Abstract
Using the leading twist approach (LTA) to nuclear shadowing, we calculate the ratios of diffractive and usual parton distributions for a heavy nucleus (Pb) and the proton, \( {R}_{A/p}=\left({f}_{i/A}^{D(3)}/{f}_{i/A}\right)/\left({f}_{i/p}^{D(3)}/{f}_{i/p}\right) \), for coherent and summed (coherent plus quasi-elastic) nuclear deep-inelastic scattering. We find that RA/p ≈ 0.5 − 1 for quarks as well as for the ratio of the diffractive and total cross sections \( {\left[\left({d\sigma}_{\textrm{diff}}/{d M}_X^2\right)/{\sigma}_{\textrm{tot}}\right]}_{eA}/{\left[\left({d\sigma}_{\textrm{diff}}/{d M}_X^2\right)/{\sigma}_{\textrm{tot}}\right]}_{ep} \) and RA/p ≈ 0.5 − 1.3 for gluons in a broad range of x, including the kinematics of the Electron-Ion Collider, which reaffirms the difference from the nuclear enhancement of RA/p predicted in the gluon saturation framework. We demonstrate that the magnitude of RA/p is controlled by the cross section of the interaction of hadronic fluctuations of the virtual photon with target nucleons, which explains an enhancement of RA/p in the color dipole model and its suppression in LTA. We argue that the black disk limit corresponds to RA/p = 1 and \( {R}_{A/p}^{\textrm{coh}} \) = 0.86 for the summed and coherent scattering, respectively. Relying on an intuitive definition of the saturation scale, we show that the ratio of the saturation scales of a heavy nucleus and proton \( {Q}_{sA}^2(b)/{Q}_{sp}^2(b)\approx 1 \) at small impact parameters b due to the strong leading twist nuclear shadowing and diluteness of the nuclear density.
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References
M. Klasen and H. Paukkunen, Nuclear PDFs After the First Decade of LHC Data, arXiv:2311.00450 [https://doi.org/10.1146/annurev-nucl-102122-022747] [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].
A. Morreale and F. Salazar, Mining for Gluon Saturation at Colliders, Universe 7 (2021) 312 [arXiv:2108.08254] [INSPIRE].
CTEQ collaboration, Handbook of perturbative QCD: Version 1.0, Rev. Mod. Phys. 67 (1995) 157 [INSPIRE].
K.J. Eskola, P. Paakkinen, H. Paukkunen and C.A. Salgado, EPPS21: a global QCD analysis of nuclear PDFs, Eur. Phys. J. C 82 (2022) 413 [arXiv:2112.12462] [INSPIRE].
R. Abdul Khalek et al., nNNPDF3.0: evidence for a modified partonic structure in heavy nuclei, Eur. Phys. J. C 82 (2022) 507 [arXiv:2201.12363] [INSPIRE].
K. Kovarik et al., nCTEQ15 — Global analysis of nuclear parton distributions with uncertainties in the CTEQ framework, Phys. Rev. D 93 (2016) 085037 [arXiv:1509.00792] [INSPIRE].
L. Frankfurt, V. Guzey and M. Strikman, Leading Twist Nuclear Shadowing Phenomena in Hard Processes with Nuclei, Phys. Rept. 512 (2012) 255 [arXiv:1106.2091] [INSPIRE].
J.-W. Qiu and I. Vitev, Resummed QCD power corrections to nuclear shadowing, Phys. Rev. Lett. 93 (2004) 262301 [hep-ph/0309094] [INSPIRE].
H. Kowalski, T. Lappi and R. Venugopalan, Nuclear enhancement of universal dynamics of high parton densities, Phys. Rev. Lett. 100 (2008) 022303 [arXiv:0705.3047] [INSPIRE].
N. Armesto, Nuclear shadowing, J. Phys. G 32 (2006) R367 [hep-ph/0604108] [INSPIRE].
L. Frankfurt, V. Guzey, M. McDermott and M. Strikman, Nuclear shadowing in deep inelastic scattering on nuclei: Leading twist versus eikonal approaches, JHEP 02 (2002) 027 [hep-ph/0201230] [INSPIRE].
L. Frankfurt and M. Strikman, Diffraction at HERA, color opacity and nuclear shadowing, Eur. Phys. J. A 5 (1999) 293 [hep-ph/9812322] [INSPIRE].
V. Guzey, E. Kryshen, M. Strikman and M. Zhalov, Evidence for nuclear gluon shadowing from the ALICE measurements of PbPb ultraperipheral exclusive J/ψ production, Phys. Lett. B 726 (2013) 290 [arXiv:1305.1724] [INSPIRE].
