Abstract
We present a detailed study of vector meson photoproduction in ultraperipheral heavy ion collisions (UPCs). Using the dipole model, we develop a framework for the joint impact parameter and transverse momentum dependent cross sections. We compute the unpolarized cross section and cos 2ϕ azimuthal angular correlation for ρ0 photoproduction with ϕ defined as the angle between the ρ0’s transverse momentum and its decay product pion meson’s transverse momentum. Our result on unpolarized coherent differential cross section gives excellent description to the STAR experimental data. A first compari- son between theoretical calculation and experimental measurement on the cos 2ϕ azimuthal asymmetry, which results from the linearly polarized photons, is performed and reasonable agreement is reached. We find out the characteristic diffractive patterns at both RHIC and LHC energies and predict the impact parameter dependent cos 2ϕ azimuthal asymmetries for ρ0 photoproduction by considering UPCs and peripheral collisions. The future experimental measurements at RHIC and LHC relevant to our calculations will provide a tool to rigorously investigate the coherent and incoherent production of vector meson in UPCs, as well as to probe the nuclear structure in heavy ion collisions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
Y. Hatta, M. Strikman, J. Xu and F. Yuan, Sub-threshold J/ψ and Υ production in γA collisions, Phys. Lett. B 803 (2020) 135321 [arXiv:1911.11706] [INSPIRE].
A. Donnachie and P.V. Landshoff, Exclusive rho Production in Deep Inelastic Scattering, Phys. Lett. B 185 (1987) 403 [INSPIRE].
M.G. Ryskin, Diffractive J/Ψ electroproduction in LLA QCD, Z. Phys. C 57 (1993) 89 [INSPIRE].
S.J. Brodsky, L. Frankfurt, J.F. Gunion, A.H. Mueller and M. Strikman, Diffractive leptoproduction of vector mesons in QCD, Phys. Rev. D 50 (1994) 3134 [hep-ph/9402283] [INSPIRE].
J. Nemchik, N.N. Nikolaev, E. Predazzi and B.G. Zakharov, Color dipole phenomenology of diffractive electroproduction of light vector mesons at HERA, Z. Phys. C 75 (1997) 71 [hep-ph/9605231] [INSPIRE].
S. Klein and J. Nystrand, Exclusive vector meson production in relativistic heavy ion collisions, Phys. Rev. C 60 (1999) 014903 [hep-ph/9902259] [INSPIRE].
S. Munier, A.M. Stasto and A.H. Mueller, Impact parameter dependent S matrix for dipole proton scattering from diffractive meson electroproduction, Nucl. Phys. B 603 (2001) 427 [hep-ph/0102291] [INSPIRE].
B.Z. Kopeliovich, J. Nemchik, A. Schafer and A.V. Tarasov, Color transparency versus quantum coherence in electroproduction of vector mesons off nuclei, Phys. Rev. C 65 (2002) 035201 [hep-ph/0107227] [INSPIRE].
H. Kowalski and D. Teaney, An impact parameter dipole saturation model, Phys. Rev. D 68 (2003) 114005 [hep-ph/0304189] [INSPIRE].
H. Kowalski, L. Motyka and G. Watt, Exclusive diffractive processes at HERA within the dipole picture, Phys. Rev. D 74 (2006) 074016 [hep-ph/0606272] [INSPIRE].
V. Rebyakova, M. Strikman and M. Zhalov, Coherent ρ and J/ψ photoproduction in ultraperipheral processes with electromagnetic dissociation of heavy ions at RHIC and LHC, Phys. Lett. B 710 (2012) 647 [arXiv:1109.0737] [INSPIRE].
T. Lappi and H. Mantysaari, Incoherent diffractive J/Ψ-production in high energy nuclear DIS, Phys. Rev. C 83 (2011) 065202 [arXiv:1011.1988] [INSPIRE].
