Analyses of whole transverse momentum distributions in pp̄ and pp collisions by using a modified version of Hagedorn’s formula

Abstract

To describe the transverse momentum [Formula: see text] distribution of charged hadrons at 1.96 TeV observed by the CDF collaboration, we propose a formula with two components, namely, hadron gas distributions and inverse power laws inspired by QCD calculus. The new formula based on a formula by Hagedorn in 1983 includes an integration of pseudo-rapidity [Formula: see text]. 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 the use of the modified version of Hagedorn’s formula are compared with those by the use of the two-component model proposed by Bylinkin, Rostovtsev and Ryskin (BRR). We investigate whether or not there is an interrelation among our modified formula, a formula proposed by ATLAS collaboration, and the BRR formula. Moreover, formulas for the [Formula: see text] distributions in the nonextensive approach are discussed.