Abstract
We study the production of forward di-jets in proton-lead and proton-proton collisions at the Large Hadron Collider. Such configurations, with both jets produced in the forward direction, impose a dilute-dense asymmetry which allows to probe the gluon density of the lead or proton target at small longitudinal momentum fractions. Even though the jet momenta are always much bigger than the saturation scale of the target, Q s, the transverse momentum imbalance of the di-jet system may be either also much larger than Q s, or of the order Q s, implying that the small-x QCD dynamics involved is either linear or non-linear, respectively. The small-x improved TMD factorization framework deals with both situations in the same formalism. In the latter case, which corresponds to nearly back-to-back jets, we find that saturation effects induce a significant suppression of the forward di-jet azimuthal correlations in proton-lead versus proton-proton collisions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Change history
25 February 2019
There was a mistake in the normalization of the histograms representing the differenial cross section as a function of the azimuthal angle between the jets: figure 3 left and figure 4 left in the original paper [1].
25 February 2019
There was a mistake in the normalization of the histograms representing the differenial cross section as a function of the azimuthal angle between the jets: figure 3 left and figure 4 left in the original paper [1].
25 February 2019
There was a mistake in the normalization of the histograms representing the differenial cross section as a function of the azimuthal angle between the jets: figure 3 left and figure 4 left in the original paper [1].
25 February 2019
There was a mistake in the normalization of the histograms representing the differenial cross section as a function of the azimuthal angle between the jets: figure 3 left and figure 4 left in the original paper [1].
25 February 2019
There was a mistake in the normalization of the histograms representing the differenial cross section as a function of the azimuthal angle between the jets: figure 3 left and figure 4 left in the original paper [1].
References
L.V. Gribov, E.M. Levin and M.G. Ryskin, Semihard Processes in QCD, Phys. Rept. 100 (1983) 1 [INSPIRE].
J.L. Albacete and C. Marquet, Azimuthal correlations of forward di-hadrons in d+Au collisions at RHIC in the Color Glass Condensate, Phys. Rev. Lett. 105 (2010) 162301 [arXiv:1005.4065] [INSPIRE].
A. Stasto, B.-W. Xiao and F. Yuan, Back-to-Back Correlations of Di-hadrons in dAu Collisions at RHIC, Phys. Lett. B 716 (2012) 430 [arXiv:1109.1817] [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].
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].
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].
C. Marquet, Forward inclusive dijet production and azimuthal correlations in pA collisions, Nucl. Phys. A 796 (2007) 41 [arXiv:0708.0231] [INSPIRE].
PHENIX collaboration, A. Adare et al., Suppression of back-to-back hadron pairs at forward rapidity in d+Au Collisions at \( \sqrt{s_{NN}}=200 \) GeV, Phys. Rev. Lett. 107 (2011) 172301 [arXiv:1105.5112] [INSPIRE].
STAR collaboration, E. Braidot, Suppression of Forward Pion Correlations in d+Au Interactions at STAR, arXiv:1005.2378 [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.H. Mueller, B.-W. Xiao and F. Yuan, Sudakov Resummation in Small-x Saturation Formalism, Phys. Rev. Lett. 110 (2013) 082301 [arXiv:1210.5792] [INSPIRE].
A.H. Mueller, B.-W. Xiao and F. Yuan, Sudakov double logarithms resummation in hard processes in the small-x saturation formalism, Phys. Rev. D 88 (2013) 114010 [arXiv:1308.2993] [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. Kutak, Hard scale dependent gluon density, saturation and forward-forward dijet production at the LHC, Phys. Rev. D 91 (2015) 034021 [arXiv:1409.3822] [INSPIRE].
M. Ciafaloni, Coherence Effects in Initial Jets at Small Q 2 /s, Nucl. Phys. B 296 (1988) 49 [INSPIRE].
S. Catani, F. Fiorani and G. Marchesini, Small x Behavior of Initial State Radiation in Perturbative QCD, Nucl. Phys. B 336 (1990) 18 [INSPIRE].
S. Catani, F. Fiorani and G. Marchesini, QCD Coherence in Initial State Radiation, Phys. Lett. B 234 (1990) 339 [INSPIRE].
