Abstract
For studying small-x gluon saturation in forward dijet production in high-energy dilute-dense collisions, the improved TMD (ITMD) factorization formula was recently proposed. In the Color Glass Condensate (CGC) framework, it represents the leading term of an expansion in inverse powers of the hard scale. It contains the leading-twist TMD factorization formula relevant for small gluon’s transverse momentum kt, but also incorporates an all-order resummation of kinematical twists, resulting in a proper matching to high-energy factorization at large kt. In this paper, we evaluate the accuracy of the ITMD formula quantitatively, for the case of quark dijet production in high-energy proton-proton(p+p) and proton-nucleus (p+A) collisions at LHC energies. We do so by comparing the quark-antiquark azimuthal angle ∆ϕ distribution to that obtained with the CGC formula. For a dijet with each quark momentum pt much larger than the target saturation scale, Qs, the ITMD formula is a good approximation to the CGC formula in a wide range of azimuthal angle. It becomes less accurate as the jet pt’s are lowered, as expected, due to the presence of genuine higher-twists contributions in the CGC framework, which represent multi-body scattering effects absent in the ITMD formula. We find that, as the hard jet momenta are lowered, the accuracy of ITMD start by deteriorating at small angles, in the high-energy-factorization regime, while in the TMD regime near ∆ϕ = π, very low values of pt are needed to see differences between the CGC and the ITMD formula. In addition, the genuine twists corrections to ITMD become visible for higher values of pt in p + A collisions, compared to p+p collisions, signaling that they are enhanced by the target saturation scale.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L.V. Gribov, E.M. Levin and M.G. Ryskin, Semihard processes in QCD, Phys. Rept. 100 (1983) 1 [INSPIRE].
A.H. Mueller and J.-W. Qiu, Gluon recombination and shadowing at small values of x, Nucl. Phys. B 268 (1986) 427 [INSPIRE].
A.H. Mueller, Parton saturation: an overview, in Cargese summer school on QCD perspectives on hot and dense matter, (2001), pg. 45 [hep-ph/0111244] [INSPIRE].
J. Jalilian-Marian, A. Kovner, A. Leonidov and H. Weigert, The BFKL equation from the Wilson renormalization group, Nucl. Phys. B 504 (1997) 415 [hep-ph/9701284] [INSPIRE].
J. Jalilian-Marian, A. Kovner and H. Weigert, The Wilson renormalization group for low x physics: gluon evolution at finite parton density, Phys. Rev. D 59 (1998) 014015 [hep-ph/9709432] [INSPIRE].
E. Iancu, A. Leonidov and L.D. McLerran, Nonlinear gluon evolution in the color glass condensate. 1, Nucl. Phys. A 692 (2001) 583 [hep-ph/0011241] [INSPIRE].
E. Ferreiro, E. Iancu, A. Leonidov and L. McLerran, Nonlinear gluon evolution in the color glass condensate. 2, Nucl. Phys. A 703 (2002) 489 [hep-ph/0109115] [INSPIRE].
H. Weigert, Unitarity at small Bjorken x, Nucl. Phys. A 703 (2002) 823 [hep-ph/0004044] [INSPIRE].
A. Kovner, M. Lublinsky and Y. Mulian, Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner evolution at next to leading order, Phys. Rev. D 89 (2014) 061704 [arXiv:1310.0378] [INSPIRE].
I. Balitsky, Operator expansion for high-energy scattering, Nucl. Phys. B 463 (1996) 99 [hep-ph/9509348] [INSPIRE].
Y.V. Kovchegov, Small-x F2 structure function of a nucleus including multiple Pomeron exchanges, Phys. Rev. D 60 (1999) 034008 [hep-ph/9901281] [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), pg. 249 [hep-ph/0303204] [INSPIRE].
F. Gelis, E. Iancu, J. Jalilian-Marian and R. Venugopalan, The color glass condensate, Ann. Rev. Nucl. Part. Sci. 60 (2010) 463 [arXiv:1002.0333] [INSPIRE].
Y.V. Kovchegov and E. Levin, Quantum chromodynamics at high energy, Cambridge University Press, Cambridge, U.K. (2012) [INSPIRE].
J.L. Albacete and C. Marquet, Gluon saturation and initial conditions for relativistic heavy ion collisions, Prog. Part. Nucl. Phys. 76 (2014) 1 [arXiv:1401.4866] [INSPIRE].
