From Tsallis Scheme of high-energy pp collisions to Generalized Multiplicity Distribution with Modified Combinants

M Ghaﬀar,H W Ang,A H Chan,A Yang,S.C.C Ng,C.H Oh,A.H Chan,K.K Phua,W.Y Wang

doi:10.1051/epjconf/201920609008

M Ghaﬀar, H W Ang + Show 7 more

Open Access

https://doi.org/10.1051/epjconf/201920609008

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Abstract

An analysis of the generalized multiplicity distribution, (GMD), has been made in high energy pp collisions. An attempt is made to reconcile the generating function of GMD with Tsallis statistics in order to find an interpretation of Tsallis parameter,(q). The modified combinants, (Cj’s), for both GMD and NBD are obtained using the generating functions of these distributions. Our results show that single NBD does not lead to the oscillatory behaviour of the observed Cj. However, for GMD the corresponding Cj not only oscillate but also show the fading-down feature of the experimentally observed Cj. This could help in future to analyse the physical process which is responsible for these oscillations.

Highlights

Long range interactions make standard statistical mechanics non-extensive
After the work of Bediaga et al [1] and Beck [2], Tsallis statistics extension to hadronic collisions become in use as it gave the good fit for the hadronic productions in e+e− annihilation
An attempt was made to cast the generating function of GMD in an attempt to reconcile it with Tsallis statistics, and to hypothesize on the physical interpretation of the q-parameter in this specific context

Summary

Introduction

Long range interactions make standard statistical mechanics non-extensive. After the work of Bediaga et al [1] and Beck [2], Tsallis statistics extension to hadronic collisions become in use as it gave the good fit for the hadronic productions in e+e− annihilation. We can cast the lowest order hard-scattering integral of transverse momentum spectra in high-energy pp collisions in the Tsallis non-extensive form as [5]. The parameter q is the Tsallis parameter and is related to the power index n of the spectrum while the parameter T is related to the average transverse momentum, (pT ). The Tsallis nonextensive distribution has been used for the description of transverse momenta of secondary particles produced in pp collisions and gives excellent fits to the transverse momentum distributions by various collaborations at the LHC as shown in Fig. 1 [5]

Connection between Tsallis approach and GMD

Modified Combinants and comparison between NBD and GMD

Remarks