Instantons in the saturation environment

Dmitri Kharzeev, Yuri V. Kovchegov*, Eugene Levin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


We show that instanton calculations in QCD become theoretically well defined in the gluon saturation environment which suppresses large-size instantons. The effective cutoff scale is determined by the inverse of the saturation scale. We concentrate on two most important cases: the small-x tail of a gluon distribution of a high-energy hadron or a large nucleus and the central rapidity region in a high-energy hadronic or heavy-ion collision. In the saturation regime the gluon density in a single large ultrarelativistic nucleus is high and gluonic fields are given by the classical solutions of the equations of motion. We show that these strong classical fields do not affect the density of instantons in the nuclear wave function compared to the instanton density in the vacuum. A classical solution with nontrivial topological charge is found for the gluon field of a single nucleus at the lowest order in the instanton perturbation theory. In the case of ultrarelativistic heavy-ion collisions a strong classical gluonic field is produced in the central rapidity region. We demonstrate that this field introduces a suppression factor of exp{-cρr nuclei, τ is the proper time and c ≈ 1 is the gluon liberation coefficient. This factor suggests that gluonic saturation effects at the early stages of nuclear collisions regulate the instanton-size distribution in the infrared region and make the instanton density finite by suppressing large-size instantons.

Original languageEnglish
Pages (from-to)745-769
Number of pages25
JournalNuclear Physics A
Issue number3-4
StatePublished - 11 Mar 2002


FundersFunder number
U.S. Department of EnergyDE-AC02-98CH10886, DE-FG03-97ER41014
Bonfils-Stanton Foundation9800276
Israel Academy of Sciences and Humanities
Israel Science Foundation


    • Heavy-ion collisions
    • Infrared safety
    • Parton saturation
    • QCD instantons


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