P. Kotko, K. Kutak, C. Marquet, E. Petreska, S. Sapeta and A. van Hameren, Improved TMD factorization for forward dijet production in dilute-dense hadronic collisions, JHEP 09 (2015) 106 [arXiv:1503.03421] [INSPIRE].
A. van Hameren, P. Kotko, K. Kutak, C. Marquet, E. Petreska and S. Sapeta, Forward di-jet production in p+Pb collisions in the small-x improved TMD factorization framework, JHEP 12 (2016) 034 [Erratum ibid. 02 (2019) 158] [arXiv:1607.03121] [INSPIRE].
T. Altinoluk, R. Boussarie and P. Kotko, Interplay of the CGC and TMD frameworks to all orders in kinematic twist, JHEP 05 (2019) 156 [arXiv:1901.01175] [INSPIRE].
T. Altinoluk and R. Boussarie, Low x physics as an infinite twist (G)TMD framework: unravelling the origins of saturation, JHEP 10 (2019) 208 [arXiv:1902.07930] [INSPIRE].
S. Wandzura and F. Wilczek, Sum rules for spin dependent electroproduction: test of relativistic constituent quarks, Phys. Lett. B 72 (1977) 195 [INSPIRE].
H. Mäntysaari, N. Mueller, F. Salazar and B. Schenke, Multigluon correlations and evidence of saturation from dijet measurements at an electron-ion collider, Phys. Rev. Lett. 124 (2020) 112301 [arXiv:1912.05586] [INSPIRE].
J. Collins and J.-W. Qiu, kT factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions, Phys. Rev. D 75 (2007) 114014 [arXiv:0705.2141] [INSPIRE].
T.C. Rogers and P.J. Mulders, No generalized TMD-factorization in hadro-production of high transverse momentum hadrons, Phys. Rev. D 81 (2010) 094006 [arXiv:1001.2977] [INSPIRE].
F. Dominguez, C. Marquet, B.-W. Xiao and F. Yuan, Universality of unintegrated gluon distributions at small x, Phys. Rev. D 83 (2011) 105005 [arXiv:1101.0715] [INSPIRE].
C. Marquet, E. Petreska and C. Roiesnel, Transverse-momentum-dependent gluon distributions from JIMWLK evolution, JHEP 10 (2016) 065 [arXiv:1608.02577] [INSPIRE].
C. Marquet, C. Roiesnel and P. Taels, Linearly polarized small-x gluons in forward heavy-quark pair production, Phys. Rev. D 97 (2018) 014004 [arXiv:1710.05698] [INSPIRE].
L.N. Lipatov, Reggeization of the vector meson and the vacuum singularity in non-Abelian gauge theories, Sov. J. Nucl. Phys. 23 (1976) 338 [Yad. Fiz. 23 (1976) 642] [INSPIRE].
E.A. Kuraev, L.N. Lipatov and V.S. Fadin, Multi-Reggeon processes in the Yang-Mills theory, Sov. Phys. JETP 44 (1976) 443 [Zh. Eksp. Teor. Fiz. 71 (1976) 840] [INSPIRE].
I.I. Balitsky and L.N. Lipatov, The Pomeranchuk singularity in quantum chromodynamics, Sov. J. Nucl. Phys. 28 (1978) 822 [Yad. Fiz. 28 (1978) 1597] [INSPIRE].
M. Deak, F. Hautmann, H. Jung and K. Kutak, Forward jet production at the Large Hadron Collider, JHEP 09 (2009) 121 [arXiv:0908.0538] [INSPIRE].
K. Kutak and S. Sapeta, Gluon saturation in dijet production in p-Pb collisions at Large Hadron Collider, Phys. Rev. D 86 (2012) 094043 [arXiv:1205.5035] [INSPIRE].
A. van Hameren, P. Kotko and K. Kutak, Three jet production and gluon saturation effects in p-p and p-Pb collisions within high-energy factorization, Phys. Rev. D 88 (2013) 094001 [Erratum ibid. 90 (2014) 039901] [arXiv:1308.0452] [INSPIRE].
A. van Hameren, P. Kotko, K. Kutak, C. Marquet and S. Sapeta, Saturation effects in forward-forward dijet production in p+Pb collisions, Phys. Rev. D 89 (2014) 094014 [arXiv:1402.5065] [INSPIRE].
