Fluctuations of the gluon distribution from the small-x effective action

Abstract

The computation of observables in high energy QCD involves an average over stochastic semiclassical small-x gluon fields. The weight of various configurations is determined by the effective action. We introduce a method to study fluctuations of observables, functionals of the small-x fields, which does not explicitly involve dipoles. We integrate out those fluctuations of the gluon field under which a given observable is invariant. Thereby we obtain the effective potential for that observable describing its fluctuations about the saddle point. We determine explicitly the effective potential for the covariant gauge gluon distribution both for the McLerran-Venugopalan (MV) model and for a (non-local) Gaussian approximation for the small-x effective action. This provides insight into the correlation of fluctuations of the number of hard gluons versus their typical transverse momentum. We find that the spectral shape of the fluctuations of the gluon distribution is fundamentally different in the MV model, where there is a pile-up of gluons near the saturation scale, versus the solution of the small-x JIMWLK renormalization group, which generates essentially scale invariant fluctuations above the absorptive boundary set by the saturation scale.

14 pages, 5 figures; v2: added section IV-A to discuss the parametric dependence of the selected fluctuations on the number of colors and on the thickness of the target; v3: version accepted to Phys. Rev. D

References in corpus (10)

• Event-by-event gluon multiplicity, energy density and eccentricities at RHIC and LHC
• Transverse-momentum-dependent gluon distributions from JIMWLK evolution
• Anisotropy of the semi-classical gluon field of a large nucleus at high energy
• Two-gluon correlations and initial conditions for small-x evolution
• Pomeron loop and running coupling effects in high energy QCD evolution
• Gluon TMDs in quarkonium production
• JIMWLK evolution of the odderon
• Liouville field theory for gluon saturation in QCD at high energy
• Fluctuations of the multiplicity of produced particles in onium-nucleus collisions
• Structure of chromomagnetic fields in the glasma

Cited by in corpus (8)

• Measuring the Weizsaecker-Williams distribution of linearly polarized gluons at an EIC through dijet azimuthal asymmetries
• Event engineering studies for heavy flavor production and hadronization in high multiplicity hadron-hadron and hadron-nucleus collisions
• Bose enhancement, the Liouville effective action and the high multiplicity tail in p-A collisions
• Transverse Energy-Energy Correlators in the Color-Glass Condensate at the Electron-Ion Collider
• Angular correlations in pA collisions from CGC: multiplicity and mean transverse momentum dependence of $v_2$
• The small-x gluon distribution in centrality biased pA and pp collisions
• The Weizsäcker-Williams distribution of linearly polarized gluons (and its fluctuations) at small x
• Double inclusive small-x gluon production and their azimuthal correlations in a biased ensemble