Rapidity spectra in high-energy collisions and longitudinal nuclear suppression from nonadditive statistics

TL;DR

The paper tackles the problem of longitudinal nuclear suppression in high-energy collisions by combining numerical simulations with analytical nonadditive-statistics models. It derives a closed-form rapidity spectrum from a nonadditive Tsallis single-particle distribution using Mellin-Barnes techniques and hypergeometric functions, and develops a nonadditive Boltzmann transport equation in the relaxation-time approximation to model medium-induced evolution, yielding a zeroth-order solution that describes data with physically meaningful parameters. The NABTE framework predicts a power-law stationary state and links parameter evolution to Lévy-walk-like diffusion, while the Tsallis-based formula captures the forward/backward rapidity trends; together, they explain NA61/NA49 $\pi^-$ data at $ msnn = 6.3$–$17.3$ GeV. The work also identifies discrepancies among common event generators (EPOS vs FTFP$_{BERT}$/HIJING) that motivate further investigation and outlines directions for future refinement, including higher-order NABTE corrections and more detailed medium interactions.

Abstract

We investigate the longitudinal nuclear suppression factor defined by a scaled ratio of rapidity distributions. To study this experimental observable, we describe three approaches involving numerical and analytical calculations. We first approach this problem by conducting model studies using EPOS, FTFP$_{BERT}$, and HIJING, and notice that while EPOS shows a decreasing trend of this ratio at forward/backward rapidities, the latter two model calculations display an increment of the ratio. The analytical approaches involve, first, the quasi-exponential distribution obtained from the Tsallis statistics, and second, the nonadditive Boltzmann transport equation in the relaxation time approximation. We notice that our analytical results satisfactorily describe NA61 experimental data (for $\sqrt{s_{NN}}$=6.3, 7.6, 8.8, 12.3, and 17.3 GeV) for the negatively charged pions.

Figures (11)

• Figure 1: Nuclear suppression factor of the $\pi^{-}$ at $\sqrt{s}$=7.6 GeV calculated from EPOS.
• Figure 2: Nuclear suppression factor of the $\pi^{-}$ at $\sqrt{s}$=7.6 GeV calculated from FTFP$_{\text{BERT}}$.
• Figure 3: The longitudinal nuclear suppression factor of the $\pi^{-}$ at $\sqrt{s}$=17.3 GeV calculated from EPOS.
• Figure 4: The longitudinal nuclear suppression factor of the $\pi^{-}$ at $\sqrt{s}$=17.3 GeV calculated from FTFP$_{\text{BERT}}$.
• Figure 5: The longitudinal nuclear suppression factor of the $\pi^{-}$ at $\sqrt{s}$=17.3 GeV calculated from HIJING.