T. Lappi and H. Mantysaari, J/ψ production in ultraperipheral Pb+Pb and p+Pb collisions at energies available at the CERN Large Hadron Collider, Phys. Rev. C 87 (2013) 032201 [arXiv:1301.4095] [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].
V. Guzey, E. Kryshen and M. Zhalov, Coherent photoproduction of vector mesons in ultraperipheral heavy ion collisions: Update for run 2 at the CERN Large Hadron Collider, Phys. Rev. C 93 (2016) 055206 [arXiv:1602.01456] [INSPIRE].
V. Guzey, E. Kryshen and M. Zhalov, Incoherent ρ meson photoproduction in ultraperipheral nuclear collisions at the CERN Large Hadron Collider, Phys. Rev. C 102 (2020) 015208 [arXiv:2002.09683] [INSPIRE].
Y.-p. Xie and X. Chen, The coherent cross section of vector mesons in ultraperipheral PbPb collisions at the LHC, Eur. Phys. J. C 76 (2016) 316 [arXiv:1602.00937] [INSPIRE].
Y.-P. Xie and X. Chen, Incoherent vector mesons production in PbPb ultraperipheral collisions at the LHC, Nucl. Phys. A 959 (2017) 56 [arXiv:1805.05901] [INSPIRE].
Y.-P. Xie and X. Chen, Photoproduction of vector mesons in proton-proton ultraperipheral collisions at the CERN Large Hadron Collider, Int. J. Mod. Phys. A 33 (2018) 1850086 [arXiv:1805.11480] [INSPIRE].
Y. Cai, W. Xiang, M. Wang and D. Zhou, Exclusive photoproduction of vector meson at next-to-leading order from Color Glass Condensate, Chin. Phys. C 44 (2020) 074110 [arXiv:2002.12610] [INSPIRE].
ZEUS collaboration, Exclusive electroproduction of ρ0 and J/ψ mesons at HERA, Eur. Phys. J. C 6 (1999) 603 [hep-ex/9808020] [INSPIRE].
ZEUS collaboration, Exclusive photoproduction of J/ψ mesons at HERA, Eur. Phys. J. C 24 (2002) 345 [hep-ex/0201043] [INSPIRE].
CMS collaboration, Coherent J/ψ photoproduction in ultra-peripheral PbPb collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV with the CMS experiment, Phys. Lett. B 772 (2017) 489 [arXiv:1605.06966] [INSPIRE].
STAR collaboration, Coherent diffractive photoproduction of ρ0 mesons on gold nuclei at 200 GeV/nucleon-pair at the Relativistic Heavy Ion Collider, Phys. Rev. C 96 (2017) 054904 [arXiv:1702.07705] [INSPIRE].
STAR collaboration, Observation of excess J/ψ yield at very low transverse momenta in Au+Au collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 200 GeV and U+U collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 193 GeV, Phys. Rev. Lett. 123 (2019) 132302 [arXiv:1904.11658] [INSPIRE].
CMS collaboration, Measurement of exclusive ρ(770)0 photoproduction in ultraperipheral pPb collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 5.02 TeV, Eur. Phys. J. C 79 (2019) 702 [arXiv:1902.01339] [INSPIRE].
ALICE collaboration, Coherent photoproduction of ρ0 vector mesons in ultra-peripheral Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 5.02 TeV, JHEP 06 (2020) 035 [arXiv:2002.10897] [INSPIRE].
STAR collaboration, Measurement of the γγ− > e+ e− Process and its Angular Correlations, talk presented in Quark Matter 2019, Wuhan, China.
A. Metz and J. Zhou, Distribution of linearly polarized gluons inside a large nucleus, Phys. Rev. D 84 (2011) 051503 [arXiv:1105.1991] [INSPIRE].
C. Li, J. Zhou and Y.-J. Zhou, Probing the linear polarization of photons in ultraperipheral heavy ion collisions, Phys. Lett. B 795 (2019) 576 [arXiv:1903.10084] [INSPIRE].
