Abstract
The cross-sections of diffractive double hadron photo- or electroproduction with large pT, on a nucleon or a nucleus, are calculated to NLO accuracy. A hybrid formalism mixing collinear factorization and high energy small-x factorization, more precisely the shockwave formalism for the latter, is used to derive the results. The cancellation of divergences is explicitly shown, and the finite parts of the NLO differential cross-sections are found. We work in arbitrary kinematics such that both photoproduction and leptoproduction are considered. The results are therefore usable, to detect saturation effects, at both the future EIC or already at LHC, using Ultra Peripheral Collisions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Wüsthoff and A.D. Martin, The QCD description of diffractive processes, J. Phys. G 25 (1999) R309–R344 [hep-ph/9909362] [INSPIRE].
G. Wolf, Review of high energy diffraction in real and virtual photon proton scattering at HERA, Rept. Prog. Phys. 73 (2010) 116202 [arXiv:0907.1217] [INSPIRE].
H1 collaboration, Diffractive deep-inelastic scattering with a leading proton at HERA, Eur. Phys. J. C 48 (2006) 749 [hep-ex/0606003] [INSPIRE].
H1 collaboration, Measurement and QCD analysis of the diffractive deep-inelastic scattering cross-section at HERA, Eur. Phys. J. C 48 (2006) 715 [hep-ex/0606004] [INSPIRE].
ZEUS collaboration, Dissociation of virtual photons in events with a leading proton at HERA, Eur. Phys. J. C 38 (2004) 43 [hep-ex/0408009] [INSPIRE].
ZEUS collaboration, Study of deep inelastic inclusive and diffractive scattering with the ZEUS forward plug calorimeter, Nucl. Phys. B 713 (2005) 3 [hep-ex/0501060] [INSPIRE].
F.D. Aaron et al., Measurement of the cross section for diffractive deep-inelastic scattering with a leading proton at HERA, Eur. Phys. J. C 71 (2011) 1578 [arXiv:1010.1476] [INSPIRE].
H1 collaboration, Inclusive measurement of diffractive deep-inelastic scattering at HERA, Eur. Phys. J. C 72 (2012) 2074 [arXiv:1203.4495] [INSPIRE].
ZEUS collaboration, Deep inelastic scattering with leading protons or large rapidity gaps at HERA, Nucl. Phys. B 816 (2009) 1 [arXiv:0812.2003] [INSPIRE].
H1 and ZEUS collaborations, Combined inclusive diffractive cross sections measured with forward proton spectrometers in deep inelastic ep scattering at HERA, Eur. Phys. J. C 72 (2012) 2175 [arXiv:1207.4864] [INSPIRE].
J.C. Collins, Proof of factorization for diffractive hard scattering, Phys. Rev. D 57 (1998) 3051 [Erratum ibid. 61 (2000) 019902] [hep-ph/9709499] [INSPIRE].
R. Boussarie, A.V. Grabovsky, L. Szymanowski and S. Wallon, Impact factor for high-energy two and three jets diffractive production, JHEP 09 (2014) 026 [arXiv:1405.7676] [INSPIRE].
R. Boussarie, A.V. Grabovsky, L. Szymanowski and S. Wallon, On the one loop \( {\gamma}^{\left(\ast \right)}\to q\overline{q} \) impact factor and the exclusive diffractive cross sections for the production of two or three jets, JHEP 11 (2016) 149 [arXiv:1606.00419] [INSPIRE].
R. Boussarie, A.V. Grabovsky, L. Szymanowski and S. Wallon, Towards a complete next-to-logarithmic description of forward exclusive diffractive dijet electroproduction at HERA: real corrections, Phys. Rev. D 100 (2019) 074020 [arXiv:1905.07371] [INSPIRE].
R. Boussarie et al., Next-to-leading order computation of exclusive diffractive light vector meson production in a saturation framework, Phys. Rev. Lett. 119 (2017) 072002 [arXiv:1612.08026] [INSPIRE].
I. Balitsky, Operator expansion for high-energy scattering, Nucl. Phys. B 463 (1996) 99 [hep-ph/9509348] [INSPIRE].
I. Balitsky, Factorization for high-energy scattering, Phys. Rev. Lett. 81 (1998) 2024 [hep-ph/9807434] [INSPIRE].
I. Balitsky, Factorization and high-energy effective action, Phys. Rev. D 60 (1999) 014020 [hep-ph/9812311] [INSPIRE].
I. Balitsky, Effective field theory for the small x evolution, Phys. Lett. B 518 (2001) 235 [hep-ph/0105334] [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].
J. Jalilian-Marian, A. Kovner, A. Leonidov and H. Weigert, Unitarization of gluon distribution in the doubly logarithmic regime at high density, Phys. Rev. D 59 (1999) 034007 [Erratum ibid. 59 (1999) 099903] [hep-ph/9807462] [INSPIRE].
A. Kovner, J.G. Milhano and H. Weigert, Relating different approaches to nonlinear QCD evolution at finite gluon density, Phys. Rev. D 62 (2000) 114005 [hep-ph/0004014] [INSPIRE].
H. Weigert, Unitarity at small Bjorken x, Nucl. Phys. A 703 (2002) 823 [hep-ph/0004044] [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].
V.S. Fadin, E.A. Kuraev and L.N. Lipatov, On the Pomeranchuk singularity in asymptotically free theories, Phys. Lett. B 60 (1975) 50 [INSPIRE].
É.A. Kuraev, L.N. Lipatov and V.S. Fadin, Multi-Reggeon processes in the Yang-Mills theory, Sov. Phys. JETP 44 (1976) 443 [INSPIRE].