V. Guzey and M. Zhalov, Exclusive J/ψ production in ultraperipheral collisions at the LHC: constrains on the gluon distributions in the proton and nuclei, JHEP 10 (2013) 207 [arXiv:1307.4526] [INSPIRE].
ALICE collaboration, Coherent J/ψ and ψ′ photoproduction at midrapidity in ultra-peripheral Pb-Pb collisions at \( \sqrt{s_{\textrm{NN}}} \) = 5.02 TeV, Eur. Phys. J. C 81 (2021) 712 [arXiv:2101.04577] [INSPIRE].
ALICE collaboration, Coherent J/ψ photoproduction at forward rapidity in ultra-peripheral Pb-Pb collisions at \( \sqrt{s_{\textrm{NN}}} \) = 5.02 TeV, Phys. Lett. B 798 (2019) 134926 [arXiv:1904.06272] [INSPIRE].
LHCb collaboration, Study of exclusive photoproduction of charmonium in ultra-peripheral lead-lead collisions, JHEP 06 (2023) 146 [arXiv:2206.08221] [INSPIRE].
CMS collaboration, Probing Small Bjorken-x Nuclear Gluonic Structure via Coherent J/ψ Photoproduction in Ultraperipheral Pb-Pb Collisions at \( \sqrt{s_{\textrm{NN}}} \) = 5.02 TeV, Phys. Rev. Lett. 131 (2023) 262301 [arXiv:2303.16984] [INSPIRE].
ALICE collaboration, Energy dependence of coherent photonuclear production of J/ψ mesons in ultra-peripheral Pb-Pb collisions at \( \sqrt{s_{\textrm{NN}}} \) = 5.02 TeV, JHEP 10 (2023) 119 [arXiv:2305.19060] [INSPIRE].
STAR collaboration, Exclusive J/ψ, ψ(2s), and e+e− pair production in Au+Au ultra-peripheral collisions at RHIC, arXiv:2311.13632 [INSPIRE].
K.J. Eskola et al., Exclusive J/ψ photoproduction in ultraperipheral Pb+Pb collisions at the CERN Large Hadron Collider calculated at next-to-leading order perturbative QCD, Phys. Rev. C 106 (2022) 035202 [arXiv:2203.11613] [INSPIRE].
K.J. Eskola et al., Next-to-leading order perturbative QCD predictions for exclusive J/ψ photoproduction in oxygen-oxygen and lead-lead collisions at energies available at the CERN Large Hadron Collider, Phys. Rev. C 107 (2023) 044912 [arXiv:2210.16048] [INSPIRE].
D. Bendova, J. Cepila, J.G. Contreras and M. Matas, Photonuclear J/ψ production at the LHC: Proton-based versus nuclear dipole scattering amplitudes, Phys. Lett. B 817 (2021) 136306 [arXiv:2006.12980] [INSPIRE].
J. Cepila, J.G. Contreras and M. Krelina, Coherent and incoherent J/ψ photonuclear production in an energy-dependent hot-spot model, Phys. Rev. C 97 (2018) 024901 [arXiv:1711.01855] [INSPIRE].
L. Frankfurt, W. Koepf and M. Strikman, Diffractive heavy quarkonium photoproduction and electroproduction in QCD, Phys. Rev. D 57 (1998) 512 [hep-ph/9702216] [INSPIRE].
T. Lappi, H. Mäntysaari and J. Penttala, Relativistic corrections to the vector meson light front wave function, Phys. Rev. D 102 (2020) 054020 [arXiv:2006.02830] [INSPIRE].
E. Iancu, A.H. Mueller, D.N. Triantafyllopoulos and S.Y. Wei, Probing gluon saturation via diffractive jets in ultra-peripheral nucleus-nucleus collisions, Eur. Phys. J. C 83 (2023) 1078 [arXiv:2304.12401] [INSPIRE].
Y.V. Kovchegov, H. Sun and Z. Tu, Novel cross section ratios as possible signals of saturation in ultraperipheral collisions, Phys. Rev. D 109 (2024) 094028 [arXiv:2311.12208] [INSPIRE].
V. Guzey and M. Klasen, Diffractive dijet photoproduction in ultraperipheral collisions at the LHC in next-to-leading order QCD, JHEP 04 (2016) 158 [arXiv:1603.06055] [INSPIRE].
V. Guzey and M. Klasen, Inclusive dijet photoproduction in ultraperipheral heavy ion collisions at the CERN Large Hadron Collider in next-to-leading order QCD, Phys. Rev. C 99 (2019) 065202 [arXiv:1811.10236] [INSPIRE].
