Abstract
We study the exclusive diffractive \( c\overline{c} \) photoproduction in ultraperipheral pA collisions. The formalism makes use of off-diagonal generalizations of the unintegrated gluon distribution, the so-called generalized transverse momentum dependent distributions (GTMDs). We present two different formulations. The first one is based directly on gluon GTMD parametrizations in momentum space. Another option is the calculation of the GTMD as a Fourier transform of the dipole-nucleon scattering amplitude N(Y, \( \overrightarrow{r} \)⊥, \( \overrightarrow{b} \)⊥). The latter approach requires some extra regularization discussed in the paper. Different dipole amplitudes from the literature are used. Compared to previous calculations in the literature, we integrate over the full phase space and therefore cross sections for realistic conditions are obtained. We present distributions in rapidity of c or \( \overline{c} \), transverse momentum of the \( c\overline{c} \) pair, four-momentum transfer squared as well as the azimuthal correlation between a sum and a difference of the c and \( \overline{c} \) transverse momenta. The azimuthal correlations are partially due to the so-called elliptic gluon Wigner distribution. Different models lead to different modulations in the azimuthal angle. The modulations are generally smaller than 5%. They depend on the range of transverse momentum selected for the calculation.
Article PDF
Similar content being viewed by others
References
D. Ashery, High momentum diffractive processes and hadronic structure, Prog. Part. Nucl. Phys. 56 (2006) 279 [INSPIRE].
N.N. Nikolaev and B.G. Zakharov, Splitting the pomeron into two jets: A Novel process at HERA, Phys. Lett. B 332 (1994) 177 [hep-ph/9403281] [INSPIRE].
N.N. Nikolaev, W. Schäfer and G. Schwiete, Coherent production of hard dijets on nuclei in QCD, Phys. Rev. D 63 (2001) 014020 [hep-ph/0009038] [INSPIRE].
X.-D. Ji, Viewing the proton through ‘color’ filters, Phys. Rev. Lett. 91 (2003) 062001 [hep-ph/0304037] [INSPIRE].
A.V. Belitsky, X.-D. Ji and F. Yuan, Quark imaging in the proton via quantum phase space distributions, Phys. Rev. D 69 (2004) 074014 [hep-ph/0307383] [INSPIRE].
S. Meissner, A. Metz and M. Schlegel, Generalized parton correlation functions for a spin-1/2 hadron, JHEP 08 (2009) 056 [arXiv:0906.5323] [INSPIRE].
C. Lorcé and B. Pasquini, Structure analysis of the generalized correlator of quark and gluon for a spin-1/2 target, JHEP 09 (2013) 138 [arXiv:1307.4497] [INSPIRE].
R. Boussarie et al., TMD Handbook, arXiv:2304.03302 [INSPIRE].
Y. Hagiwara, Y. Hatta and T. Ueda, Wigner, Husimi, and generalized transverse momentum dependent distributions in the color glass condensate, Phys. Rev. D 94 (2016) 094036 [arXiv:1609.05773] [INSPIRE].
B.Z. Kopeliovich, L.I. Lapidus and A.B. Zamolodchikov, Dynamics of Color in Hadron Diffraction on Nuclei, JETP Lett. 33 (1981) 595 [INSPIRE].
N.N. Nikolaev and B.G. Zakharov, Pomeron structure function and diffraction dissociation of virtual photons in perturbative QCD, Z. Phys. C 53 (1992) 331 [INSPIRE].
B.Z. Kopeliovich, H.J. Pirner, A.H. Rezaeian and I. Schmidt, Azimuthal anisotropy of direct photons, Phys. Rev. D 77 (2008) 034011 [arXiv:0711.3010] [INSPIRE].
E. Iancu and A.H. Rezaeian, Elliptic flow from color-dipole orientation in pp and pA collisions, Phys. Rev. D 95 (2017) 094003 [arXiv:1702.03943] [INSPIRE].
Y. Hatta, B.-W. Xiao and F. Yuan, Probing the Small-x Gluon Tomography in Correlated Hard Diffractive Dijet Production in Deep Inelastic Scattering, Phys. Rev. Lett. 116 (2016) 202301 [arXiv:1601.01585] [INSPIRE].
