Progress in the Glauber model at collider energies

Abstract

We review the theoretical and experimental progress in the Glauber model of multiple nucleon and/or parton scatterings, after the last 10-15 years of operation with proton and nuclear beams at the CERN Large Hadron Collider (LHC) and with various light and heavy colliding ions at the BNL Relativistic Heavy Ion Collider (RHIC). The main developments and the state-of-the-art of the field are summarized. These encompass measurements of the inclusive inelastic proton and nuclear cross sections, advances in the description of the proton and nuclear density profiles and their fluctuations, inclusion of subnucleonic degrees of freedom, experimental procedures and issues related to the determination of the collision centrality, validation of the binary scaling prescription for hard scattering cross sections, and constraints on transport properties of quark-gluon matter from varying initialstate conditions in relativistic hydrodynamics calculations. These advances confirm the validity and usefulness of the Glauber formalism for quantitative studies of QCD matter produced in high-energy collisions of systems, from protons to uranium nuclei, of vastly different size.

Estimation of Impact Parameter and Transverse Spherocity in heavy-ion collisions at the LHC energies using Machine Learning

“…However, theoretical techniques, using the so-called Glauber formalism [42][43][44][45] have been developed to allow estimation of impact parameter and number of participants from experimental data, which consider multiple scattering of nucleons in nuclear targets. AMPT and PYTHIA8 (Angantyr) model internally depend on Glauber picture to model the early stage of heavy-ion collisions with a proper computation of the number of inelastic sub-collisions for a particular centrality class [46]. Here, we briefly describe how the total inelastic cross-section, number of binary collisions and number of participants are related to the impact parameter.…”

Centrality dependence of electroweak boson production in PbPb collisions at the LHC

“…see Ref. [9]). The centrality classification, which relies on measurements dominated by soft particle production, biases the average multiplicity of individual NN collisions, and hence can affect the normalization of yields of collisions dominated by hard processes due to a correlation between soft-and-hard particle production [21].…”

“…by comparing the measured yields of bosons of type i=W + , W − or Z in PbPb collisions to the yields measured in inelastic pp collisions scaled by the number of incoherent nucleonnucleon (NN) collisions for a given collision centrality. The determination of collision centrality as well as the calculation of the number of collisions N coll and the nuclear overlap T AA relies on the Glauber model [8,9]. In the Glauber model a nucleus-nucleus (AA) collision is approximated in the eikonal formalism, where nucleons in the projectile travel along straight lines and undergo multiple independent collisions with nucleons in the target using the inelastic NN cross section σ NN as inter-nucleon interaction strength, so that N coll = T AA σ NN .…”

Prospects for quarkonium studies at the high-luminosity LHC

“…However a study looking at the A dependence of F 2 measured by the NMC collaboration [628] found that data is best described with c values between 1.5 and 3 [629]. Another way to extrapolate the initial condition of a proton to a nucleus is to use, as in [630], the optical Glauber model, which assumes that at x = x 0 the high-energy probe scatters independently off the nucleons, which are distributed according to the standard Woods-Saxon distribution [631]. These two methods were shown to lead to results in good agreement with experimental data [632][633][634].…”

“…Namely, σ eff can be written as a function of the pp overlap T (b) at impact parameter b, computable from the transverse parton-density profile of the proton ρ(b) in a Glauber approach [631]. For conventional transverse parton ρ(b) distributions of the proton, such as those typically implemented in the modern pp Monte Carlo (MC) event generators pythia 8 [850], and herwig++ [851], one expects values of σ eff ≈ 15−25 mb.…”