Abstract
We extend the study of corrections to the eikonal approximation that was initiated in ref. [1] to higher orders. These corrections associated with the finite width of the target are investigated and the gluon propagator in background field is calculated at next-to-next-to-eikonal accuracy. The result is then applied to the single inclusive gluon production cross section at central rapidities and the single transverse spin asymmetry with a transversely polarized target, in pA collisions, in order to analyze these observables beyond the eikonal limit. The next-to-next-to-eikonal corrections to the unpolarized cross section are non-zero and provide the first corrections to the usual k ⊥-factorized expression. In contrast, the eikonal and next-to-next-to-eikonal contributions to the single transverse spin asymmetry vanish, while the next-to-eikonal ones are non-zero.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T. Altinoluk, N. Armesto, G. Beuf, M. Martínez and C.A. Salgado, Next-to-eikonal corrections in the CGC: gluon production and spin asymmetries in pA collisions, JHEP 07 (2014) 068 [arXiv:1404.2219] [INSPIRE].
J.C. Collins, D.E. Soper and G.F. Sterman, Factorization of Hard Processes in QCD, Adv. Ser. Direct. High Energy Phys. 5 (1989) 1 [hep-ph/0409313] [INSPIRE].
S. Catani, M. Ciafaloni and F. Hautmann, High-energy factorization and small x heavy flavor production, Nucl. Phys. B 366 (1991) 135 [INSPIRE].
E.M. Levin, M.G. Ryskin, Yu. M. Shabelski and A.G. Shuvaev, Heavy quark production in semihard nucleon interactions, Sov. J. Nucl. Phys. 53 (1991) 657 [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].
Y.V. Kovchegov and K. Tuchin, Inclusive gluon production in DIS at high parton density, Phys. Rev. D 65 (2002) 074026 [hep-ph/0111362] [INSPIRE].
A. Dumitru and L.D. McLerran, How protons shatter colored glass, Nucl. Phys. A 700 (2002) 492 [hep-ph/0105268] [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].
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].
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].
A. Dumitru, A. Hayashigaki and J. Jalilian-Marian, The Color glass condensate and hadron production in the forward region, Nucl. Phys. A 765 (2006) 464 [hep-ph/0506308] [INSPIRE].
T. Altinoluk and A. Kovner, Particle Production at High Energy and Large Transverse Momentum: ‘The Hybrid Formalism’ Revisited, Phys. Rev. D 83 (2011) 105004 [arXiv:1102.5327] [INSPIRE].
G.A. Chirilli, B.-W. Xiao and F. Yuan, Inclusive Hadron Productions in pA Collisions, Phys. Rev. D 86 (2012) 054005 [arXiv:1203.6139] [INSPIRE].
A.M. Stasto, B.-W. Xiao and D. Zaslavsky, Towards the Test of Saturation Physics Beyond Leading Logarithm, Phys. Rev. Lett. 112 (2014) 012302 [arXiv:1307.4057] [INSPIRE].
A.M. Stasto, B.-W. Xiao, F. Yuan and D. Zaslavsky, Matching collinear and small x factorization calculations for inclusive hadron production in pA collisions, Phys. Rev. D 90 (2014) 014047 [arXiv:1405.6311] [INSPIRE].
Z.-B. Kang, I. Vitev and H. Xing, Next-to-leading order forward hadron production in the small-x regime: rapidity factorization, Phys. Rev. Lett. 113 (2014) 062002 [arXiv:1403.5221] [INSPIRE].
B.-W. Xiao and F. Yuan, Comment on “Next-to-leading order forward hadron production in the small-x regime: rapidity factorization” arXiv:1403.5221 by Kang et al., arXiv:1407.6314 [INSPIRE].
T. Altinoluk, N. Armesto, G. Beuf, A. Kovner and M. Lublinsky, Single-inclusive particle production in proton-nucleus collisions at next-to-leading order in the hybrid formalism, Phys. Rev. D 91 (2015) 094016 [arXiv:1411.2869] [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].
E. Laenen, G. Stavenga and C.D. White, Path integral approach to eikonal and next-to-eikonal exponentiation, JHEP 03 (2009) 054 [arXiv:0811.2067] [INSPIRE].
E. Laenen, L. Magnea, G. Stavenga and C.D. White, Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach, JHEP 01 (2011) 141 [arXiv:1010.1860] [INSPIRE].
A.V. Efremov and O.V. Teryaev, QCD Asymmetry and Polarized Hadron Structure Functions, Phys. Lett. B 150 (1985) 383 [INSPIRE].
