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Advances in High Energy Physics
Volume 2017 (2017), Article ID 2379319, 7 pages
https://doi.org/10.1155/2017/2379319
Research Article

Meson Photoproduction in Ultrarelativistic Heavy Ion Collisions

1CAS Key Laboratory of High Precision Nuclear Spectroscopy and Center for Nuclear Matter Science, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
2Department of Physics, Yunnan University, Kunming 650091, China
3School of Physics and Electronic Information Engineering, Zhaotong University, Zhaotong 657000, China

Correspondence should be addressed to Gong-Ming Yu

Received 10 August 2017; Revised 29 October 2017; Accepted 7 December 2017; Published 28 December 2017

Academic Editor: Enrico Lunghi

Copyright © 2017 Gong-Ming Yu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Abstract

The transverse momentum distributions for inclusive meson described by gluon-gluon interactions from photoproduction processes in relativistic heavy ion collisions are calculated. We considered the color-singlet (CS) and color-octet (CO) components within the framework of Nonrelativistic Quantum Chromodynamics (NRQCD) in the production of heavy quarkonium. The phenomenological values of the matrix elements for the color-singlet and color-octet components give the main contribution to the production of heavy quarkonium from the gluon-gluon interaction caused by the emission of additional gluon in the initial state. The numerical results indicate that the contribution of photoproduction processes cannot be negligible for midrapidity in p-p and Pb-Pb collisions at the Large Hadron Collider (LHC) energies.

1. Introduction

Heavy quarkonium is a multiscale system which can probe all regimes of Quantum Chromodynamics (QCD) and present an ideal laboratory for testing the interplay between perturbative and nonperturbative QCD within a controlled environment. In recent years, many measurement reports have been published by ALICE collaboration [1, 2], CMS collaboration [3, 4], ATLAS collaboration [5, 6], and LHCb collaboration [7, 8] at the Large Hadron Collider (LHC) energies; several theoretical approaches have been proposed such as the color-singlet (CS) mechanism [9, 10], the color-octet (CO) mechanism [11, 12], the color evaporation mechanism [13, 14], the color-dipole mechanism [1518], the mixed heavy-quark hybrids mechanism [19], the recombination mechanism [2024], the photoproduction mechanism [2531], the potential Nonrelativistic Quantum Chromodynamics (pNRQCD) approach [3234], the transverse-momentum-dependent factorization approach [35], the transport approach [3641], the -factorization approach [4245], the fragmentation approach [4652], and the Nonrelativistic Quantum Chromodynamics (NRQCD) approach [5367]. Among them, the NRQCD approach, which takes into account contributions of color-singlet component and color-octet components with the nonperturbative long-distance matrix elements (LDME), is the most successful in phenomenological studies. The long-distance matrix elements are process-independent and can be classified in terms of the relative velocity for the heavy quarks in the bound state. But, the heavy quarkonium production mechanism is still not fully understood.

In this study, we extend the hard photoproduction mechanism [68] to the heavy quarkonium production and investigate the production of inclusive meson in p-p and Pb-Pb collisions at the LHC. According to [69], the light contributions for heavy quarkonium production are negligible; therefore in this work we only consider the contributions of gluon-gluon processes caused by the emission of additional gluons, which is different from our previous work [26] based on the method developed in [70, 71]. In high energy collisions, the partons from the nucleus can emit high energy photons that can fluctuate into gluons and then interact with the partons of the other nucleus. Hence we consider that the hard photoproduction processes of a charged parton of the incident nucleon can emit a high energy photon in high energy nucleus-nucleus collisions.

The paper is organized as follows. In Section 2 we present the photoproduction of inclusive from gluon-gluon interactions at LHC. The numerical results for large- meson production in p-p collisions and Pb-Pb collisions at LHC are given in Section 3. Finally, the conclusion is given in Section 4.

2. General Formalism

In relativistic heavy ion collisions, the production of mesons by the gluon-gluon (g-g) processes from the initial parton interaction can be divided into three processes: direct g-g processes, semielastic resolved photoproduction, and inelastic resolved photoproduction processes.

In direct processes, the parton (gluon) of the incident nucleus interacts with the parton (gluon) of another incident nucleus by the interaction of . The invariant cross section of large- meson of the process is described in the pQCD parton model on the basis of the factorization theorem and can be written as where the variables and are the momentum fractions of the partons, is the momentum fraction of the final charmed-meson, , , , , and is the mass of the meson; and are the parton distribution functions (PDF) for the colliding partons and carrying fractional momenta and in the interacting nucleons [72]: where is the nuclear modification factor [73] and is the gluon distribution function of nucleon.

