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  • Open Access

First insight into transverse-momentum-dependent fragmentation physics at photon-photon colliders

Simone Anedda1,2,*, Francesco Murgia2,†, and Cristian Pisano1,2,‡

  • *Contact author: sanedda@dsf.unica.it
  • †Contact author: francesco.murgia@ca.infn.it
  • ‡Contact author: cristian.pisano@unica.it

Phys. Rev. D 112, 014013 – Published 7 July, 2025

DOI: https://doi.org/10.1103/p6w2-dn9z

Abstract

Future planned lepton colliders, both in the circular and linear configurations, can effectively work as virtual and quasireal photon-photon colliders and are expected to stimulate an intense physics program in the next few years. In this paper, we suggest to consider photon-photon scattering as a useful source of information on transverse-momentum-dependent fragmentation functions (TMD FFs), complementing semi-inclusive deeply inelastic scattering and e+e− annihilation processes, which provide most of the present phenomenological information on TMD FFs. As a first illustrative example, we study two-hadron azimuthal asymmetries around the jet thrust axis in the process ℓ+ℓ−→γ*γ→qq¯→h1h2+X, in which in a circular lepton collider one tagged, deeply virtual photon scatters off an untagged quasireal photon, both originating from the initial lepton beams, producing inclusively an almost back-to-back light-hadron pair with large transverse momentum, in the γ*γ center-of-mass frame. Similar processes, in a more complicated environment due to the presence of initial hadronic states, can also be studied in ultraperipheral collisions at the LHC and the planned future hadron colliders.

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References (41)

