Quasi-power laws in multiparticle production processes

TL;DR

This paper reviews the occurrence of quasi-power law distributions in multiparticle production, linking them to intrinsic fluctuations and Tsallis statistics, and discusses complex nonextensivity parameters to explain observed log-oscillations in high-energy collisions.

Contribution

It introduces the use of complex nonextensivity parameter q in Tsallis distribution to describe log-oscillations in high-energy particle data.

Findings

Quasi-power law distributions are prevalent in multiparticle production.

Tsallis distribution with complex q explains log-oscillations in data.

Intrinsic fluctuations may underlie the observed distributions.

Abstract

We review the ubiquitous presence in multiparticle production processes of quasi-power law distributions (i.e., distributions following pure power laws for large values of the argument but remaining finite, usually exponential, for small values). Special emphasis is placed on the conjecture that this reflects the presence in the produced hadronic systems of some intrinsic fluctuations. If described by parameter q they form, together with the scale parameter $T$ ("temperature"), basis of Tsallis distribution, ${f(X)\sim [1 - (1-q)X/T]^{1/(1-q)}}$, frequently used to describe the relevant distributions (the X being usually a transverse momentum). We discuss the origin of such quasi-power law behavior based on our experience with the description of multiparticle production processes. In particular, we discuss Tsallis distribution with complex nonextensivity parameter q and argue that it is needed to describe log-oscillations as apparently observed in recent data on large momentum distributions in very high energy p-p collisions.