described by the quark condensate. Our results reveal a clear dichotomy: while the Polyakov-loop kinetic term critically shapes GWs from confinement transitions, it has a negligible impact on the dynamics of the chiral transition, which is dominated by fermion condensation effects.

hep-ph↗

arXiv2025

VacuumTunneling: A package to solve bounce equation with renormalization factor

The Vacuum tunneling rate $\Gamma$ from the effective action is a key to studying the cosmological first-order phase transition(FOPT). One solid way to compute the $\Gamma$ is to start with the derivative expansion of the effective action and solve the bounce equation numerically. In this process, the renormalization factor $Z$ of the tunneling field may play a center rule, which is not considered in existing packages. Therefore, we present a \texttt{Mathematica} package \vt to compute the bounce action with or without the renormalization factor. Applying the \vt package, we find that the presence of $Z$ has a significant impact on the action, as well on the tunneling path. We provide some concrete examples to demonstrate the difference between the solution with and without the renormalization factor, both in the action and tunneling path. This package is based on the modified shooting and path deformation method. We also made some optimizations for the super-cooling phase transition(thick wall scenario), in which other numerical package works poorly. This package works as long as the expressions can give values of the potential and the renormalization at a certain field point. This means the input potential and the renormalization can be merely numerical quantities without analytical expressions. The computation time can be as short as 1 second in single-field tunneling and several seconds in multi-field cases.

hep-ph↗