Abstract
We study forward dijet production in dilute-dense hadronic collisions. By considering the appropriate limits, we show that both the transverse-momentum-dependent (TMD) and the high-energy factorization formulas can be derived from the Color Glass Condensate framework. Respectively, this happens when the transverse momentum imbalance of the dijet system, k t , is of the order of either the saturation scale, or the hard jet momenta, the former being always much smaller than the latter. We propose a new formula for forward dijets that encompasses both situations and is therefore applicable regardless of the magnitude of k t . That involves generalizing the TMD factorization formula for dijet production to the case where the incoming small-x gluon is off-shell. The derivation is performed in two independent ways, using either Feynman diagram techniques, or color-ordered amplitudes.
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].
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].
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].
C. Marquet, Forward inclusive dijet production and azimuthal correlations in p(A) 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.
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, 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].
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].
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, 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].
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 [arXiv:1308.0452] [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].
M.L. Mangano and S.J. Parke, Multiparton amplitudes in gauge theories, Phys. Rept. 200 (1991) 301 [hep-th/0509223] [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].
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].
E. Iancu and J. Laidet, Gluon splitting in a shockwave, Nucl. Phys. A 916 (2013) 48 [arXiv:1305.5926] [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].
A. van Hameren, P. Kotko and K. Kutak, Multi-gluon helicity amplitudes with one off-shell leg within high energy factorization, JHEP 12 (2012) 029 [arXiv:1207.3332] [INSPIRE].
A. van Hameren, P. Kotko and K. Kutak, Helicity amplitudes for high-energy scattering, JHEP 01 (2013) 078 [arXiv:1211.0961] [INSPIRE].
L.N. Lipatov, Reggeization of the vector meson and the vacuum singularity in nonabelian gauge theories, Sov. J. Nucl. Phys. 23 (1976) 338 [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].
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].
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 J. Kwiecinski, Screening effects in the ultrahigh-energy neutrino interactions, Eur. Phys. J. C 29 (2003) 521 [hep-ph/0303209] [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].
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].
L.N. Lipatov, Gauge invariant effective action for high-energy processes in QCD, Nucl. Phys. B 452 (1995) 369 [hep-ph/9502308] [INSPIRE].
E.N. Antonov, L.N. Lipatov, E.A. Kuraev and I.O. Cherednikov, Feynman rules for effective Regge action, Nucl. Phys. B 721 (2005) 111 [hep-ph/0411185] [INSPIRE].
P. Kotko, Wilson lines and gauge invariant off-shell amplitudes, JHEP 07 (2014) 128 [arXiv:1403.4824] [INSPIRE].
A. van Hameren, BCFW recursion for off-shell gluons, JHEP 07 (2014) 138 [arXiv:1404.7818] [INSPIRE].
L.J. Dixon, A brief introduction to modern amplitude methods, arXiv:1310.5353.
V. Del Duca, L.J. Dixon and F. Maltoni, New color decompositions for gauge amplitudes at tree and loop level, Nucl. Phys. B 571 (2000) 51 [hep-ph/9910563] [INSPIRE].
J.C. Collins, D.E. Soper and G.F. Sterman, Transverse momentum distribution in Drell-Yan pair and W and Z boson production, Nucl. Phys. B 250 (1985) 199 [INSPIRE].
M.A. Kimber, A.D. Martin and M.G. Ryskin, Unintegrated parton distributions and prompt photon hadroproduction, Eur. Phys. J. C 12 (2000) 655 [hep-ph/9911379] [INSPIRE].
M.A. Kimber, A.D. Martin and M.G. Ryskin, Unintegrated parton distributions, Phys. Rev. D 63 (2001) 114027 [hep-ph/0101348] [INSPIRE].
J. Collins and T. Rogers, Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel, Phys. Rev. D 91 (2015) 074020 [arXiv:1412.3820] [INSPIRE].
K. Kutak, K. Golec-Biernat, S. Jadach and M. Skrzypek, Nonlinear equation for coherent gluon emission, JHEP 02 (2012) 117 [arXiv:1111.6928] [INSPIRE].
K. Kutak, Resummation in nonlinear equation for high energy factorisable gluon density and its extension to include coherence, JHEP 12 (2012) 033 [arXiv:1206.5757] [INSPIRE].
X.-d. Ji, J.-p. Ma and F. Yuan, QCD factorization for semi-inclusive deep-inelastic scattering at low transverse momentum, Phys. Rev. D 71 (2005) 034005 [hep-ph/0404183] [INSPIRE].
F. Dominguez, A.H. Mueller, S. Munier and B.-W. Xiao, On the small-x evolution of the color quadrupole and the Weizsácker-Williams gluon distribution, Phys. Lett. B 705 (2011) 106 [arXiv:1108.1752] [INSPIRE].
V.S. Fadin, R. Fiore, M.G. Kozlov and A.V. Reznichenko, Proof of the multi-Regge form of QCD amplitudes with gluon exchanges in the NLA, Phys. Lett. B 639 (2006) 74 [hep-ph/0602006] [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: 1503.03421
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
Kotko, P., Kutak, K., Marquet, C. et al. Improved TMD factorization for forward dijet production in dilute-dense hadronic collisions. J. High Energ. Phys. 2015, 106 (2015). https://doi.org/10.1007/JHEP09(2015)106
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2015)106