É.A. Kuraev, L.N. Lipatov and V.S. Fadin, The Pomeranchuk singularity in non-Abelian gauge theories, Sov. Phys. JETP 45 (1977) 199.
I.I. Balitsky and L.N. Lipatov, The Pomeranchuk singularity in quantum chromodynamics, Sov. J. Nucl. Phys. 28 (1978) 822 [INSPIRE].
V.S. Fadin and L.N. Lipatov, BFKL pomeron in the next-to-leading approximation, Phys. Lett. B 429 (1998) 127 [hep-ph/9802290] [INSPIRE].
M. Ciafaloni and G. Camici, Energy scale(s) and next-to-leading BFKL equation, Phys. Lett. B 430 (1998) 349 [hep-ph/9803389] [INSPIRE].
V.S. Fadin and R. Fiore, Non-forward BFKL pomeron at next-to-leading order, Phys. Lett. B 610 (2005) 61 [Erratum ibid. 621 (2005) 320] [hep-ph/0412386] [INSPIRE].
V.S. Fadin and R. Fiore, Non-forward NLO BFKL kernel, Phys. Rev. D 72 (2005) 014018 [hep-ph/0502045] [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].
Y.V. Kovchegov, Unitarization of the BFKL pomeron on a nucleus, Phys. Rev. D 61 (2000) 074018 [hep-ph/9905214] [INSPIRE].
G.A. Chirilli and Y.V. Kovchegov, Solution of the NLO BFKL equation and a strategy for solving the all-order BFKL equation, JHEP 06 (2013) 055 [arXiv:1305.1924] [INSPIRE].
A.V. Grabovsky, On the solution to the NLO forward BFKL equation, JHEP 09 (2013) 098 [arXiv:1307.3152] [INSPIRE].
J. Collins, Foundations of perturbative QCD, Cambridge University Press, Cambridge, U.K. (2013) [INSPIRE].
G. Altarelli, R.K. Ellis, G. Martinelli and S.-Y. Pi, Processes involving fragmentation functions beyond the leading order in QCD, Nucl. Phys. B 160 (1979) 301 [INSPIRE].
V.N. Gribov and L.N. Lipatov, Deep inelastic ep scattering in perturbation theory, Sov. J. Nucl. Phys. 15 (1972) 438 [INSPIRE].
L.N. Lipatov, The parton model and perturbation theory, Yad. Fiz. 20 (1974) 181 [INSPIRE].
G. Altarelli and G. Parisi, Asymptotic freedom in parton language, Nucl. Phys. B 126 (1977) 298 [INSPIRE].
Y.L. Dokshitzer, Calculation of the structure functions for deep inelastic scattering and e+e− annihilation by perturbation theory in quantum chromodynamics, Sov. Phys. JETP 46 (1977) 641 [INSPIRE].
D.Y. Ivanov and A. Papa, Inclusive production of a pair of hadrons separated by a large interval of rapidity in proton collisions, JHEP 07 (2012) 045 [arXiv:1205.6068] [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].
G. Beuf, T. Lappi and R. Paatelainen, Massive quarks in NLO dipole factorization for DIS: transverse photon, Phys. Rev. D 106 (2022) 034013 [arXiv:2204.02486] [INSPIRE].
K. Roy and R. Venugopalan, NLO impact factor for inclusive photon + dijet production in e + A DIS at small x, Phys. Rev. D 101 (2020) 034028 [arXiv:1911.04530] [INSPIRE].
P. Caucal, F. Salazar and R. Venugopalan, Dijet impact factor in DIS at next-to-leading order in the color glass condensate, JHEP 11 (2021) 222 [arXiv:2108.06347] [INSPIRE].
P. Caucal, F. Salazar, B. Schenke and R. Venugopalan, Back-to-back inclusive dijets in DIS at small x: Sudakov suppression and gluon saturation at NLO, JHEP 11 (2022) 169 [arXiv:2208.13872] [INSPIRE].
F. Bergabo and J. Jalilian-Marian, Single inclusive hadron production in DIS at small x: next to leading order corrections, JHEP 01 (2023) 095 [arXiv:2210.03208] [INSPIRE].
F. Bergabo and J. Jalilian-Marian, One-loop corrections to dihadron production in DIS at small x, Phys. Rev. D 106 (2022) 054035 [arXiv:2207.03606] [INSPIRE].
E. Iancu and Y. Mulian, Dihadron production in DIS at NLO: the real corrections, arXiv:2211.04837 [INSPIRE].
H. Mäntysaari and J. Penttala, Exclusive production of light vector mesons at next-to-leading order in the dipole picture, Phys. Rev. D 105 (2022) 114038 [arXiv:2203.16911] [INSPIRE].
H. Mäntysaari and J. Penttala, Exclusive heavy vector meson production at next-to-leading order in the dipole picture, Phys. Lett. B 823 (2021) 136723 [arXiv:2104.02349] [INSPIRE].
H. Mäntysaari and J. Penttala, Complete calculation of exclusive heavy vector meson production at next-to-leading order in the dipole picture, JHEP 08 (2022) 247 [arXiv:2204.14031] [INSPIRE].
G. Beuf et al., Diffractive deep inelastic scattering at NLO in the dipole picture: the \( q\overline{q}g \) contribution, Phys. Rev. D 106 (2022) 094014 [arXiv:2206.13161] [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: 2211.05774
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
Fucilla, M., Grabovsky, A., Li, E. et al. NLO computation of diffractive di-hadron production in a saturation framework. J. High Energ. Phys. 2023, 159 (2023). https://doi.org/10.1007/JHEP03(2023)159
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2023)159