J.-w. Qiu and G.F. Sterman, Single transverse spin asymmetries, Phys. Rev. Lett. 67 (1991) 2264 [INSPIRE].
J.-w. Qiu and G.F. Sterman, Single transverse spin asymmetries in hadronic pion production, Phys. Rev. D 59 (1999) 014004 [hep-ph/9806356] [INSPIRE].
A. Bacchetta, M. Diehl, K. Goeke, A. Metz, P.J. Mulders and M. Schlegel, Semi-inclusive deep inelastic scattering at small transverse momentum, JHEP 02 (2007) 093 [hep-ph/0611265] [INSPIRE].
S.J. Brodsky, D.S. Hwang and I. Schmidt, Final state interactions and single spin asymmetries in semiinclusive deep inelastic scattering, Phys. Lett. B 530 (2002) 99 [hep-ph/0201296] [INSPIRE].
V. Barone, F. Bradamante and A. Martin, Transverse-spin and transverse-momentum effects in high-energy processes, Prog. Part. Nucl. Phys. 65 (2010) 267 [arXiv:1011.0909] [INSPIRE].
D. Boer et al., Gluons and the quark sea at high energies: Distributions, polarization, tomography, arXiv:1108.1713 [INSPIRE].
T. Liou, A.H. Mueller and B. Wu, Radiative p ⊥ -broadening of high-energy quarks and gluons in QCD matter, Nucl. Phys. A 916 (2013) 102 [arXiv:1304.7677] [INSPIRE].
J.-P. Blaizot and Y. Mehtar-Tani, Renormalization of the jet-quenching parameter, Nucl. Phys. A 929 (2014) 202 [arXiv:1403.2323] [INSPIRE].
E. Iancu, The non-linear evolution of jet quenching, JHEP 10 (2014) 95 [arXiv:1403.1996] [INSPIRE].
R. Abir, Small-x evolution of jet quenching parameter, Phys. Lett. B 748 (2015) 467 [arXiv:1504.06356] [INSPIRE].
J.D. Bjorken, J.B. Kogut and D.E. Soper, Quantum Electrodynamics at Infinite Momentum: Scattering from an External Field, Phys. Rev. D 3 (1971) 1382 [INSPIRE].
J.C. Collins, D.E. Soper and G.F. Sterman, Heavy Particle Production in High-Energy Hadron Collisions, Nucl. Phys. B 263 (1986) 37 [INSPIRE].
M. Gyulassy and X.-n. Wang, Multiple collisions and induced gluon Bremsstrahlung in QCD, Nucl. Phys. B 420 (1994) 583 [nucl-th/9306003] [INSPIRE].
R. Baier, Y.L. Dokshitzer, A.H. Mueller, S. Peigne and D. Schiff, Radiative energy loss of high-energy quarks and gluons in a finite volume quark-gluon plasma, Nucl. Phys. B 483 (1997) 291 [hep-ph/9607355] [INSPIRE].
B.G. Zakharov, Fully quantum treatment of the Landau-Pomeranchuk-Migdal effect in QED and QCD, JETP Lett. 63 (1996) 952 [hep-ph/9607440] [INSPIRE].
B.G. Zakharov, Light cone path integral approach to the Landau-Pomeranchuk-Migdal effect, Phys. Atom. Nucl. 61 (1998) 838 [hep-ph/9807540] [INSPIRE].
U.A. Wiedemann, Gluon radiation off hard quarks in a nuclear environment: Opacity expansion, Nucl. Phys. B 588 (2000) 303 [hep-ph/0005129] [INSPIRE].
Y. Mehtar-Tani, Relating the description of gluon production in pA collisions and parton energy loss in AA collisions, Phys. Rev. C 75 (2007) 034908 [hep-ph/0606236] [INSPIRE].
F. Gelis and R. Venugopalan, Particle production in field theories coupled to strong external sources, Nucl. Phys. A 776 (2006) 135 [hep-ph/0601209] [INSPIRE].
Y.V. Kovchegov and M.D. Sievert, Sivers function in the quasiclassical approximation, Phys. Rev. D 89 (2014) 054035 [arXiv:1310.5028] [INSPIRE].
Y.V. Kovchegov, D. Pitonyak and M.D. Sievert, Helicity Evolution at Small-x, arXiv:1511.06737 [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: 1505.01400
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
Altinoluk, T., Armesto, N., Beuf, G. et al. Next-to-next-to-eikonal corrections in the CGC. J. High Energ. Phys. 2016, 114 (2016). https://doi.org/10.1007/JHEP01(2016)114
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2016)114