Two-Gluon Correlations in Heavy-Light Ion Collisions: Energy and Geometry Dependence, IR Divergences, and $k_T$-Factorization

Abstract

We study the properties of the cross section for two-gluon production in heavy-light ion collisions derived in our previous paper on the subject in the saturation/Color Glass Condensate framework. Concentrating on the energy and geometry dependence of the corresponding correlation functions we find that the two-gluon correlator is a much slower function of the center-of-mass energy than the one- and two-gluon production cross sections. The geometry dependence of the correlation function leads to stronger azimuthal near- and away-side correlations in the tip-on-tip U+U collisions than in the side-on-side U+U collisions, an exactly opposite behavior from the correlations generated by the elliptic flow of the quark-gluon plasma: a study of azimuthal correlations in the U+U collisions may thus help to disentangle the two sources of correlations. We demonstrate that the cross section for two-gluon production in heavy-light ion collisions contains a power-law infrared (IR) divergence even for fixed produced gluon momenta: while saturation effects in the target regulate some of the power-law IR-divergent terms in the lowest-order expression for the two-gluon correlator, other power-law IR-divergent terms remain, possibly due to absence of saturation effects in the dilute projectile. Finally we rewrite our result for the two-gluon production cross-section in a $k_T$-factorized form, obtaining a new factorized expression involving a convolution of one- and two-gluon Wigner distributions over both the transverse momenta and impact parameters. We show that the two-gluon production cross-section depends on two different types of unintegrated two-gluon Wigner distribution functions.

30 pages, 6 figures; v2: typos corrected, references added

References in corpus (26)

• The Color Glass Condensate
• Observation of long-range near-side angular correlations in proton-lead collisions at the LHC
• Universality of Unintegrated Gluon Distributions at small x
• NLO evolution of color dipoles
• Quark contribution to the small-$x$ evolution of color dipole
• Dihadron azimuthal correlations in Au+Au collisions at sqrt(s_NN)=200 GeV
• Triumvirate of Running Couplings in Small-x Evolution
• The ridge in proton-proton collisions at the LHC
• Long Range Correlations and the Soft Ridge in Relativistic Nuclear Collisions
• Explanation of systematics of CMS p+Pb high multiplicity di-hadron data at ${\sqrt{s}}_{\mathrm{NN}}=5.02$ TeV
• Evidence for BFKL and saturation dynamics from di-hadron spectra at the LHC
• Angular Correlations in Gluon Production at High Energy
• High energy factorization in nucleus-nucleus collisions
• Particle multiplicities in Lead-Lead collisions at the LHC from non-linear evolution with running coupling
• High energy factorization in nucleus-nucleus collisions II - Multigluon correlations
• Running coupling and power corrections in nonlinear evolution at the high--energy limit
• High energy factorization in nucleus-nucleus collisions III. Long range rapidity correlations
• Long Range Forward-Backward Correlations and the Color Glass Condensate
• Transverse nucleon structure and diagnostics of hard parton-parton processes at LHC
• One gluon, two gluon: multigluon production via high energy evolution
• Two-particle correlations in high energy collisions and the gluon four-point function
• Running Coupling Corrections to High Energy Inclusive Gluon Production
• On the long-range correlations in hadron-nucleus collisions
• Gluon Saturation Effects in Relativistic U+U Collisions
• BFKL Pomeron with massive gluons
• Inability to find justification of a $k_T$-factorization formula by following chains of citations

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• Non-eikonal corrections to multi-particle production in the Color Glass Condensate
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• When gluons go odd: how classical gluon fields generate odd azimuthal harmonics for the two-gluon correlation function in high-energy collisions
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• The Collectivity of Heavy Mesons in Proton-Nucleus Collisions
• Onset of the ridge structure in AA, pA and pp collisions
• Directed flow from C-odd gluon correlations at small $x$
• Particle correlations from the initial state
• Photon-jet ridge at RHIC and the LHC
• Does shape matter? v_2 vs eccentricity in small x gluon production
• Di-photon "Ridge" in p+p and p+A collisions at RHIC and the LHC
• Multiparticle production in proton-nucleus collisions beyond eikonal accuracy
• Correlations and the ridge in the Color Glass Condensate beyond the glasma graph approximation
• Multi-particle production in proton-nucleus collisions in the Color Glass Condensate
• Lensing Mechanism Meets Small-$x$ Physics: Single Transverse Spin Asymmetry in $p^{\uparrow }+p$ and $p^{\uparrow }+A$ Collisions
• Exploring the Collective Phenomenon at the Electron-Ion Collider
• Bose enhancement, the Liouville effective action and the high multiplicity tail in p-A collisions
• On the rapidity dependence of the average transverse momentum in hadronic collisions
• Angular correlations in pA collisions from CGC: multiplicity and mean transverse momentum dependence of $v_2$
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• Ultracentral Collisions of Small and Deformed Systems at RHIC: $UU$, $dAu$, ${}^{9}BeAu$, ${}^{9}Be{}^{9}Be$, ${}^{3}He{}^{3}He$, and ${}^{3}HeAu$ Collisions
• CGC for Ultra-Peripheral Pb+Pb Collisions at the Large Hadron Collider: a more realistic calculation
• Double inclusive small-x gluon production and their azimuthal correlations in a biased ensemble
• Two-Particle Correlations in Heavy-Light Ion Collisions
• Anisotropic flow and the valence quark skeleton of hadrons