Impact of Thermal Cutoff Modifications on Thermodynamics and Net-Baryon Number Fluctuations in the (P)NJL Model: An RG-Consistency Perspective

Abstract We investigate the thermodynamic properties, chiral phase transitions, and net-baryon number fluctuations in the two-flavor NJL and PNJL models from the perspective of renormalization group (RG) consistency. In effective field theories with a fixed vacuum cutoff $\Lambda_0$, finite-temperature medium effects require that high-momentum thermal fluctuations above the Matsubara scale ($\Lambda \gtrsim \pi T$) be adequately accounted for, which is practically achieved by taking an unrestricted thermal momentum integration ($\Lambda_T = k\Lambda_0 \to \infty$). This treatment partially restores RG consistency and ensures proper convergence toward the Stefan-Boltzmann limit at high temperatures. To systematically assess the regularization artifacts arising from finite thermal cutoffs commonly used in the literature, we introduce the truncation factor $k$ not as an additional free model parameter, but as an exploratory diagnostic tool mapping the phase-space transition between the strictly truncated scheme ($k=1$) and the unregularized thermal continuum ($k \to \infty$). Our analysis shows that while taking $k \to \infty$ smoothly resolves causality violations ($v_s^2 > 1$) in the standard NJL model by binding the speed of sound to the conformal limit $1/3$, the PNJL model exhibits a more intricate, non-monotonic sensitivity to $k$, wherein intermediate truncation scales ($k \approx 3$) lead to a temporary overshoot of the conformal bound due to the non-trivial competition between Polyakov-loop confinement dynamics and thermal integration boundaries. Furthermore, while the unregularized ($k \to \infty$) PNJL framework significantly improves the qualitative description of net-baryon number fluctuations ($\kappa\sigma^2$) relative to lattice QCD data at vanishing chemical potential, the pronounced amplification of fluctuation extrema at high baryon density underscores the model's sensitivity to high-momentum thermal modes. This work clarifies the role of thermal regularization and provides critical insights into the interplay between confinement dynamics and thermal boundaries in effective chiral theories.