The Novel Scaling of Tsallis Parameters from the Transverse Momentum Spectra of Charged Particles in Heavy-Ion Collisions

Abstract

The transverse momentum (pT) spectra of charged particles measured in Au + Au collisions from the beam energy scan (BES) program, Cu + Cu collisions at sNN=62.4, 200 GeV at the RHIC and Pb + Pb, Xe + Xe collisions at the LHC are investigated in the framework of Tsallis thermodynamics. The theory can describe the experimental data well for all the collision systems, energies and centralities investigated. The collision energy and centrality dependence of the Tsallis distribution parameters, i.e., the temperature T and the nonextensive parameter q, for the A + A collisions are also studied and discussed. A novel scaling between the temperature divided by the natural logarithm of collision energy (T/lns) and the nonextensive parameter q is presented.

Quantifying the underlying event: investigating angular dependence of multiplicity classes and transverse-momentum spectra in high-energy pp collisions at LHC energies

“…We note Tsallis entropy formalism has the freedom to use various formulae for such fit procedures. Moreover, choosing a particular form of Tsallis entropy formalism based on precision is also not straightforward [50,51] and further formulae can be applied taking into account the flavour fraction and degeneracy [52].…”

On the Convergence of an Adaptive Momentum Method for Adversarial Attacks

“…There are two proposals for momentum parameter to guarantee convergence, but completely opposite. Specifically, one assumes a strictly monotonically decreasing schedule (β 1,t−1 > β 1,t , β 1,t → 0) (Kingma and Ba 2015) (Reddi, Kale, and Kumar 2018) (Wang et al 2020) (Zhuang et al 2020) while the other demands an increasing schedule (β 1,t−1 < β 1,t , β 1,t → 1) (Ghadimi, Feyzmahdavian, and Johansson 2015) (Yang, Lin, and Li 2016) (Tao et al 2021) (Li, Liu, and Orabona 2022), which not only creates a theory-practice gap but also causes confusion when selecting hyper-parameters in practice. On the other hand, (Ghadimi, Feyzmahdavian, and Johansson 2015) utilizes a constant momentum parameter, which guarantees the convergence of HB, but relies on strong assumptions of strong convexity and smoothness in the objective function.…”

Proton-Proton Collisions in View of Thermo-Statistical Approach

“…These could also indicate the excitation degree of the interacting system [3]. To describe the transverse momentum spectra of the particles, numerous theoretical models have been considered such as the Tsallis statistics which has recognized much attention due to its successful applications to the particle transverse momentum spectra and the pseudo-rapidity distribution of charged particles produced in high energy proton-proton and heavy-ion collisions [4] [5] [6] [7].…”