According to NRQCD scaling rules [74, 75], the color-singlet as well as -wave and -wave color-octet components give the main contributions to the production process under consideration [76]: The subprocesses cross section of , , and state are, respectively, given by [77, 78] where , , and . Here , , and are the Mandelstam variables. is the wave function value of meson for the color-singlet state at the origin [7984], where is the mass of the heavy-quark pairs. The LDMEs of the color-octet components are used as follows: For the meson they are [56] and for meson they are [85, 86] where () is the mass of charm (bottom).

In the semielastic resolved photoproduction g-g processes, the parton (gluon) from resolved photon of the incident nucleus interacts with the parton (gluon) of another incident nucleus , and the cross section is given by where is the photon spectrum of the nucleus, and is the parton distribution function of the resolved photon [87].

For p-p collisions, the photon spectrum function of a proton can be written as [8890] where is the momentum fraction of photon, , with Here is the mass of the proton and at high energies    is given by .

For Pb-Pb collisions, the photon spectrum obtained from a semiclassical description of high energy electromagnetic collisions for low photon energies is given by [91, 92] where is the photon energy, and is the nucleus radius.

In inelastic resolved photoproduction g-g processes, the parton (gluon) from resolved photon emitted by the charged parton of the incident nucleus interacts with the parton (gluon) of another incident nucleus , and the expression of the cross section is given by where is the photon spectrum from the charged parton of the incident nucleus. In relativistic hadron-hadron and nucleus-nucleus collisions [69] we have with being the photon momentum fraction.

3. Numerical Results

In ultrarelativistic high energy nucleus-nucleus collisions, the equivalent photon spectrum obtained with a semiclassical description of high energy electromagnetic collisions for the nucleus is . At LHC energies, the Lorentz factor becomes very important. Indeed, the equivalent photon spectrum function with Weizscker-Williams approximation for the proton is , where is the proton mass and is the centre-of-mass energy per nucleon pair. Since is very high, the photon spectrum function becomes very large. Therefore the contribution of meson produced by semielastic hard photoproduction g-g processes cannot be negligible at LHC energies. For the inelastic photoproduction processes, the equivalent photon spectrum function of the charged parton is , where is the charged parton mass. Hence, the photon spectrum for the charged parton becomes prominent at LHC energies. The numerical results of our calculations for large- mesons produced by the hard photoproduction gluon-gluon processes in relativistic heavy ion collisions are plotted in Figures 1 and 2.

Figure 1: The invariant cross section of large- meson production from gluon-gluon interaction at midrapidity in p-p collisions ( and ) and Pb-Pb collisions ( and ) at the LHC. The dashed line (red line) is for the initial gluon-gluon interaction (LO), the dotted line (blue line) for the semielastic hard photoproduction g-g processes (semi.), the dashed-dotted line (wine line) for the inelastic hard photoproduction g-g processes (inel.), and the solid line (black line) for the sum of the above processes.
Figure 2: The same as Figure 1 but for large- meson production from gluon-gluon interaction at midrapidity in p-p and Pb-Pb collisions at the LHC.

In Figure 1 (Figure 2), we plot the contributions from the hard photoproduction gluon-gluon processes to the () meson at midrapidity in p-p and Pb-Pb collisions at LHC energies. Compared with the production of the initial gluon-gluon interaction (the dashed line), the contribution of meson produced by semielastic hard photoproduction g-g processes (the dotted line) is not prominent in p-p collisions with and , but the contribution of inelastic photoproduction g-g processes (the dashed-dotted line) becomes evident in p-p collisions [see Figures 1(a), 1(b), 2(a), and 2(b)]. Indeed, for Pb-Pb collisions with and , the contribution of semielastic photoproduction g-g processes (the dotted line) and inelastic photoproduction g-g processes (the dashed-dotted line) cannot be negligible at LHC energies [see Figures 1(c), 1(d), 2(c), and 2(d)].

