Abstract
In high energy proton-nucleus collisions, the gluon saturation effects from the nucleus are fully incorporated into the light-like Wilson lines. The gluon saturation effects from the proton, which are anticipated to be important either in the extreme high energy limit or towards the dense-dense (nucleus-nucleus) collision regimes, have been studied perturbatively within the Color Glass Condensate effective theory in previous papers of this series. A configuration-by-configuration expression for the single inclusive semi-hard gluon production including the first saturation correction was obtained. In this paper, we perform ensemble averaging in the McLerran-Venugopalan model and the Dipole Approximation. We find that, in the saturation correction, the effects of the initial state interactions are negligible while the final state interactions play most important role and give a positive-valued contribution to the semi-hard gluon spectrum. Furthermore, we show that the single gluon spectrum scales approximately 1/\( {k}_{\perp}^4 \) at small k⊥, suggesting that a resummation of higher order saturation corrections is required to regulate the infrared region of the gluon spectrum.
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References
M. Li and V.V. Skokov, First saturation correction in high energy proton-nucleus collisions. Part I. Time evolution of classical Yang-Mills fields beyond leading order, JHEP 06 (2021) 140 [arXiv:2102.01594] [INSPIRE].
M. Li and V.V. Skokov, First saturation correction in high energy proton-nucleus collisions. Part II. Single inclusive semi-hard gluon production, JHEP 06 (2021) 141 [arXiv:2104.01879] [INSPIRE].
L.D. McLerran, The color glass condensate and small x physics: four lectures, Lect. Notes Phys. 583 (2002) 291 [hep-ph/0104285] [INSPIRE].
E. Iancu and R. Venugopalan, The color glass condensate and high-energy scattering in QCD, in Quark-gluon plasma 4, R.C. Hwa and X.-N. Wang eds., World Scientific, Singapore (2003) [hep-ph/0303204] [INSPIRE].
Y.V. Kovchegov and E. Levin, Quantum chromodynamics at high energy, Cambridge University Press, Cambridge U.K. (2012) [INSPIRE].
A. Kovner and M. Lublinsky, Angular correlations in gluon production at high energy, Phys. Rev. D 83 (2011) 034017 [arXiv:1012.3398] [INSPIRE].
L.D. McLerran and R. Venugopalan, Computing quark and gluon distribution functions for very large nuclei, Phys. Rev. D 49 (1994) 2233 [hep-ph/9309289] [INSPIRE].
L.D. McLerran and R. Venugopalan, Gluon distribution functions for very large nuclei at small transverse momentum, Phys. Rev. D 49 (1994) 3352 [hep-ph/9311205] [INSPIRE].
A. Dumitru, V. Skokov and T. Stebel, Subfemtometer scale color charge correlations in the proton, Phys. Rev. D 101 (2020) 054004 [arXiv:2001.04516] [INSPIRE].
A. Dumitru and R. Paatelainen, Sub-femtometer scale color charge fluctuations in a proton made of three quarks and a gluon, Phys. Rev. D 103 (2021) 034026 [arXiv:2010.11245] [INSPIRE].
A. Dumitru, H. Mäntysaari and R. Paatelainen, Color charge correlations in the proton at NLO: Beyond geometry based intuition, Phys. Lett. B 820 (2021) 136560 [arXiv:2103.11682] [INSPIRE].
A. Kovner and A.H. Rezaeian, Double parton scattering in the CGC: Double quark production and effects of quantum statistics, Phys. Rev. D 96 (2017) 074018 [arXiv:1707.06985] [INSPIRE].
A. Krasnitz and R. Venugopalan, The initial gluon multiplicity in heavy ion collisions, Phys. Rev. Lett. 86 (2001) 1717 [hep-ph/0007108] [INSPIRE].
A. Krasnitz, Y. Nara and R. Venugopalan, Coherent gluon production in very high-energy heavy ion collisions, Phys. Rev. Lett. 87 (2001) 192302 [hep-ph/0108092] [INSPIRE].
T. Lappi, Production of gluons in the classical field model for heavy ion collisions, Phys. Rev. C 67 (2003) 054903 [hep-ph/0303076] [INSPIRE].
J.P. Blaizot, T. Lappi and Y. Mehtar-Tani, On the gluon spectrum in the glasma, Nucl. Phys. A 846 (2010) 63 [arXiv:1005.0955] [INSPIRE].