A. van Hameren, P. Kotko, K. Kutak and S. Sapeta, Small-x dynamics in forward-central dijet decorrelations at the LHC, Phys. Lett. B 737 (2014) 335 [arXiv:1404.6204] [INSPIRE].
K. Watanabe and B.-W. Xiao, Forward hadron productions in proton-proton collisions in small-x formalism, Phys. Rev. D 94 (2016) 094046 [arXiv:1607.04726] [INSPIRE].
C.J. Bomhof, P.J. Mulders and F. Pijlman, The construction of gauge-links in arbitrary hard processes, Eur. Phys. J. C 47 (2006) 147 [hep-ph/0601171] [INSPIRE].
D. Boer and P.J. Mulders, Color gauge invariance in the Drell-Yan process, Nucl. Phys. B 569 (2000) 505 [hep-ph/9906223] [INSPIRE].
A.V. Belitsky, X. Ji and F. Yuan, Final state interactions and gauge invariant parton distributions, Nucl. Phys. B 656 (2003) 165 [hep-ph/0208038] [INSPIRE].
D. Boer, P.J. Mulders and F. Pijlman, Universality of T odd effects in single spin and azimuthal asymmetries, Nucl. Phys. B 667 (2003) 201 [hep-ph/0303034] [INSPIRE].
W. Vogelsang and F. Yuan, Hadronic dijet imbalance and transverse-momentum dependent parton distributions, Phys. Rev. D 76 (2007) 094013 [arXiv:0708.4398] [INSPIRE].
B.-W. Xiao and F. Yuan, Non-universality of transverse momentum dependent parton distributions at small-x, Phys. Rev. Lett. 105 (2010) 062001 [arXiv:1003.0482] [INSPIRE].
H. Fujii, F. Gelis and R. Venugopalan, Quark pair production in high energy pA collisions: general features, Nucl. Phys. A 780 (2006) 146 [hep-ph/0603099] [INSPIRE].
C. Marquet, Forward inclusive dijet production and azimuthal correlations in p(A) collisions, Nucl. Phys. A 796 (2007) 41 [arXiv:0708.0231] [INSPIRE].
Y.V. Kovchegov, J. Kuokkanen, K. Rummukainen and H. Weigert, Subleading-Nc corrections in non-linear small-x evolution, Nucl. Phys. A 823 (2009) 47 [arXiv:0812.3238] [INSPIRE].
C. Marquet and H. Weigert, New observables to test the color glass condensate beyond the large-Nc limit, Nucl. Phys. A 843 (2010) 68 [arXiv:1003.0813] [INSPIRE].
A. Dumitru, J. Jalilian-Marian, T. Lappi, B. Schenke and R. Venugopalan, Renormalization group evolution of multi-gluon correlators in high energy QCD, Phys. Lett. B 706 (2011) 219 [arXiv:1108.4764] [INSPIRE].
E. Iancu and D.N. Triantafyllopoulos, JIMWLK evolution in the Gaussian approximation, JHEP 04 (2012) 025 [arXiv:1112.1104] [INSPIRE].
M. Alvioli, G. Soyez and D.N. Triantafyllopoulos, Testing the Gaussian approximation to the JIMWLK equation, Phys. Rev. D 87 (2013) 014016 [arXiv:1212.1656] [INSPIRE].
J. Pumplin, D.R. Stump, J. Huston, H.L. Lai, P.M. Nadolsky and W.K. Tung, New generation of parton distributions with uncertainties from global QCD analysis, JHEP 07 (2002) 012 [hep-ph/0201195] [INSPIRE].
I. Balitsky, Quark contribution to the small-x evolution of color dipole, Phys. Rev. D 75 (2007) 014001 [hep-ph/0609105] [INSPIRE].
H. Fujii and K. Watanabe, Heavy quark pair production in high energy pA collisions: quarkonium, Nucl. Phys. A 915 (2013) 1 [arXiv:1304.2221] [INSPIRE].
Y.-Q. Ma, R. Venugopalan, K. Watanabe and H.-F. Zhang, ψ(2S) versus J/ψ suppression in proton-nucleus collisions from factorization violating soft color exchanges, Phys. Rev. C 97 (2018) 014909 [arXiv:1707.07266] [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].
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].
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.L. Albacete, G. Giacalone, C. Marquet and M. Matas, Forward dihadron back-to-back correlations in pA collisions, Phys. Rev. D 99 (2019) 014002 [arXiv:1805.05711] [INSPIRE].