4. Conclusions

In summary, we have investigated the production of heavy quarkonium meson from the gluon-gluon interactions in p-p collisions and Pb-Pb collisions at LHC energies. The color-singlet and color-octet mechanisms have been used for heavy quarkonium production processes. At the early stages of relativistic high energy nucleus-nucleus collisions, the ultrarelativistic nucleus (charged parton) can emit hadron-like photons that can fluctuate into a gluon; then the gluon interacts with a gluon of the other incident nucleus by gluon-gluon interaction. Our results indicate that the contribution of meson produced by the hard photoproduction processes cannot be negligible in p-p and Pb-Pb collisions at LHC energies.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work has been supported by the National Basic Research Program of China (973 Program, 2014CB845405), the China Postdoctoral Science Foundation funded project (2017M610663), and the Applied Basic Research Plan of Yunnan Province (Youth Project, 2017FD147).

References

  1. B. Abelev et al., “Upgrade of the ALICE Experiment: Letter Of Intent,” Journal of Physics G: Nuclear and Particle Physics, vol. 740, no. 105, 2014. View at Publisher · View at Google Scholar
  2. B. Abelev et al., “Upgrade of the ALICE Experiment: Letter Of Intent,” Journal of Physics G: Nuclear and Particle Physics, vol. 738, no. 361, 2014. View at Publisher · View at Google Scholar
  3. V. Khachatryan et al., “CMS Collaboration,” Physical Review Letters, vol. 114, Article ID 191802, 2015. View at Google Scholar
  4. V. Khachatryan et al., “CMS Collaboration,” Physics Letters B, vol. 749, no. 14, 2015. View at Google Scholar
  5. G. Aad et al., “ATLAS collaboration,” Physical Review C, vol. 91, no. 11, 2015. View at Publisher · View at Google Scholar
  6. G. Aad et al., “ATLAS collaboration,” Journal of High Energy Physics, vol. 7, no. 154, 2014. View at Google Scholar
  7. R. Aaij et al., “LHCb collaboration,” European Physical Journal C, vol. 75, no. 311, 2015. View at Google Scholar
  8. R. Aaij et al., “LHCb collaboration,” Journal of High Energy Physics, vol. 10, no. 115, 2013. View at Google Scholar
  9. A. Petrelli, M. Cacciari, M. Greco, F. Maltoni, and M. L. Mangano, “NLO production and decay of quarkonium,” Nuclear Physics B, vol. 514, no. 1-2, pp. 245–309, 1998. View at Publisher · View at Google Scholar · View at Scopus
  10. E. Braaten and S. Fleming, “Color-octet fragmentation and the ψ sssssurplus at the fermilab tevatron,” Physical Review Letters, vol. 74, no. 17, pp. 3327–3330, 1995. View at Publisher · View at Google Scholar · View at Scopus
  11. G. C. Nayak, M. X. Liu, and F. Cooper, “Color octet contribution to high,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 68, no. 3, 2003. View at Publisher · View at Google Scholar
  12. M. Klasen, B. A. Kniehl, L. N. Mihaila, and M. Steinhauser, “Evidence for the Color-Octet Mechanism from CERN LEP2,” Physical Review Letters, vol. 89, no. 3, 2002. View at Publisher · View at Google Scholar
  13. R. M. Godbole, A. Misra, A. Mukherjee, and V. S. Rawoot, “Transverse single spin asymmetries and charmonium production,” Nuclear Physics B—Proceedings Supplements, vol. 251-252, pp. 56–61, 2014. View at Publisher · View at Google Scholar · View at Scopus
  14. H. Fujii and K. Watanabe, “Heavy quark pair production in high-energy pA collisions: Quarkonium,” Nuclear Physics A, vol. 915, no. 1, 2013. View at Google Scholar
  15. V. P. Goncalves, B. D. Moreira, and F. S. Navarra, “Exclusive ϒ photoproduction in hadronic collisions at CERN LHC energies,” Physics Letters B, vol. 742, no. 172, 2015. View at Google Scholar
  16. T. Song, “Charmonia formation in quark-gluon plasma,” Physical Review C, vol. 89, Article ID 044903, 2014. View at Google Scholar
  17. J. Qiu, P. Sun, B. Xiao, and F. Yuan, “Universal suppression of heavy quarkonium production in,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 89, no. 3, 2014. View at Publisher · View at Google Scholar