J. Jalilian-Marian and Y.V. Kovchegov, Saturation physics and deuteron-Gold collisions at RHIC, Prog. Part. Nucl. Phys. 56 (2006) 104 [hep-ph/0505052] [INSPIRE].
Y.V. Kovchegov and A.H. Mueller, Gluon production in current nucleus and nucleon - nucleus collisions in a quasiclassical approximation, Nucl. Phys. B 529 (1998) 451 [hep-ph/9802440] [INSPIRE].
B.Z. Kopeliovich, A.V. Tarasov and A. Schafer, Bremsstrahlung of a quark propagating through a nucleus, Phys. Rev. C 59 (1999) 1609 [hep-ph/9808378] [INSPIRE].
A. Kovner and U.A. Wiedemann, Eikonal evolution and gluon radiation, Phys. Rev. D 64 (2001) 114002 [hep-ph/0106240] [INSPIRE].
A. Dumitru and L.D. McLerran, How protons shatter colored glass, Nucl. Phys. A 700 (2002) 492 [hep-ph/0105268] [INSPIRE].
J.P. Blaizot, F. Gelis and R. Venugopalan, High-energy pA collisions in the color glass condensate approach. 1. Gluon production and the Cronin effect, Nucl. Phys. A 743 (2004) 13 [hep-ph/0402256] [INSPIRE].
H. Kowalski and D. Teaney, An impact parameter dipole saturation model, Phys. Rev. D 68 (2003) 114005 [hep-ph/0304189] [INSPIRE].
H. Mäntysaari and B. Schenke, Evidence of strong proton shape fluctuations from incoherent diffraction, Phys. Rev. Lett. 117 (2016) 052301 [arXiv:1603.04349] [INSPIRE].
H. Fujii, Penetration of a high-energy \( Q\overline{Q} \) bound state through SU(N) color background, Nucl. Phys. A 709 (2002) 236 [nucl-th/0205066] [INSPIRE].
J.P. Blaizot, F. Gelis and R. Venugopalan, High-energy pA collisions in the color glass condensate approach. 2. Quark production, Nucl. Phys. A 743 (2004) 57 [hep-ph/0402257] [INSPIRE].
K. Fukushima and Y. Hidaka, Light projectile scattering off the color glass condensate, JHEP 06 (2007) 040 [arXiv:0704.2806] [INSPIRE].
K. Fukushima and Y. Hidaka, General formulae for dipole Wilson line correlators with the Color Glass Condensate, JHEP 11 (2017) 114 [arXiv:1708.03051] [INSPIRE].
J.L. Albacete, N. Armesto, J.G. Milhano, P. Quiroga-Arias and C.A. Salgado, AAMQS: a non-linear QCD analysis of new HERA data at small-x including heavy quarks, Eur. Phys. J. C 71 (2011) 1705 [arXiv:1012.4408] [INSPIRE].
J.L. Albacete, A. Dumitru, H. Fujii and Y. Nara, CGC predictions for p + Pb collisions at the LHC, Nucl. Phys. A 897 (2013) 1 [arXiv:1209.2001] [INSPIRE].
T. Lappi and H. Mäntysaari, Single inclusive particle production at high energy from HERA data to proton-nucleus collisions, Phys. Rev. D 88 (2013) 114020 [arXiv:1309.6963] [INSPIRE].
J. Jalilian-Marian and Y.V. Kovchegov, Inclusive two-gluon and valence quark-gluon production in DIS and pA, Phys. Rev. D 70 (2004) 114017 [Erratum ibid. 71 (2005) 079901] [hep-ph/0405266] [INSPIRE].
F. Dominguez, C. Marquet, A.M. Stasto and B.-W. Xiao, Universality of multiparticle production in QCD at high energies, Phys. Rev. D 87 (2013) 034007 [arXiv:1210.1141] [INSPIRE].
Y.V. Kovchegov and D.E. Wertepny, Long-range rapidity correlations in heavy-light ion collisions, Nucl. Phys. A 906 (2013) 50 [arXiv:1212.1195] [INSPIRE].
T. Altinoluk, N. Armesto, A. Kovner and M. Lublinsky, Double and triple inclusive gluon production at mid rapidity: quantum interference in p-A scattering, Eur. Phys. J. C 78 (2018) 702 [arXiv:1805.07739] [INSPIRE].
