Analyses of whole transverse momentum distributions in $p\bar p$ and $pp$ collisions by using a modified version of Hagedorn's formula

TL;DR

This paper introduces a modified Hagedorn's formula to analyze transverse momentum distributions in proton-proton and proton-antiproton collisions across various energies, comparing it with other models and exploring their interrelations.

Contribution

The study presents a new modified version of Hagedorn's formula and demonstrates its effectiveness in describing experimental data, also highlighting its relation to other existing models.

Findings

Modified Hagedorn's formula fits the data well across energies.

The model shows consistency with other two-component models.

Interrelations among different formulas are established.

Abstract

To describe the transverse distribution of charged hadrons at 1.96 TeV observed by the CDF collaboration, we propose a formula with two component, namely, hadron gas distributions and inverse power laws. The data collected at 0.9, 2.76, 7, and 13 TeV by the ALICE, CMS, and ATLAS collaborations are also analyzed using various models including single component models as well as two component models. The results by using modified version of Hagedorn's formula are compared with those by using the two component model proposed by Bylinkin, Rostovtsev and Ryskin (BRR). Moreover, we show that there is an interesting interrelation among our the modified version of Hagedorn's formula, a formula proposed by ATLAS collaboration, and the BRR formula.