  18. D. E. Kharzeev, E. M. Levin, and K. Tuchin, “Nuclear modification of the J/ψ transverse momentum distributions in high energy pA and AA collisions,” Nuclear Physics A, vol. 924, pp. 47–64, 2014. View at Publisher · View at Google Scholar · View at Scopus
  19. L. S. Kisslinger, M. X. Liu, and P. McGaughey, “Heavy-quark-state production in,” Physical Review C: Nuclear Physics, vol. 89, no. 2, 2014. View at Publisher · View at Google Scholar
  20. B. Y. Chen and J. X. Zhao, “Bottomonium continuous production from unequilibrium bottom quarks in ultrarelativistic heavy ion collisions,” Physics Letters B, vol. 772, p. 819, 2017. View at Publisher · View at Google Scholar
  21. B. Y. Chen, “Elliptic flow as a probe for the ψ(2S) production mechanism in relativistic heavy ion collisions,” Physical Review C, vol. 95, Article ID 034908, 2017. View at Google Scholar
  22. S. Ganesh and M. Mishra, “pQCD approach to charmonium regeneration in QGP at the LHC,” Nuclear Physics A, vol. 947, no. 38, 2016. View at Publisher · View at Google Scholar
  23. S. Cho, “Enhanced production of ψ(2S) mesons in heavy ion collisions,” Physical Review C, vol. 91, Article ID 054914, 2015. View at Google Scholar
  24. E. G. Ferreiro, “Charmonium dissociation and recombination at LHC: Revisiting comovers,” Physics Letters B, vol. 731, no. 57, 2014. View at Google Scholar
  25. G.-M. Yu, Y.-C. Yu, Y.-D. Li, and J.-S. Wang, “Charmonium production in ultra-peripheral heavy ion collisions with two-photon processes,” Nuclear Physics B, vol. 917, p. 234, 2017. View at Publisher · View at Google Scholar
  26. G. Yu, Y. Cai, Y. Li, and J. Wang, “Publisher's Note: Heavy quarkonium photoproduction in ultrarelativistic heavy ion collisions [Phys. Rev. C,” Physical Review C: Nuclear Physics, vol. 95, no. 6, 2017. View at Publisher · View at Google Scholar
  27. V. P. Goncalves and G. G. da Silveira, “Probing the photon flux in the diffractive quarkonium photoproduction at the LHC,” Physical Review D, vol. 91, Article ID 054013, 2015. View at Google Scholar
  28. V. P. Goncalves and W. K. Sauter, “ production in photon-induced interactions at a fixed target experiment at LHC as a probe of the odderon,” Physical Review D, vol. 91, Article ID 094014, 2015. View at Google Scholar
  29. G. Chen, X. Wu, H. Fu, H. Han, and Z. Sun, “Photoproduction of heavy quarkonium at the ILC,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 90, no. 3, 2014. View at Publisher · View at Google Scholar
  30. N. Armesto and A. H. Rezaeian, “Exclusive vector meson production at high energies and gluon saturation,” Physical Review D, vol. 90, Article ID 054003, 2014. View at Google Scholar
  31. G. S. dos Santos and M. V. Machado, “Exclusive photoproduction of quarkonium in proton-nucleus collisions at energies available at the CERN Large Hadron Collider,” Physical Review C: Nuclear Physics, vol. 89, no. 2, 2014. View at Publisher · View at Google Scholar
  32. A. Pineda, “Collective phenomena in ultra-relativistic nuclear collisions: anisotropic flow and more,” Progress in Particle and Nuclear Physics, vol. 67, no. 2, pp. 541–546, 2012. View at Publisher · View at Google Scholar
  33. B. A. Kniehl, A. A. Penin, V. A. Smirnov, and M. Steinhauser, “Deduction, ordering, and operations in quantum logic,” Foundations of Physics, vol. 635, no. 357, 2002. View at Publisher · View at Google Scholar
  34. N. Brambilla, A. Pineda, J. Soto, and A. Vairo, “Potential NRQCD: An effective theory for heavy quarkonium,” Nuclear Physics B, vol. 566, no. 1-2, pp. 275–310, 2000. View at Publisher · View at Google Scholar · View at Scopus
  35. J. P. Ma, J. X. Wang, and S. Zhao, “The entropy of the noncommutative acoustic black hole based on generalized uncertainty principle,” Physics Letters B, vol. 737, no. 103, pp. 6–11, 2014. View at Publisher · View at Google Scholar
  36. B. Y. Chen, T. C. Guo, Y. P. Liu, and P. F. Zhuang, “Cold and hot nuclear matter effects on charmonium production in p+Pb collisions at LHC energy,” Physics Letters, vol. 765, no. 323, 2017. View at Publisher · View at Google Scholar