A. Accardi et al., Electron Ion Collider: The Next QCD Frontier: Understanding the glue that binds us all, Eur. Phys. J. A 52 (2016) 268 [arXiv:1212.1701] [INSPIRE].
T. Lappi, A.D. Le and H. Mäntysaari, Rapidity gap distribution of diffractive small-xp events at HERA and at the EIC, Phys. Rev. D 108 (2023) 114023 [arXiv:2307.16486] [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].
T.H. Bauer, R.D. Spital, D.R. Yennie and F.M. Pipkin, The Hadronic Properties of the Photon in High-Energy Interactions, Rev. Mod. Phys. 50 (1978) 261 [Erratum ibid. 51 (1979) 407] [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].
H. De Vries, C.W. De Jager and C. De Vries, Nuclear charge and magnetization density distribution parameters from elastic electron scattering, Atom. Data Nucl. Data Tabl. 36 (1987) 495 [INSPIRE].
V. Guzey and M. Strikman, Color fluctuation approximation for multiple interactions in leading twist theory of nuclear shadowing, Phys. Lett. B 687 (2010) 167 [arXiv:0908.1149] [INSPIRE].
K.J. Golec-Biernat and A. Luszczak, Diffractive parton distributions from the analysis with higher twist, Phys. Rev. D 76 (2007) 114014 [arXiv:0704.1608] [INSPIRE].
M. Salajegheh et al., Global QCD analysis of diffractive parton distribution function considering higher twist corrections within the xFitter framework, Phys. Rev. D 106 (2022) 054012 [arXiv:2206.13788] [INSPIRE].
L. Frankfurt, V. Guzey and M. Strikman, Leading twist coherent diffraction on nuclei in deep inelastic scattering at small x and nuclear shadowing, Phys. Lett. B 586 (2004) 41 [hep-ph/0308189] [INSPIRE].
G. Alberi and G. Goggi, Diffraction of Subnuclear Waves, Phys. Rept. 74 (1981) 1 [INSPIRE].
M. Goharipour, H. Khanpour and V. Guzey, First global next-to-leading order determination of diffractive parton distribution functions and their uncertainties within the xFitter framework, Eur. Phys. J. C 78 (2018) 309 [arXiv:1802.01363] [INSPIRE].
M. Salajegheh et al., Determination of diffractive PDFs from a global QCD analysis of inclusive diffractive DIS and dijet cross-section measurements at HERA, Phys. Rev. D 107 (2023) 094038 [arXiv:2301.10284] [INSPIRE].
L. Frankfurt, V. Guzey, A. Stasto and M. Strikman, Selected topics in diffraction with protons and nuclei: past, present, and future, Rept. Prog. Phys. 85 (2022) 126301 [arXiv:2203.12289] [INSPIRE].
L. Frankfurt, M. Strikman and C. Weiss, Transverse nucleon structure and diagnostics of hard parton-parton processes at LHC, Phys. Rev. D 83 (2011) 054012 [arXiv:1009.2559] [INSPIRE].
T. Rogers, V. Guzey, M. Strikman and X. Zu, Determining the proximity of γ*N scattering to the black body limit using DIS and J/ψ production, Phys. Rev. D 69 (2004) 074011 [hep-ph/0309099] [INSPIRE].
H. Mäntysaari and B. Schenke, Evidence of strong proton shape fluctuations from incoherent diffraction, Phys. Rev. Lett. 117 (2016) 052301 [arXiv:1603.04349] [INSPIRE].
H. Mäntysaari and B. Schenke, Probing subnucleon scale fluctuations in ultraperipheral heavy ion collisions, Phys. Lett. B 772 (2017) 832 [arXiv:1703.09256] [INSPIRE].
Acknowledgments
The research of V.G. was funded by the Academy of Finland project 330448, the Center of Excellence in Quark Matter of the Academy of Finland (projects 346325 and 346326), and the European Research Council project ERC-2018-ADG-835105 YoctoLHC. The research of M.S. was supported by the US Department of Energy Office of Science, Office of Nuclear Physics under Award No. DE-FG02-93ER40771.
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Guzey, V., Strikman, M. Suppression of diffraction in deep-inelastic scattering on nuclei and dynamical mechanism of leading twist nuclear shadowing. J. High Energ. Phys. 2024, 45 (2024). https://doi.org/10.1007/JHEP07(2024)045
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DOI: https://doi.org/10.1007/JHEP07(2024)045