K. Dusling, F. Gelis, T. Lappi and R. Venugopalan, Long range two-particle rapidity correlations in A+A collisions from high energy QCD evolution, Nucl. Phys. A 836 (2010) 159 [arXiv:0911.2720] [INSPIRE].
H. Fujii and K. Watanabe, Leptons from heavy-quark semileptonic decay in pA collisions within the CGC framework, Nucl. Phys. A 951 (2016) 45 [Erratum ibid. 961 (2017) 218] [arXiv:1511.07698] [INSPIRE].
K. Watanabe, Quarkonium production at collider energies in small-x formalism, Few Body Syst. 58 (2017) 134 [arXiv:1611.00700] [INSPIRE].
H. Fujii and K. Watanabe, Nuclear modification of forward D production in pPb collisions at the LHC, arXiv:1706.06728 [INSPIRE].
Y.-Q. Ma, R. Venugopalan and H.-F. Zhang, J/ψ production and suppression in high energy proton-nucleus collisions, Phys. Rev. D 92 (2015) 071901 [arXiv:1503.07772] [INSPIRE].
H. Fujii and K. Watanabe, Heavy quark pair production in high energy pA collisions: open heavy flavors, Nucl. Phys. A 920 (2013) 78 [arXiv:1308.1258] [INSPIRE].
T. Lappi and H. Mantysaari, Forward dihadron correlations in deuteron-gold collisions with the Gaussian approximation of JIMWLK, Nucl. Phys. A 908 (2013) 51 [arXiv:1209.2853] [INSPIRE].
H. Fujii, F. Gelis and R. Venugopalan, Quantitative study of the violation of k-perpendicular-factorization in hadroproduction of quarks at collider energies, Phys. Rev. Lett. 95 (2005) 162002 [hep-ph/0504047] [INSPIRE].
E. Akcakaya, A. Schäfer and J. Zhou, Azimuthal asymmetries for quark pair production in pA collisions, Phys. Rev. D 87 (2013) 054010 [arXiv:1208.4965] [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].
A. Dumitru, T. Lappi and V. Skokov, Distribution of linearly polarized gluons and elliptic azimuthal anisotropy in deep inelastic scattering dijet production at high energy, Phys. Rev. Lett. 115 (2015) 252301 [arXiv:1508.04438] [INSPIRE].
D. Boer, P.J. Mulders, C. Pisano and J. Zhou, Asymmetries in heavy quark pair and dijet production at an EIC, JHEP 08 (2016) 001 [arXiv:1605.07934] [INSPIRE].
A. Dumitru, V. Skokov and T. Ullrich, Measuring the Weizsäcker-Williams distribution of linearly polarized gluons at an electron-ion collider through dijet azimuthal asymmetries, Phys. Rev. C 99 (2019) 015204 [arXiv:1809.02615] [INSPIRE].
S. Benić and A. Dumitru, Prompt photon-jet angular correlations at central rapidities in p+A collisions, Phys. Rev. D 97 (2018) 014012 [arXiv:1710.01991] [INSPIRE].
T. Altinoluk, R. Boussarie, C. Marquet and P. Taels, TMD factorization for dijets + photon production from the dilute-dense CGC framework, JHEP 07 (2019) 079 [arXiv:1810.11273] [INSPIRE].
T. Altinoluk, R. Boussarie, C. Marquet and P. Taels, Photoproduction of three jets in the CGC: gluon TMDs and dilute limit, JHEP 07 (2020) 143 [arXiv:2001.00765] [INSPIRE].
A. Stasto, S.-Y. Wei, B.-W. Xiao and F. Yuan, On the dihadron angular correlations in forward pA collisions, Phys. Lett. B 784 (2018) 301 [arXiv:1805.05712] [INSPIRE].
A. van Hameren, P. Kotko, K. Kutak and S. Sapeta, Broadening and saturation effects in dijet azimuthal correlations in p-p and p-Pb collisions at \( \sqrt{s} \) = 5.02 TeV, Phys. Lett. B 795 (2019) 511 [arXiv:1903.01361] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2006.16279
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Fujii, H., Marquet, C. & Watanabe, K. Comparison of improved TMD and CGC frameworks in forward quark dijet production. J. High Energ. Phys. 2020, 181 (2020). https://doi.org/10.1007/JHEP12(2020)181
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2020)181