  37. B. Y. Chen, “Magnetic-field-induced squeezing effect at energies available at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider,” Physical Review C: Nuclear Physics, vol. 93, no. 4, Article ID 044919, 2016. View at Publisher · View at Google Scholar
  38. B. Y. Chen, “Forbidden nonunique decays and effective values of weak coupling constants,” Physical Review C: Nuclear Physics, vol. 93, no. 3, Article ID 034308, 2016. View at Publisher · View at Google Scholar
  39. Y. Liu, C. Ko, and T. Song, “Hot medium effects on production in p+Pb collisions at ,” Physics Letters B, vol. 728, pp. 437–442, 2014. View at Publisher · View at Google Scholar
  40. T. Song, K. C. Han, and C. M. Ko, “Effects of initial fluctuations on bottomonia suppression in relativistic heavy-ion collisions,” Nuclear Physics A, vol. 897, no. 141, 2013. View at Publisher · View at Google Scholar
  41. B. Chen, K. Zhou, and P. Zhuang, “Mean field effect on,” Physical Review C: Nuclear Physics, vol. 86, no. 3, 2012. View at Publisher · View at Google Scholar
  42. S. P. Baranov, A. V. Lipatov, and N. P. Zotov, “Prompt,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 85, no. 1, 2012. View at Publisher · View at Google Scholar
  43. B. A. Kniehl, D. V. Vasin, and V. A. Saleev, “Charmonium production at high energy in the kT-factorization approach,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 73, no. 7, Article ID 074022, 2006. View at Publisher · View at Google Scholar · View at Scopus
  44. S. P. Baranov, “TeV astrophysics constraints on Planck scale Lorentz violation,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 66, Article ID 081302, 2002. View at Publisher · View at Google Scholar
  45. P. Hagler, R. Kirschner, A. Schäfer, L. Szymanowski, and O. V. Teryaev, “Towards a Solution of the Charmonium Production Controversy:,” Physical Review Letters, vol. 86, no. 8, pp. 1446–1449, 2001. View at Publisher · View at Google Scholar
  46. P. Artoiseneta and E. Braaten, “The carotid body and its relevance in pathophysiology,” Experimental Physiology, vol. 100, no. 2, pp. 121–123, 2015. View at Publisher · View at Google Scholar · View at Scopus
  47. G. T. Bodwin, H. S. Chung, U.-R. Kim, and J. Lee, “Quark fragmentation into spin-triplet S-wave quarkonium,” Physical Review D, vol. 91, Article ID 074013, 2015. View at Google Scholar
  48. G. T. Bodwin, H. S. Chung, U.-R. Kim, and J. Lee, “Fragmentation contributions to J/ψ photoproduction at HERA,” Physical Review D, vol. 92, Article ID 074042, 2015. View at Google Scholar
  49. G. T. Bodwin, H. S. Chung, U.-R. Kim, and J. Lee, “Fragmentation contributions to production at the Tevatron and the LHC,” Physical Review Letters, vol. 113, Article ID 022001, 2014. View at Publisher · View at Google Scholar
  50. Y.-Q. Ma, J.-W. Qiu, and H. Zhang, “Heavy quarkonium fragmentation functions from a heavy quark pair,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 89, Article ID 094030, 2014. View at Publisher · View at Google Scholar
  51. Y.-Q. Ma, J.-W. Qiu, and H. Zhang, “Heavy quarkonium fragmentation functions from a heavy quark pair. I. S wave,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 89, Article ID 094029, 2014. View at Publisher · View at Google Scholar
  52. G. T. Bodwin, U.-R. Kim, and J. Lee, “Provider and patient correlates of provider decisions to recommend HCV treatment to HIV Co-infected patients,” Journal of the International Association of Physicians in AIDS Care, vol. 11, no. 4, pp. 245–251, 2012. View at Publisher · View at Google Scholar · View at Scopus
  53. Y. Feng, B. Gong, L.-P. Wan, and J.-X. Wang, “An updated study of Upsilon production and polarization at the Tevatron and LHC,” Chinese Physics C, vol. 39, Article ID 123102, 2015. View at Google Scholar
  54. J.-X. Wang and H.-F. Zhang, “Uncertainties in nuclear matrix elements for neutrinoless double-beta decay,” Journal of Physics G: Nuclear and Particle Physics, vol. 42, no. 3, Article ID 034017, 2015. View at Google Scholar
  55. Z. He and B. A. Kniehl, “Complete Nonrelativistic-QCD Prediction for Prompt Double,” Physical Review Letters, vol. 115, no. 2, 2015. View at Publisher · View at Google Scholar
