- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Better angle on hadron transverse momentum distributions at the Electron-Ion Collider

Anjie Gao*, Johannes K. L. Michel†, Iain W. Stewart‡, and Zhiquan Sun§

  • Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • *anjiegao@mit.edu
  • †jklmich@mit.edu
  • ‡iains@mit.edu
  • §zqsun@mit.edu
PDF

Phys. Rev. D 107, L091504 – Published 17 May, 2023

DOI: https://doi.org/10.1103/PhysRevD.107.L091504

Abstract

We propose an observable q* sensitive to transverse momentum dependence (TMD) in eN→ehX, with q*/EN defined purely by lab-frame angles. In 3D measurements of confinement and hadronization this resolves the crippling issue of accurately reconstructing small transverse momentum PhT. We prove factorization for dσh/dq* for q*≪Q with standard TMD functions, enabling q* to substitute for PhT. A double-angle reconstruction method is given which is exact to all orders in QCD for q*≪Q. q* enables an order-of-magnitude improvement in the expected experimental resolution at the EIC.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (47)

  1. J. Collins, Foundations of Perturbative QCD, Cambridge Monographs on Particle Physics, Nuclear Physics, and Cosmology (Cambridge University Press, New York, NY, 2011).
  2. A. Airapetian et al. (HERMES Collaboration), Multiplicities of charged pions and kaons from semi-inclusive deep-inelastic scattering by the proton and the deuteron, Phys. Rev. D 87, 074029 (2013).
  3. A. Airapetian et al. (HERMES Collaboration), Beam-helicity asymmetries for single-hadron production in semi-inclusive deep-inelastic scattering from unpolarized hydrogen and deuterium targets, Phys. Lett. B 797, 134886 (2019).
  4. A. Airapetian et al. (HERMES Collaboration), Azimuthal single- and double-spin asymmetries in semi-inclusive deep-inelastic lepton scattering by transversely polarized protons, J. High Energy Phys. 12 (2020) 010.
  5. M. Alekseev et al. (COMPASS Collaboration), Collins and Sivers asymmetries for pions and kaons in muon-deuteron DIS, Phys. Lett. B 673, 127 (2009).
  6. M. Aghasyan et al. (COMPASS Collaboration), Transverse-momentum-dependent Multiplicities of Charged Hadrons in Muon-Deuteron Deep Inelastic Scattering, Phys. Rev. D 97, 032006 (2018).
  7. B. Parsamyan, Measurement of longitudinal-target-polarization dependent azimuthal asymmetries in SIDIS at COMPASS experiment, Proc. Sci., DIS2017 (2018) 259 [arXiv:1801.01488].
  8. E.-C. Aschenauer, A. Bazilevsky, M. Diehl, J. Drachenberg, K. O. Eyser et al., The RHIC SPIN program: Achievements and future opportunities, arXiv:1501.01220.
  9. L. Adamczyk et al. (STAR Collaboration), Measurement of the Transverse Single-Spin Asymmetry in p↑+p→W±/Z0 at RHIC, Phys. Rev. Lett. 116, 132301 (2016).
  10. H. Avakian et al. (CLAS Collaboration), Measurement of beam-spin asymmetries for π+ electroproduction above the baryon resonance region, Phys. Rev. D 69, 112004 (2004).
  11. S. Jawalkar et al. (CLAS Collaboration), Semi-Inclusive π0 target and beam-target asymmetries from 6 GeV electron scattering with CLAS, Phys. Lett. B 782, 662 (2018).
  12. S. Moran et al. (CLAS Collaboration), Measurement of charged-pion production in deep-inelastic scattering off nuclei with the CLAS detector, Phys. Rev. C 105, 015201 (2022).
  13. I. Scimemi and A. Vladimirov, Non-perturbative structure of semi-inclusive deep-inelastic and Drell-Yan scattering at small transverse momentum, J. High Energy Phys. 06 (2020) 137.
  14. A. Bacchetta, V. Bertone, C. Bissolotti, G. Bozzi, F. Delcarro, F. Piacenza, and M. Radici, Transverse-momentum-dependent parton distributions up to NLL3 from Drell-Yan data, J. High Energy Phys. 07 (2020) 117.
  15. M. Bury, A. Prokudin, and A. Vladimirov, Extraction of the Sivers function from SIDIS, Drell-Yan, and W±/Z boson production data with TMD evolution, J. High Energy Phys. 05 (2021) 151.
  16. R. Abdul Khalek et al., Science requirements and detector concepts for the electron-ion collider: EIC yellow report, Nucl. Phys. A1026, 122447 (2022).
  17. M. A. Ebert, I. W. Stewart, and Y. Zhao, Determining the nonperturbative Collins-Soper kernel from lattice QCD, Phys. Rev. D 99, 034505 (2019).
  18. P. Shanahan, M. Wagman, and Y. Zhao, Collins-Soper kernel for TMD evolution from lattice QCD, Phys. Rev. D 102, 014511 (2020).
  19. P. Shanahan, M. Wagman, and Y. Zhao, Lattice QCD calculation of the Collins-Soper kernel from quasi-TMDPDFs, Phys. Rev. D 104, 114502 (2021).
  20. M. Schlemmer, A. Vladimirov, C. Zimmermann, M. Engelhardt, and A. Schäfer, Determination of the collins-soper kernel from lattice QCD, J. High Energy Phys. 08 (2021) 004.
  21. Y. Li et al., Lattice QCD Study of Transverse-Momentum Dependent Soft Function, Phys. Rev. Lett. 128, 062002 (2022).
