Scattering from an external field in quantum chromodynamics at high energies: from foundations to interdisciplinary connections

Abstract

We review the factorization of the $S$-matrix elements in the context of particle scattering off an external field, which can serve as a model for the field of a large nucleus. The factorization takes the form of a convolution of light cone wave functions describing the physical incoming and outgoing states in terms of bare partons, and products of Wilson lines. The latter represent the interaction between the bare partons and the external field. Specializing to elastic scattering amplitudes of onia at very high energies, we introduce the color dipole model, which formulates the calculation of the modulus-squared of the wave functions in quantum chromodynamics with the help of a branching random walk, and the scattering amplitudes as observables on this classical stochastic process. Methods developed for general branching processes produce analytical formulas for the asymptotics of such observables, and thus enable one to derive exact large-rapidity expressions for onium-nucleus cross sections, from which electron-nucleus cross sections may be inferred.

101 pages, 23 figures. Lecture notes of the QCD Master Class, Saint-Jacut-de-la-Mer, September 2021. v2: Substantial revisions, mainly in the review section 2. Exposition of the main research results put forward in these notes unchanged. v3: Added some clarifications, minor corrections, and references

References in corpus (66)

• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• Operator expansion for high-energy scattering
• Quantum Chromodynamics and Other Field Theories on the Light Cone
• Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum
• Nonlinear Gluon Evolution in the Color Glass Condensate: I
• Saturation Effects in Deep Inelastic Scattering at low $Q^2$ and its Implications on Diffraction
• The Wilson renormalization group for low x physics: towards the high density regime
• Nonlinear Gluon Evolution in the Color Glass Condensate: II
• Unitarization of the BFKL Pomeron on a Nucleus
• The Renormalization Group Equation for the Color Glass Condensate
• The Intrinsic Glue Distribution at Very Small x
• Unitarity at small Bjorken x
• An Impact Parameter Dipole Saturation Model
• Exclusive diffractive processes at HERA within the dipole picture
• Geometric scaling for the total gamma^* p cross section in the low x region
• Shift in the velocity of a front due to a cut-off
• Saturation and BFKL dynamics in the HERA data at small x
• Unitarity and the BFKL Pomeron
• Non-Abelian Weizsacker-Williams field and a two-dimensional effective color charge density for a very large nucleus
• The Energy Dependence of the Saturation Momentum
• TikZ-Feynman: Feynman diagrams with TikZ
• Geometric Scaling above the Saturation Scale
• Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts
• Geometric scaling as traveling waves
• AAMQS: A non-linear QCD analysis of new HERA data at small-x including heavy quarks
• High energy pA collisions in the color glass condensate approach II. Quark production
• The Large Hadron-Electron Collider at the HL-LHC
• Saturation and Universality in QCD at small x
• Universal features of JIMWLK and BK evolution at small x
• Energy Dependence of the Cronin Effect from Non-Linear QCD Evolution
• Universal behavior of QCD amplitudes at high energy from general tools of statistical physics
• Small-x physics beyond the Kovchegov equation
• A phenomenological theory giving the full statistics of the position of fluctuating pulled fronts
• A Langevin equation for high energy evolution with pomeron loops
• Diffractive Dissociation Including Multiple Pomeron Exchanges in High Parton Density QCD
• Towards a symmetric approach to high energy evolution: generating functional with Pomeron loops
• A branching random walk seen from the tip
• Dipole factorization for DIS at NLO I: Loop correction to the photon to quark-antiquark light-front wave-functions
• A Linear Evolution for Non-Linear Dynamics and Correlations in Realistic Nuclei
• Froissart Bound from Gluon Saturation
• Statistics at the tip of a branching random walk and the delay of traveling waves
• No Froissart Bound from Gluon Saturation
• NLO corrections for the dipole factorization of DIS structure functions at low x
• A collinear model for small-x physics
• High energy scattering in Quantum Chromodynamics
• Saturation physics at HERA and RHIC: An unified description
• The high energy asymptotics of scattering processes in QCD
• Systematics of geometric scaling
• pT-Broadening and production processes versus dipole/quadrupole amplitudes at next-to-leading order
• Reggeon Field Theory for Large Pomeron Loops
• Exact solution and precise asymptotics of a Fisher-KPP type front
• QCD Reggeon Calculus From KLWMIJ/JIMWLK Evolution: Vertices, Reggeization and All
• OEDIPUS: Onium Evolution, Dipole Interaction and Perturbative Unitarisation Simulation
• Analytical asymptotics for hard diffraction
• Birdtracks for SU(N)
• Understanding Search Trees via Statistical Physics
• The case for an EIC Theory Alliance: Theoretical Challenges of the EIC
• Rapidity gap distribution in diffractive deep-inelastic scattering and parton genealogy
• Diffractive electron-nucleus scattering and ancestry in branching random walks
• The Description of $F_2$ at Very High Parton Densities
• Correlations in impact-parameter space in a hierarchical saturation model for QCD at high energy
• Lecture notes on "Quantum chromodynamics and statistical physics"
• Travelling waves and impact-parameter correlations
• How to generate the tip of branching random walks evolved to large times
• Gluon density fluctuations in dilute hadrons
• On Certain Two Dimensional Integrals that Appear In Conformal Field Theory