  56. H.-F. Zhang, Z. Sun, W.-L. Sang, and R. Li, “Nature of isomerism in exotic sulfur isotopes,” Physical Review Letters, vol. 114, no. 3, Article ID 032501, 2015. View at Publisher · View at Google Scholar
  57. H. Han, Y.-Q. Ma, C. Meng, H.-S. Shao, and K.-T. Chao, “ production at LHC and implications for the understanding of production,” Physical Review Letters, vol. 114, Article ID 092005, 2015. View at Publisher · View at Google Scholar
  58. M. Butenschoen, Z. He, and B. A. Kniehl, Physical Review Letters, vol. 114, no. 9, 2015. View at Publisher · View at Google Scholar
  59. Z. He and B. A. Kniehl, “Erratum: Relativistic corrections to prompt,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 94, no. 7, 2016. View at Publisher · View at Google Scholar
  60. Z.-B. Kang, Y.-Q. Ma, J.-W. Qiu, and G. Sterman, “Anomalous nuclear enhancement in deeply inelastic scattering and photoproduction,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 91, no. 3, pp. 1951–1971, 2015. View at Publisher · View at Google Scholar
  61. Z.-B. Kang, Y.-Q. Ma, J.-W. Qiu, and G. Sterman, “Anomalous nuclear enhancement in deeply inelastic scattering and photoproduction,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 90, no. 3, pp. 1951–1971, 2014. View at Publisher · View at Google Scholar
  62. S. P. Baranov, “Determining neutrino oscillation parameters from atmospheric muon neutrino disappearance with three years of IceCube DeepCore data,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 91, no. 7, Article ID 072004, 2015. View at Publisher · View at Google Scholar
  63. Z. He and B. A. Kniehl, “Relativistic corrections to,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 92, no. 1, 2015. View at Publisher · View at Google Scholar
  64. Z. Sun, X.-G. Wu, and H. F. Zhang, “Searching for a heavy Higgs boson in a Higgs-portal B-L model,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 92, Article ID 074021, 2015. View at Publisher · View at Google Scholar
  65. B. Gong, L.-P. Wan, J.-X. Wang, and H.-F. Zhang, “Polarization for prompt J/ψ and ψ(2s) production at the Tevatron and LHC,” Physical Review Letters, vol. 110, Article ID 042002, 2013. View at Publisher · View at Google Scholar
  66. Z. Kang, J. Qiu, and G. Sterman, “Heavy Quarkonium Production and Polarization,” Physical Review Letters, vol. 108, no. 10, 2012. View at Publisher · View at Google Scholar
  67. M. Butenschoen and B. A. Kniehl, “Reconciling production at HERA, RHIC, tevatron, and LHC with nonrelativistic QCD factorization at next-to-leading order,” Physical Review Letters, vol. 106, Article ID 022003, 2011. View at Publisher · View at Google Scholar
  68. G.-M. Yu and Y.-D. Li, “Photoproduction of dileptons, photons, and light vector mesons in ultrarelativistic heavy ion collisions,” Physical Review C, vol. 91, Article ID 044908, 2015. View at Google Scholar
  69. B. A. Knieehl, “Elastic ep scattering and the Weizsäcker-Williams approximation,” Physics Letters B, vol. 254, no. 267, 1991. View at Google Scholar
  70. A. K. Likhoded, A. V. Luchinsky, and S. V. Poslavsky, “Production of χ b mesons at the LHC,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 86, no. 7, Article ID 074027, 2012. View at Publisher · View at Google Scholar · View at Scopus
  71. M. Klasen, B. A. Kniehl, L. N. Mihaila, and M. Steinhauser, “Charmonium production in polarized high-energy collisions,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 68, no. 3, Article ID 034017, 2003. View at Publisher · View at Google Scholar · View at Scopus
  72. M. Gluck, E. Reya, and A. Vogt, “Parton distributions for high energy collisions,” Zeitschrift für Physik C: Particles and Fields, vol. 53, p. 127, 1992. View at Google Scholar
  73. X.-N. Wang and M. Gyulassy, “Hijing: a Monte Carlo model for multiple jet production in pp, pA, and AA collisions,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 44, no. 11, pp. 3501–3516, 1991. View at Publisher · View at Google Scholar · View at Scopus