C. Li, J. Zhou and Y.-J. Zhou, Impact parameter dependence of the azimuthal asymmetry in lepton pair production in heavy ion collisions, Phys. Rev. D 101 (2020) 034015 [arXiv:1911.00237] [INSPIRE].
F. Dominguez, J.-W. Qiu, B.-W. Xiao and F. Yuan, On the linearly polarized gluon distributions in the color dipole model, Phys. Rev. D 85 (2012) 045003 [arXiv:1109.6293] [INSPIRE].
D. Boer, S.J. Brodsky, P.J. Mulders and C. Pisano, Direct Probes of Linearly Polarized Gluons inside Unpolarized Hadrons, Phys. Rev. Lett. 106 (2011) 132001 [arXiv:1011.4225] [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].
A. Dumitru, T. Lappi and V. Skokov, Distribution of Linearly Polarized Gluons and Elliptic Azimuthal Anisotropy in Deep Inelastic Scattering Dijet Production at High Energy, Phys. Rev. Lett. 115 (2015) 252301 [arXiv:1508.04438] [INSPIRE].
P. Kotko, K. Kutak, C. Marquet, E. Petreska, S. Sapeta and A. van Hameren, Improved TMD factorization for forward dijet production in dilute-dense hadronic collisions, JHEP 09 (2015) 106 [arXiv:1503.03421] [INSPIRE].
D. Boer, P.J. Mulders, J. Zhou and Y.-j. Zhou, Suppression of maximal linear gluon polarization in angular asymmetries, JHEP 10 (2017) 196 [arXiv:1702.08195] [INSPIRE].
C. Marquet, C. Roiesnel and P. Taels, Linearly polarized small-x gluons in forward heavy-quark pair production, Phys. Rev. D 97 (2018) 014004 [arXiv:1710.05698] [INSPIRE].
D. Gutierrez-Reyes, S. Leal-Gomez, I. Scimemi and A. Vladimirov, Linearly polarized gluons at next-to-next-to leading order and the Higgs transverse momentum distribution, JHEP 11 (2019) 121 [arXiv:1907.03780] [INSPIRE].
F. Scarpa, D. Boer, M.G. Echevarria, J.-P. Lansberg, C. Pisano and M. Schlegel, Studies of gluon TMDs and their evolution using quarkonium-pair production at the LHC, Eur. Phys. J. C 80 (2020) 87 [arXiv:1909.05769] [INSPIRE].
R. Kishore and A. Mukherjee, Accessing linearly polarized gluon distribution in J/ψ production at the electron-ion collider, Phys. Rev. D 99 (2019) 054012 [arXiv:1811.07495] [INSPIRE].
STAR collaboration, Probing Extreme Electromagnetic Fields with the Breit-Wheeler Process, arXiv:1910.12400 [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].
J. Zhou, Elliptic gluon generalized transverse-momentum-dependent distribution inside a large nucleus, Phys. Rev. D 94 (2016) 114017 [arXiv:1611.02397] [INSPIRE].
M. Vidovic, M. Greiner, C. Best and G. Soff, Impact parameter dependence of the electromagnetic particle production in ultrarelativistic heavy ion collisions, Phys. Rev. C 47 (1993) 2308 [INSPIRE].
K. Hencken, D. Trautmann and G. Baur, Electromagnetic electron-positron pair production in heavy ion collisions with impact parameter zero, Phys. Rev. A 49 (1994) 1584 [INSPIRE].
K. Hencken, D. Trautmann and G. Baur, Impact parameter dependence of the total probability for the electromagnetic electron-positron pair production in relativistic heavy ion collisions, Phys. Rev. A 51 (1995) 1874 [nucl-th/9410014] [INSPIRE].
S.R. Klein and J. Nystrand, Interference in exclusive vector meson production in heavy ion collisions, Phys. Rev. Lett. 84 (2000) 2330 [hep-ph/9909237] [INSPIRE].
STAR collaboration, Observation of Two-source Interference in the Photoproduction Reaction AuAu → AuAuρ0 , Phys. Rev. Lett. 102 (2009) 112301 [arXiv:0812.1063] [INSPIRE].