D. Boer and C. Setyadi, GTMD model predictions for diffractive dijet production at EIC, Phys. Rev. D 104 (2021) 074006 [arXiv:2106.15148] [INSPIRE].
T. Altinoluk, N. Armesto, G. Beuf and A.H. Rezaeian, Diffractive Dijet Production in Deep Inelastic Scattering and Photon-Hadron Collisions in the Color Glass Condensate, Phys. Lett. B 758 (2016) 373 [arXiv:1511.07452] [INSPIRE].
H. Mäntysaari, N. Mueller and B. Schenke, Diffractive Dijet Production and Wigner Distributions from the Color Glass Condensate, Phys. Rev. D 99 (2019) 074004 [arXiv:1902.05087] [INSPIRE].
F. Salazar and B. Schenke, Diffractive dijet production in impact parameter dependent saturation models, Phys. Rev. D 100 (2019) 034007 [arXiv:1905.03763] [INSPIRE].
Y. Hagiwara, Y. Hatta, R. Pasechnik, M. Tasevsky and O. Teryaev, Accessing the gluon Wigner distribution in ultraperipheral pA collisions, Phys. Rev. D 96 (2017) 034009 [arXiv:1706.01765] [INSPIRE].
M. Reinke Pelicer, E. Gräve De Oliveira and R. Pasechnik, Exclusive heavy quark-pair production in ultraperipheral collisions, Phys. Rev. D 99 (2019) 034016 [arXiv:1811.12888] [INSPIRE].
R. Staszewski, Forward proton physics at LHC, in proceedings of the 30th International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2023), East Lansing, MI, U.S.A., 27–31 March 2023, arXiv:2309.02097 [INSPIRE].
ATLAS collaboration, Prospects for Proton-Proton Measurements with Tagged Protons in ATLAS, in proceedings of the International Conference on the Structure and the Interactions of the Photon (Photon 2019), Frascati, Italy, 3–7 June 2019, pp. 144–149 [arXiv:1909.10827] [INSPIRE].
CMS and TOTEM collaborations, The CMS Precision Proton Spectrometer: Precision timing with scCVD diamond crystals, Nucl. Instrum. Meth. A 1047 (2023) 167823 [INSPIRE].
J. Nemchik, N.N. Nikolaev, E. Predazzi, B.G. Zakharov and V.R. Zoller, The Diffraction cone for exclusive vector meson production in deep inelastic scattering, J. Exp. Theor. Phys. 86 (1998) 1054 [hep-ph/9712469] [INSPIRE].
G. Baur, K. Hencken, D. Trautmann, S. Sadovsky and Y. Kharlov, Coherent γγ and γA interactions in very peripheral collisions at relativistic ion colliders, Phys. Rep. 364 (2002) 359 [hep-ph/0112211] [INSPIRE].
Y.V. Kovchegov and E. Levin, Quantum Chromodynamics at High Energy, in Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology 33, Cambridge University Press (2012) [ISBN: 9780521112574] [https://doi.org/10.1017/9781009291446] [INSPIRE].
V. Barone and E. Predazzi, High-Energy Particle Diffraction, in Texts and Monographs in Physics 565, Springer-Verlag, Berlin Heidelberg (2002) [INSPIRE].
N.N. Nikolaev and B.G. Zakharov, On determination of the large 1/x gluon distribution at HERA, Phys. Lett. B 332 (1994) 184 [hep-ph/9403243] [INSPIRE].
N.N. Nikolaev, A.V. Pronyaev and B.G. Zakharov, Azimuthal asymmetry as a new handle on σL/σT in diffractive DIS, Phys. Rev. D 59 (1999) 091501 [hep-ph/9812212] [INSPIRE].
I.P. Ivanov, N.N. Nikolaev and A.A. Savin, Diffractive vector meson production at HERA: From soft to hard QCD, Phys. Part. Nucl. 37 (2006) 1 [hep-ph/0501034] [INSPIRE].
