Scaling violations: Connections between elastic and inelastic hadron scattering in a geometrical approach

Abstract

Starting from a short range expansion of the inelastic overlap function, capable of describing quite well the elastic pp and pp scattering data, we obtain extensions to the inelastic channel, through unitarity and an impact parameter approach. Based on geometrical arguments we infer some characteristics of the elementary hadronic process and this allows an excellent description of the inclusive multiplicity distributions in pp and pp collisions. With this approach we quantitatively correlate the violations of both geometrical and KNO scaling in an analytical way. The physical picture from both channels is that the geometrical evolution of the hadronic constituents is principally reponsible for the energy dependence of the physical quantities rather than the dynamical (elementary) interaction itself.

A multiparton model for pp / p$\bar{p}$ inelastic scattering

“…In previous studies, the average multiplicity data in e − e + annihilations were fitted by Eq. (11), giving A = 0.198 ± 0.004 (χ 2 /N DF = 1.7) in the interval 10 GeV < √ s ≤ 183 GeV [5], and A = 0.200±0.006 (χ 2 /N DF = 0.94) for the set in the interval 10 GeV < √ s ≤ 200 GeV [3]. The parameter A is essencially the same in both fits.…”

“…We assume that the i strings formed in the collision are fused to from just one larger final chain and that this final fused chain decays producing particles and, for each value of b, follows a gamma distribution normalized to 2 [5] …”

“…which is characterized by the parameter k. Experimental data for e − e + multiplicity distributions, covering the interval 22.0 GeV ≤ √ s ≤ 161 GeV, were fitted obtaining k=10.775 ± 0.064 (χ 2 /N DF = 2.61) [5]. The gamma distribution is know to arise as a limiting form (with certain correction terms which depend on details of the evolution equation) for the parton number variable, when the dynamical theory (as in QCD case) allows each existing parton to act as a source to emit additional partons (parton branching) [6].…”

A new scheme for calculation of the multiplicity distributions in hadronic interactions

“…A geometrical approach has been discussed in reference [3] and, for completeness and especially to define the notation, we shall briefly review the main points here. In this approach hadrons are drawn as composite objects with some internal structure and the impact parameter formalism is used.…”

“…The idea of string formation for multiparticle production is similar to Lund model [1] and it has been applied also for hadron-hadron collisions by Rio de Janeiro group [2]. Two fit values of A = 0.258 and A = 0.198 have been obtained in the previous study [3], the first one giving a better account of lower energy data whereas the second one higher energy data. However, when the formalism is applied to multiplicity distribution in √ s = 546 GeVpp collisions, the latter, which was expected to be more appropriate for this case, yielded a too narrow distribution, whereas the former, which overestimate the multiplicity in high energy region, gave a better account of the existing data [4].…”