S. Catani, M. Ciafaloni and F. Hautmann, High-energy factorization and small x heavy flavor production, Nucl. Phys. B 366 (1991) 135 [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].
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].
F. Dominguez, B.-W. Xiao and F. Yuan, k t -factorization for Hard Processes in Nuclei, Phys. Rev. Lett. 106 (2011) 022301 [arXiv:1009.2141] [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].
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, A. Leonidov and H. Weigert, The Wilson renormalization group for low x physics: Towards the high density regime, Phys. Rev. D 59 (1998) 014014 [hep-ph/9706377] [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. Iancu, A. Leonidov and L.D. McLerran, The renormalization group equation for the color glass condensate, Phys. Lett. B 510 (2001) 133 [hep-ph/0102009] [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].
I. Balitsky, Operator expansion for high-energy scattering, Nucl. Phys. B 463 (1996) 99 [hep-ph/9509348] [INSPIRE].
Y.V. Kovchegov, Small x F(2) structure function of a nucleus including multiple Pomeron exchanges, Phys. Rev. D 60 (1999) 034008 [hep-ph/9901281] [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].
J. Kwiecinski, A.D. Martin and A.M. Stasto, A unified BFKL and GLAP description of F2 data, Phys. Rev. D 56 (1997) 3991 [hep-ph/9703445] [INSPIRE].
K. Kutak and J. Kwiecinski, Screening effects in the ultrahigh-energy neutrino interactions, Eur. Phys. J. C 29 (2003) 521 [hep-ph/0303209] [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].
J. Collins and J.-W. Qiu, k T factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions, Phys. Rev. D 75 (2007) 114014 [arXiv:0705.2141] [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].
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].
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].
L.N. Lipatov, Reggeization of the Vector Meson and the Vacuum Singularity in Nonabelian 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 [Erratum ibid. 45 (1977) 199] [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].
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 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. D 90 (2014) 039901] [arXiv:1308.0452] [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].
Y.V. Kovchegov, J. Kuokkanen, K. Rummukainen and H. Weigert, Subleading-N(c) 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-N c 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].
K.J. Golec-Biernat and M. Wusthoff, Saturation effects in deep inelastic scattering at low Q 2 and its implications on diffraction, Phys. Rev. D 59 (1998) 014017 [hep-ph/9807513] [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].
F. Gelis and A. Peshier, Probing colored glass via \( q\overline{q} \) photoproduction, Nucl. Phys. A 697 (2002) 879 [hep-ph/0107142] [INSPIRE].
D. Kharzeev, Y.V. Kovchegov and K. Tuchin, Cronin effect and high p T suppression in pA collisions, Phys. Rev. D 68 (2003) 094013 [hep-ph/0307037] [INSPIRE].
K. Kutak and A.M. Stasto, Unintegrated gluon distribution from modified BK equation, Eur. Phys. J. C 41 (2005) 343 [hep-ph/0408117] [INSPIRE].
A. van Hameren, PARNI for importance sampling and density estimation, Acta Phys. Polon. B 40 (2009) 259 [arXiv:0710.2448] [INSPIRE].
A. van Hameren, Kaleu: A General-Purpose Parton-Level Phase Space Generator, arXiv:1003.4953 [INSPIRE].
M. Bury and A. van Hameren, Numerical evaluation of multi-gluon amplitudes for High Energy Factorization, Comput. Phys. Commun. 196 (2015) 592 [arXiv:1503.08612] [INSPIRE].
P. Kotko, LxJet, http://annapurna.ifj.edu.pl/~pkotko/LxJet.html.
H.-L. Lai et al., New parton distributions for collider physics, Phys. Rev. D 82 (2010) 074024 [arXiv:1007.2241] [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].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1607.03121
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
van Hameren, A., Kotko, P., Kutak, K. et al. Forward di-jet production in p+Pb collisions in the small-x improved TMD factorization framework. J. High Energ. Phys. 2016, 34 (2016). https://doi.org/10.1007/JHEP12(2016)034
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2016)034