  74. S. S. Biswal and K. Sridhar, “Transverse momentum distributions of strange hadrons produced in nucleus–nucleus collisions at ,” Journal of Physics G: Nuclear and Particle Physics, vol. 39, no. 2, Article ID 025009, 2012. View at Publisher · View at Google Scholar
  75. G. T. Bodwin, E. Braaten, and G. P. Legage, “Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 51, no. 3, pp. 1125–1171, 1995. View at Publisher · View at Google Scholar
  76. A. K. Likhoded, A. V. Luchinsky, and S. V. Poslavsky, “Production of η,” Modern Physics Letters A, vol. 30, no. 07, p. 1550032, 2015. View at Publisher · View at Google Scholar
  77. M. M. Meijer, J. Smith, and W. L. van Neerven, “Helicity amplitudes for charmonium production in hadron-hadron and photon-hadron collisions,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 77, no. 3, 2008. View at Publisher · View at Google Scholar
  78. R. Gastmans, W. Troost, and T. T. Wu, “Production of heavy quarkonia from gluons,” Nuclear Physics B, vol. 291, no. C, pp. 731–745, 1987. View at Publisher · View at Google Scholar · View at Scopus
  79. C. R. Munz, “Two-photon decays of mesons in a relativistic quark model,” Nuclear Physics A, vol. 609, no. 3, pp. 364–376, 1996. View at Publisher · View at Google Scholar
  80. D. Ebert, R. N. Faustov, and V. O. Galkin, “Two-photon decay rates of heavy quarkonia in the relativistic quark model,” Modern Physics Letters A, vol. 18, no. 9, pp. 601–607, 2003. View at Publisher · View at Google Scholar · View at Scopus
  81. V. V. Anisovich, L. G. Dakhno, M. A. Matveev, V. A. Nikonov, and A. V. Sarantsev, “Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Bottomonia,” Physics of Atomic Nuclei, vol. 70, no. 1, pp. 63–92, 2007. View at Publisher · View at Google Scholar · View at Scopus
  82. G.-L. Wang, “Radiation of scalar oscillons in 2 and 3 dimensions,” Physics Letters B, vol. 674, no. 4-5, pp. 319–324, 2009. View at Publisher · View at Google Scholar
  83. B.-Q. Li and K.-T. Chao, “New agegraphic dark energy in Brans-Dicke theory,” Communications in Theoretical Physics, vol. 52, no. 4, p. 761, 2009. View at Publisher · View at Google Scholar
  84. C.-W. Hwang and R.-S. Guo, “Search for a Lorentz-violating sidereal signal with atmospheric neutrinos in IceCube,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 82, Article ID 034021, 2010. View at Publisher · View at Google Scholar
  85. R. Sharma and I. Vitev, “High transverse momentum quarkonium production and dissociation in heavy ion collisions,” Physical Review C: Nuclear Physics, vol. 87, no. 4, 2013. View at Publisher · View at Google Scholar
  86. E. Braaten, S. Fleming, and A. K. Leibovich, “Nonrelativistic QCD analysis of bottomonium production at the Fermilab Tevatron,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 63, no. 9, Article ID 094006, 2001. View at Publisher · View at Google Scholar · View at Scopus
  87. M. Gluck, E. Reya, and I. Schienbein, “Erratum: Radiatively generated parton distributions of real and virtual photons,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 62, no. 1, 2000. View at Publisher · View at Google Scholar
  88. N. Baron and G. Baur, “Physics at relativistic heavy-ion colliders,” Physical Review C: Nuclear Physics, vol. 49, no. 2, pp. 1127–1131, 1994. View at Publisher · View at Google Scholar · View at Scopus
  89. M. Drees, R. M. Godbole, M. Nowakowski, and S. D. Rindani, “γγ processes at high energy pp colliders,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 50, no. 3, pp. 2335–2338, 1994. View at Publisher · View at Google Scholar · View at Scopus
  90. M. Drees and D. Zeppenfeld, “Production of supersymmetric particles in elastic ep collisions,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 39, no. 9, pp. 2536–2546, 1989. View at Publisher · View at Google Scholar · View at Scopus
  91. J. D. Jackson, Classical Electrodynamics, Wiley, New York, NY, USA, 1962. View at MathSciNet
  92. E. Papageorgiu, “Two-photon physics with ultrahigh-energy heavy-ion beams,” Physics Letters B, vol. 250, no. 1-2, pp. 155–160, 1990. View at Publisher · View at Google Scholar