P. Agostini, T. Altinoluk and N. Armesto, Multi-particle production in proton-nucleus collisions in the color glass condensate, Eur. Phys. J. C 81 (2021) 760 [arXiv:2103.08485] [INSPIRE].
T. Lappi, Wilson line correlator in the MV model: relating the glasma to deep inelastic scattering, Eur. Phys. J. C 55 (2008) 285 [arXiv:0711.3039] [INSPIRE].
S. Schlichting and V. Skokov, Saturation corrections to dilute-dense particle production and azimuthal correlations in the color glass condensate, Phys. Lett. B 806 (2020) 135511 [arXiv:1910.12496] [INSPIRE].
B. Schenke, P. Tribedy and R. Venugopalan, Fluctuating Glasma initial conditions and flow in heavy ion collisions, Phys. Rev. Lett. 108 (2012) 252301 [arXiv:1202.6646] [INSPIRE].
B. Schenke, P. Tribedy and R. Venugopalan, Event-by-event gluon multiplicity, energy density, and eccentricities in ultrarelativistic heavy-ion collisions, Phys. Rev. C 86 (2012) 034908 [arXiv:1206.6805] [INSPIRE].
T. Altinoluk, A. Kovner, E. Levin and M. Lublinsky, Reggeon field theory for large Pomeron loops, JHEP 04 (2014) 075 [arXiv:1401.7431] [INSPIRE].
G.P. Lepage, A new algorithm for adaptive multidimensional integration, J. Comput. Phys. 27 (1978) 192 [INSPIRE].
T. Hahn, CUBA: A Library for multidimensional numerical integration, Comput. Phys. Commun. 168 (2005) 78 [hep-ph/0404043] [INSPIRE].
K. Dusling and R. Venugopalan, Azimuthal collimation of long range rapidity correlations by strong color fields in high multiplicity hadron-hadron collisions, Phys. Rev. Lett. 108 (2012) 262001 [arXiv:1201.2658] [INSPIRE].
K. Dusling and R. Venugopalan, Evidence for BFKL and saturation dynamics from dihadron spectra at the LHC, Phys. Rev. D 87 (2013) 051502 [arXiv:1210.3890] [INSPIRE].
K. Dusling and R. Venugopalan, Explanation of systematics of CMS p+Pb high multiplicity di-hadron data at \( {\sqrt{s}}_{\mathrm{NN}} \) = 5.02 TeV, Phys. Rev. D 87 (2013) 054014 [arXiv:1211.3701] [INSPIRE].
K. Dusling and R. Venugopalan, Comparison of the color glass condensate to dihadron correlations in proton-proton and proton-nucleus collisions, Phys. Rev. D 87 (2013) 094034 [arXiv:1302.7018] [INSPIRE].
F. Salazar, B. Schenke and A. Soto-Ontoso, Accessing subnuclear fluctuations and saturation with multiplicity dependent J/ψ production in p+p and p+Pb collisions, arXiv:2112.04611.
L. McLerran and V. Skokov, Odd Azimuthal Anisotropy of the Glasma for pA Scattering, Nucl. Phys. A 959 (2017) 83 [arXiv:1611.09870] [INSPIRE].
Y.V. Kovchegov and V.V. Skokov, How classical gluon fields generate odd azimuthal harmonics for the two-gluon correlation function in high-energy collisions, Phys. Rev. D 97 (2018) 094021 [arXiv:1802.08166] [INSPIRE].
A. Metz and J. Zhou, Distribution of linearly polarized gluons inside a large nucleus, Phys. Rev. D 84 (2011) 051503 [arXiv:1105.1991] [INSPIRE].
F. Dominguez, J.-W. Qiu, B.-W. Xiao and F. Yuan, On the linearly polarized gluon distributions in the color dipole model, Phys. Rev. D 85 (2012) 045003 [arXiv:1109.6293] [INSPIRE].
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Li, M., Skokov, V.V. First saturation correction in high energy proton-nucleus collisions. Part III. Ensemble averaging. J. High Energ. Phys. 2022, 160 (2022). https://doi.org/10.1007/JHEP01(2022)160
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DOI: https://doi.org/10.1007/JHEP01(2022)160