  1. R. Boussarie et al., TMD handbook, arXiv:2304.03302.
  2. X.-d. Ji, J.-P. Ma, and F. Yuan, QCD factorization for spin-dependent cross sections in DIS and Drell-Yan processes at low transverse momentum, Phys. Lett. B 597, 299 (2004).
  3. X.-d. Ji, J.-p. Ma, and F. Yuan, QCD factorization for semi-inclusive deep-inelastic scattering at low transverse momentum, Phys. Rev. D 71, 034005 (2005).
  4. J. Collins, Foundations of Perturbative QCD (Cambridge University Press, Cambridge, England, 2011), Vol. 32.
  5. M. G. Echevarria, A. Idilbi, and I. Scimemi, Factorization theorem for Drell-Yan at low qT and transverse momentum distributions on-the-light-cone, J. High Energy Phys. 07 (2012) 002.
  6. P. J. Mulders and R. D. Tangerman, The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction, Nucl. Phys. B461, 197 (1996).
  7. A. Bacchetta, M. Diehl, K. Goeke, A. Metz, P. J. Mulders, and M. Schlegel, Semi-inclusive deep inelastic scattering at small transverse momentum, J. High Energy Phys. 02 (2007) 093.
  8. M. Anselmino, M. Boglione, U. D’Alesio, S. Melis, F. Murgia, E. R. Nocera, and A. Prokudin, General helicity formalism for polarized semi-inclusive deep inelastic scattering, Phys. Rev. D 83, 114019 (2011).
  9. S. Arnold, A. Metz, and M. Schlegel, Dilepton production from polarized hadron hadron collisions, Phys. Rev. D 79, 034005 (2009).
  10. D. Boer, R. Jakob, and P. J. Mulders, Asymmetries in polarized hadron production in e+e− annihilation up to order 1/Q, Nucl. Phys. B504, 345 (1997).
  11. U. D’Alesio, F. Murgia, and M. Zaccheddu, General helicity formalism for two-hadron production in e+e− annihilation within a TMD approach, J. High Energy Phys. 10 (2021) 078.
  12. D. Boer, W. J. den Dunnen, C. Pisano, M. Schlegel, and W. Vogelsang, Linearly polarized gluons and the Higgs transverse momentum distribution, Phys. Rev. Lett. 108, 032002 (2012).
  13. P. Sun, B.-W. Xiao, and F. Yuan, Gluon distribution functions and Higgs boson production at moderate transverse momentum, Phys. Rev. D 84, 094005 (2011).
  14. J.-W. Qiu, M. Schlegel, and W. Vogelsang, Probing gluonic spin-orbit correlations in photon pair production, Phys. Rev. Lett. 107, 062001 (2011).
  15. 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, 87 (2020).
  16. W. J. den Dunnen, J. P. Lansberg, C. Pisano, and M. Schlegel, Accessing the transverse dynamics and polarization of gluons inside the proton at the LHC, Phys. Rev. Lett. 112, 212001 (2014).
  17. D. Boer and C. Pisano, Polarized gluon studies with charmonium and bottomonium at LHCb and AFTER, Phys. Rev. D 86, 094007 (2012).
  18. N. Kato, L. Maxia, and C. Pisano, Spin asymmetries for C-even quarkonium production as a probe of gluon distributions, Phys. Rev. D 110, 034038 (2024).
  19. T. C. Rogers and P. J. Mulders, No generalized TMD-factorization in hadro-production of high transverse momentum hadrons, Phys. Rev. D 81, 094006 (2010).
  20. V. M. Budnev, I. F. Ginzburg, G. V. Meledin, and V. G. Serbo, The two photon particle production mechanism. Physical problems. Applications. Equivalent photon approximation, Phys. Rep. 15, 181 (1975).
  21. I. F. Ginzburg, G. L. Kotkin, V. G. Serbo, and V. I. Telnov, Colliding ge and gg beams based on the single pass e±e− colliders (VLEPP type). Nucl. Instrum. Methods Phys. Res. 205, 47 (1983).
  22. I. F. Ginzburg, G. L. Kotkin, S. L. Panfil, V. G. Serbo, and V. I. Telnov, Colliding γe and γγ beams based on the single pass e+e− accelerators. 2. Polarization effects. Monochromatization improvement, Nucl. Instrum. Methods Phys. Res., Sect. A 219, 5 (1984).
  23. H. Kolanoski, Two-Photon Physics at e+e− Storage Rings (Springer-Verlag, Berlin, 1984), Vol. 105.
  24. L. Schoeffel, C. Baldenegro, H. Hamdaoui, S. Hassani, C. Royon, and M. Saimpert, Photon–photon physics at the LHC and laser beam experiments, present and future, Prog. Part. Nucl. Phys. 120, 103889 (2021).
  25. C. F. v. Weizsäcker, Radiation emitted in collisions of very fast electrons, Z. Phys. 88, 612 (1934).
  26. E. J. Williams, Nature of the high-energy particles of penetrating radiation and status of ionization and radiation formulae, Phys. Rev. 45, 729 (1934).
  27. J. C. Collins and A. Metz, Universality of soft and collinear factors in hard-scattering factorization, Phys. Rev. Lett. 93, 252001 (2004).
  28. F. Yuan, Azimuthal asymmetric distribution of hadrons inside a jet at hadron collider, Phys. Rev. Lett. 100, 032003 (2008).
  29. L. P. Gamberg, A. Mukherjee, and P. J. Mulders, A model independent analysis of gluonic pole matrix elements and universality of TMD fragmentation functions, Phys. Rev. D 83, 071503 (2011).
  30. J. C. Collins and D. E. Soper, Back-to-back jets in QCD, Nucl. Phys. B193, 381 (1981).
  31. J. C. Collins and D. E. Soper, Back-to-back jets: Fourier transform from b to kT, Nucl. Phys. B197, 446 (1982).
  32. J. C. Collins, D. E. Soper, and G. Sterman, Transverse momentum distribution in Drell-Yan pair and W and Z boson production, Nucl. Phys. B250, 199 (1985).
  33. M. G. Echevarria, A. Idilbi, A. Schäfer, and I. Scimemi, Model-independent evolution of transverse momentum dependent distribution functions (TMDs) at NNLL, Eur. Phys. J. C 73, 2636 (2013).
  34. M. G. Echevarria, A. Idilbi, and I. Scimemi, Soft and collinear factorization and transverse momentum dependent parton distribution functions, Phys. Lett. B 726, 795 (2013).
  35. U. D’Alesio, L. Gamberg, F. Murgia, and M. Zaccheddu, Transverse Λ polarization in e+e− processes within a TMD factorization approach and the polarizing fragmentation function, J. High Energy Phys. 12 (2022) 074.
  36. U. D’Alesio, L. Gamberg, F. Murgia, and M. Zaccheddu, Transverse Λ polarization in e+e− annihilations and in SIDIS processes at the EIC within TMD factorization, Phys. Rev. D 108, 094004 (2023).
  37. C. Pisano, D. Boer, S. J. Brodsky, M. G. A. Buffing, and P. J. Mulders, Linear polarization of gluons and photons in unpolarized collider experiments, J. High Energy Phys. 10 (2013) 024.
  38. K. Schilling and G. Wolf, How to analyze vector meson production in inelastic lepton scattering, Nucl. Phys. B61, 381 (1973).
  39. M. Anselmino, M. Bertini, F. Murgia, and B. Pire, Off diagonal helicity density matrix elements for heavy vector mesons inclusively produced in NN, γN and ℓN interactions, Phys. Lett. B 438, 347 (1998).
  40. M. Anselmino, M. Boglione, U. D’Alesio, E. Leader, S. Melis, and F. Murgia, The general partonic structure for hadronic spin asymmetries, Phys. Rev. D 73, 014020 (2006).
  41. J. C. Collins, Fragmentation of transversely polarized quarks probed in transverse momentum distributions, Nucl. Phys. B396, 161 (1993).

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