A. Cisek, W. Schäfer and A. Szczurek, Exclusive production of ρ meson in gamma-proton collisions: dσ/dt and the role of helicity flip processes, Phys. Lett. B 836 (2023) 137595 [arXiv:2209.06578] [INSPIRE].
K.J. Golec-Biernat and M. Wüsthoff, Saturation effects in deep inelastic scattering at low Q2 and its implications on diffraction, Phys. Rev. D 59 (1998) 014017 [hep-ph/9807513] [INSPIRE].
L.S. Moriggi, G.M. Peccini and M.V.T. Machado, Investigating the inclusive transverse spectra in high-energy pp collisions in the context of geometric scaling framework, Phys. Rev. D 102 (2020) 034016 [arXiv:2005.07760] [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].
K.J. Golec-Biernat and A.M. Stasto, On solutions of the Balitsky-Kovchegov equation with impact parameter, Nucl. Phys. B 668 (2003) 345 [hep-ph/0306279] [INSPIRE].
J. Berger and A. Stasto, Numerical solution of the nonlinear evolution equation at small x with impact parameter and beyond the LL approximation, Phys. Rev. D 83 (2011) 034015 [arXiv:1010.0671] [INSPIRE].
J. Berger and A.M. Stasto, Small x nonlinear evolution with impact parameter and the structure function data, Phys. Rev. D 84 (2011) 094022 [arXiv:1106.5740] [INSPIRE].
S.S. Gubser, Conformal symmetry and the Balitsky-Kovchegov equation, Phys. Rev. D 84 (2011) 085024 [arXiv:1102.4040] [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].
H. Kowalski and D. Teaney, An Impact parameter dipole saturation model, Phys. Rev. D 68 (2003) 114005 [hep-ph/0304189] [INSPIRE].
H. Mäntysaari, K. Roy, F. Salazar and B. Schenke, Gluon imaging using azimuthal correlations in diffractive scattering at the Electron-Ion Collider, Phys. Rev. D 103 (2021) 094026 [arXiv:2011.02464] [INSPIRE].
V.P. Gonçalves, G. Sampaio dos Santos and C.R. Sena, Exclusive heavy quark photoproduction in pp, pPb and PbPb collisions at the LHC and FCC energies, Nucl. Phys. A 1000 (2020) 121862 [arXiv:1911.03453] [INSPIRE].
Y. Hatta, B.-W. Xiao, F. Yuan and J. Zhou, Azimuthal angular asymmetry of soft gluon radiation in jet production, Phys. Rev. D 104 (2021) 054037 [arXiv:2106.05307] [INSPIRE].
LHCb collaboration, Measurement of differential \( b\overline{b} \)- and \( c\overline{c} \)-dijet cross-sections in the forward region of pp collisions at \( \sqrt{s} \) = 13 TeV, JHEP 02 (2021) 023 [arXiv:2010.09437] [INSPIRE].
R. Maciula and A. Szczurek, Far-forward production of charm mesons and neutrinos at forward physics facilities at the LHC and the intrinsic charm in the proton, Phys. Rev. D 107 (2023) 034002 [arXiv:2210.08890] [INSPIRE].
Acknowledgments
The authors would like to thank Yoshitaka Hatta for providing grids for numerical solution of the BK equation. This work was partially supported by the Polish National Science Center grant UMO-2018/31/B/ST2/03537 and by the Center for Innovation and Transfer of Natural Sciences and Engineering Knowledge in Rzeszów. R.P. is supported in part by the Swedish Research Council grant, contract number 2016-05996, as well as by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 668679).
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: 2308.00457
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
Linek, B., Łuszczak, A., Łuszczak, M. et al. Probing proton structure with \( \textrm{c}\overline{\textrm{c}} \) correlations in ultraperipheral pA collisions. J. High Energ. Phys. 2023, 179 (2023). https://doi.org/10.1007/JHEP10(2023)179
Received:
Revised:
Accepted:
Published:
Version of record:
DOI: https://doi.org/10.1007/JHEP10(2023)179