  22. M.-H. Chu et al. (LPC Collaboration), Nonperturbative determination of Collins-Soper kernel from quasi transverse-momentum dependent wave functions, Phys. Rev. D 106, 034509 (2022).
  23. A. Banfi, S. Redford, M. Vesterinen, P. Waller, and T. R. Wyatt, Optimisation of variables for studying dilepton transverse momentum distributions at hadron colliders, Eur. Phys. J. C 71, 1600 (2011).
  24. V. M. Abazov et al. (D0 Collaboration), Precise Study of the Z/γ* Boson Transverse Momentum Distribution in pp¯ Collisions using a Novel Technique, Phys. Rev. Lett. 106, 122001 (2011).
  25. R. Aaij et al. (LHCb Collaboration), Measurement of the cross-section for Z→e+e− production in pp collisions at s=7  TeV, J. High Energy Phys. 02 (2013) 106.
  26. G. Aad et al. (ATLAS Collaboration), Measurement of the transverse momentum and ϕη* distributions of Drell–Yan lepton pairs in proton–proton collisions at s=8  TeV with the ATLAS detector, Eur. Phys. J. C 76, 291 (2016).
  27. R. Aaij et al. (LHCb Collaboration), Measurement of the forward Z boson production cross-section in pp collisions at s=7  TeV, J. High Energy Phys. 08 (2015) 039.
  28. G. Aad et al. (ATLAS Collaboration), Measurement of the transverse momentum distribution of Drell–Yan lepton pairs in proton–proton collisions at s=13  TeV with the ATLAS detector, Eur. Phys. J. C 80, 616 (2020).
  29. CMS Collaboration, Measurement of the mass dependence of the transverse momentum of lepton pairs in Drell-Yan production in proton-proton collisions at s=13  TeV, arXiv:2205.04897.
  30. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevD.107.L091504 for discussions on A) hadron mass effects, B) power corrections to the observables, C) definitions for the spin components from angular measurements, D) momentum-space factorization formula, E) additional plots for resolution curves in other regions of the phase space, and F) details on the statistical analysis.
  31. X. Liu, F. Ringer, W. Vogelsang, and F. Yuan, Lepton-jet Correlations in Deep Inelastic Scattering at the Electron-Ion Collider, Phys. Rev. Lett. 122, 192003 (2019).
  32. X. Liu, F. Ringer, W. Vogelsang, and F. Yuan, Lepton-jet correlation in deep inelastic scattering, Phys. Rev. D 102, 094022 (2020).
  33. A. Bacchetta, U. D’Alesio, M. Diehl, and C. A. Miller, Single-spin asymmetries: The Trento conventions, Phys. Rev. D 70, 117504 (2004).
  34. S. Bentvelsen, J. Engelen, and P. Kooijman, Reconstruction of (x, Q**2) and extraction of structure functions in neutral current scattering at HERA, in Workshop on Physics at HERA (1992), https://inspirehep.net/literature/332514.
  35. 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).
  36. 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).
  37. 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.
  38. D. Boer, L. Gamberg, B. Musch, and A. Prokudin, Bessel-weighted asymmetries in semi inclusive deep inelastic scattering, J. High Energy Phys. 10 (2011) 021.
  39. D. Boer and P. J. Mulders, Time reversal odd distribution functions in leptoproduction, Phys. Rev. D 57, 5780 (1998).
  40. J. C. Collins, Fragmentation of transversely polarized quarks probed in transverse momentum distributions, Nucl. Phys. B396, 161 (1993).
  41. M. A. Ebert, A. Gao, and I. W. Stewart, Factorization for azimuthal asymmetries in SIDIS at next-to-leading power, J. High Energy Phys. 06 (2022) 007.
  42. A. Banfi, M. Dasgupta, and R. M. Duran Delgado, The aT distribution of the Z boson at hadron colliders, J. High Energy Phys. 12 (2009) 022.
  43. A. Banfi, M. Dasgupta, and S. Marzani, QCD predictions for new variables to study dilepton transverse momenta at hadron colliders, Phys. Lett. B 701, 75 (2011).
  44. M. A. Ebert, J. K. L. Michel, I. W. Stewart, and F. J. Tackmann, Drell-Yan qT resummation of fiducial power corrections at NLL3, J. High Energy Phys. 04 (2021) 102.
  45. C. Bierlich et al., A comprehensive guide to the physics and usage of pythia 8.3, SciPost Phys. Codebases 8 (2022), arXiv:2203.11601.
  46. A. Bacchetta, V. Bertone, C. Bissolotti, G. Bozzi, M. Cerutti, F. Piacenza, M. Radici, and A. Signori, Unpolarized Transverse Momentum Distributions from a global fit of Drell-Yan and Semi-Inclusive Deep-Inelastic Scattering data, J. High Energy Phys. 10 (2022) 127.
  47. M. A. Ebert, J. K. L. Michel, F. J. Tackmann et al., scetlib: A c++ package for numerical calculations in qcd and soft-collinear effective theory, Report No. DESY-17-099, 2018, http://scetlib.desy.de.

Outline

Information

Phys. Rev. D 107, L091504– Published 17 May, 2023
  • Received 4 October 2022
  • Accepted 17 April 2023
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation