McLerran–Venugopalan model

McLerran–Venugopalan model
Name	McLerran–Venugopalan model
Field	Theoretical physics
Introduced	1993
Creators	Larry McLerran; Raju Venugopalan
Related	Color glass condensate; Quantum chromodynamics; Saturation physics

McLerran–Venugopalan model. The McLerran–Venugopalan model was introduced to describe high-energy Large Hadron Collider and Relativistic Heavy Ion Collider collisions in terms of dense gluon fields, and it provides a semiclassical framework linking Quantum chromodynamics with observable multiparticle production; its origin traces to work by Larry McLerran and Raju Venugopalan motivated by data from Hadron Collider experiments and theoretical developments at institutions like Brookhaven National Laboratory and CERN. The model has been influential in bridging concepts used by researchers affiliated with Stanford University, Massachusetts Institute of Technology, and Columbia University with evolution equations studied by theorists associated with Brookhaven National Laboratory, Fermilab, and Yale University.

Overview and physical motivation

The model arose to explain gluon saturation phenomena suggested by measurements at Hadron-Electron Ring Accelerator and by theoretical analyses connected to HERA and SPS (accelerator) results, building on parton model intuition developed by researchers at University of California, Berkeley and Caltech, and motivated by the need to reconcile high multiplicity events seen at RHIC and LHC with perturbative methods advocated by groups at Institute for Advanced Study and Perimeter Institute. It treats fast-moving valence color charges associated with nuclei studied at Brookhaven National Laboratory and CERN as static sources for low-x gluon fields, an approach influenced by semiclassical techniques used in analyses at Princeton University and Rutgers University. The physical picture informed subsequent experimental programs at CERN and Brookhaven National Laboratory and theoretical efforts linked to SLAC National Accelerator Laboratory, Jefferson Lab, and University of Tokyo.

Theoretical formulation

The theoretical formulation posits random classical color sources representing valence partons inspired by work at Yale University and Columbia University, where these color charge densities are treated using Gaussian correlators in a framework developed contemporaneously with research at MIT and Caltech; the formulation employs the Yang–Mills equations central to Quantum chromodynamics research at CERN and mathematical techniques explored at Princeton University and Harvard University. The model uses light-cone coordinates popularized by authors from University of Pennsylvania and University of Chicago, and introduces a separation scale between fast and slow modes paralleling ideas discussed at Institute for Advanced Study and Perimeter Institute, with renormalization concepts influenced by studies at Stony Brook University and Brown University.

Classical color sources and gauge fields

In this approach valence partons from nuclei studied at Brookhaven National Laboratory are modelled as static random color charge densities, producing classical gauge fields obtained by solving the Yang–Mills equations in covariant or light-cone gauge as analyzed by theorists at Harvard University and Columbia University; these classical fields generate gluon distributions analogous to those explored in lattice studies at CERN and Brookhaven National Laboratory. The color charge correlators are typically taken Gaussian following prescriptions similar to methods used at Yale University and Rutgers University, and the resulting gauge potentials mirror solutions investigated by researchers at Stanford University and University of California, Berkeley.

Gluon distribution and saturation scale

The model predicts an enhanced gluon occupation number and defines a saturation momentum scale Q_s that grows with nuclear size and energy, a concept that connected researchers at CERN and Brookhaven National Laboratory with phenomenology pursued at Jefferson Lab and SLAC National Accelerator Laboratory; Q_s serves as a semihard scale enabling weak-coupling treatments favored in analyses at MIT and Caltech. Computations of unintegrated gluon distributions within this framework informed comparisons with deep inelastic scattering data from HERA and with particle production measurements at RHIC and LHC, guiding experimental programs at Brookhaven National Laboratory, CERN, and Fermilab.

Extensions and phenomenological applications

Extensions include running-coupling improvements, impact-parameter dependent implementations, and inclusion of fluctuations developed by groups at University of Washington and Institut de Physique Théorique, which enabled applications to multiplicity distributions, ridge correlations, and nuclear modification factors measured at RHIC and LHC and analyzed by collaborations such as ALICE (A Large Ion Collider Experiment), ATLAS, CMS, and PHENIX. The framework has been coupled to hydrodynamic simulations originating in work at Duke University and Bielefeld University to model heavy-ion evolution, and used in predictions for future programs at facilities like Electron-Ion Collider and proposals associated with FAIR (facility).

Relation to color glass condensate and evolution equations

The McLerran–Venugopalan model provides the initial condition for the color glass condensate effective theory and interfaces with renormalization-group evolution equations such as the Jalilian-Marian–Iancu–McLerran–Weigert–Leonidov–Kovner hierarchy and the Balitsky–Kovchegov equation, topics developed by researchers at Institute for Advanced Study, Brookhaven National Laboratory, and CERN and expanded upon by theorists affiliated with University of Regensburg and Università di Roma. Its Gaussian source approximation is generalized by quantum evolution via small-x evolution studied at Saclay, Hamburg, and Trieste, connecting the model to global analyses performed by collaborations at CERN and Jefferson Lab.

Category:Quantum chromodynamics