(Multiple) Hard Parton Interactions in Heavy-Ion Collisions

Klaus Reygers Physikalisches Institut, Universität Heidelberg, Philosophenweg 12, 69120 Heidelberg, Germany

Abstract

Multiple hard interactions of partons in the same p + p(p̄) collision are a useful concept in the description of these collisions at collider energies. In particular, they play a crucial role for the understanding of the background (the so-called underlying event) in the reconstruction of jets. In nucleus-nucleus collisions multiple hard parton interactions and the corresponding production of mini-jets are expected to contribute significantly to the total particle multiplicity. In this article a brief overview of results on particle production at high-p_{T} in proton-proton and nucleus-nucleus at RHIC will be given. Moreover, the observed centrality dependence of the charged particle multiplicity in Au+Au collisions will be discussed in light of multiple partonic interactions.

1 Introduction

In a p + p(p̄) collision the location of a hard parton-parton scattering in which a parton with transverse momentum p_{T} ≳ 2 GeV/c is produced is well defined (Δr ∼ 1/p_{T} ≲ 0.1 fm in the plane transverse to the beam axis) and much smaller than the radius of proton (r ≈ 0.8 fm). Thus, it is expected that multiple hard parton scatterings can contribute incoherently to the total hard scattering cross section [1, 2]. When going from p+p to nucleus-nucleus (A+A) collisions and neglecting nuclear effects the increase in the number of hard scatterings is given by the nuclear geometry expressed via the nuclear overlap function T_{AB} [3]. For a given range of the impact parameter b of the A+A collisions the yield of produced partons with a transverse momentum p_{T} can thus be calculated from the corresponding cross section in p+p collisions according to

\frac{1}{N_{inel}^{A+A}} \frac{dN}{dp_{T}} |_{A+A} = \frac{∫ d^{2}b T_{AB}(b)}{∫ d^{2}b (1 − exp (−T_{AB} · σ_{inel}^{NN}))} · \frac{dσ}{dp_{T}} |_{p+p}  (1)

where N_{inel}^{A+A} denotes the total number of inelastic A+A collisions and σ_{inel}^{NN} the inelastic nucleonnucleon cross section. This corresponds to a scaling of the yield of produced high-p_{T} partons (and hence also of the yield of hadrons at high p_{T}) with the number of binary nucleon-nucleon collisions (N_{coll}). On the other hand, the yield of particles at low p_{T} ≲ 1 GeV/c is expected to scale with the number N_{part} of nucleons that suffered at least one inelastic nucleon-nucleon collision. Based on this separation of soft and hard processes the centrality dependence of the charged particle multiplicity in nucleus-nucleus collisions can be predicted.