W. Zha, L. Ruan, Z. Tang, Z. Xu and S. Yang, Double-slit experiment at Fermi scale: coherent photoproduction in heavy-ion collisions, Phys. Rev. C 99 (2019) 061901 [arXiv:1810.10694] [INSPIRE].
D. Boer, P.J. Mulders and C. Pisano, Dijet imbalance in hadronic collisions, Phys. Rev. D 80 (2009) 094017 [arXiv:0909.4652] [INSPIRE].
J. Bartels, K.J. Golec-Biernat and K. Peters, On the dipole picture in the nonforward direction, Acta Phys. Polon. B 34 (2003) 3051 [hep-ph/0301192] [INSPIRE].
Y. Hatta, B.-W. Xiao and F. Yuan, Gluon Tomography from Deeply Virtual Compton Scattering at Small-x, Phys. Rev. D 95 (2017) 114026 [arXiv:1703.02085] [INSPIRE].
Y. Hagiwara, Y. Hatta, R. Pasechnik and J. Zhou, Spin-dependent Pomeron and Odderon in elastic proton-proton scattering, Eur. Phys. J. C 80 (2020) 427 [arXiv:2003.03680] [INSPIRE].
J. Bartels, K.J. Golec-Biernat and H. Kowalski, A modification of the saturation model: DGLAP evolution, Phys. Rev. D 66 (2002) 014001 [hep-ph/0203258] [INSPIRE].
K.J. Golec-Biernat and M. Wusthoff, Saturation effects in deep inelastic scattering at low Q2 and its implications on diffraction, Phys. Rev. D 59 (1998) 014017 [hep-ph/9807513] [INSPIRE].
K.J. Golec-Biernat and M. Wusthoff, Saturation in diffractive deep inelastic scattering, Phys. Rev. D 60 (1999) 114023 [hep-ph/9903358] [INSPIRE].
S. Klein, A.H. Mueller, B.-W. Xiao and F. Yuan, Acoplanarity of a Lepton Pair to Probe the Electromagnetic Property of Quark Matter, Phys. Rev. Lett. 122 (2019) 132301 [arXiv:1811.05519] [INSPIRE].
S. Klein, A.H. Mueller, B.-W. Xiao and F. Yuan, Lepton Pair Production Through Two Photon Process in Heavy Ion Collisions, arXiv:2003.02947 [INSPIRE].
W. Zha, J.D. Brandenburg, Z. Tang and Z. Xu, Initial transverse-momentum broadening of Breit-Wheeler process in relativistic heavy-ion collisions, Phys. Lett. B 800 (2020) 135089 [arXiv:1812.02820] [INSPIRE].
C.A. Bertulani and G. Baur, Electromagnetic Processes in Relativistic Heavy Ion Collisions, Phys. Rept. 163 (1988) 299 [INSPIRE].
S.R. Klein, J. Nystrand, J. Seger, Y. Gorbunov and J. Butterworth, STARlight: A Monte Carlo simulation program for ultra-peripheral collisions of relativistic ions, Comput. Phys. Commun. 212 (2017) 258 [arXiv:1607.03838] [INSPIRE].
G. Baur, K. Hencken and D. Trautmann, Photon-photon physics in very peripheral collisions of relativistic heavy ions, J. Phys. G 24 (1998) 1657 [hep-ph/9804348] [INSPIRE].
W. Zha, J.D. Brandenburg, L. Ruan, Z. Tang and Z. Xu, Exploring the double-slit interference with linearly polarized photons, arXiv:2006.12099 [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: 2006.06206
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
Xing, H., Zhang, C., Zhou, J. et al. The cos 2ϕ azimuthal asymmetry in ρ0 meson production in ultraperipheral heavy ion collisions. J. High Energ. Phys. 2020, 64 (2020). https://doi.org/10.1007/JHEP10(2020)064
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2020)064