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  • Letter
  • Open Access

First analysis of world polarized DIS data with small-x helicity evolution

Daniel Adamiak1,*, Yuri V. Kovchegov1,†, W. Melnitchouk2, Daniel Pitonyak3,‡, Nobuo Sato2,§, and Matthew D. Sievert4,∥ (Jefferson Lab Angular Momentum Collaboration)

  • 1Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
  • 2Jefferson Lab, Newport News, Virginia 23606, USA
  • 3Department of Physics, Lebanon Valley College, Annville, Pennsylvania 17003, USA
  • 4Department of Physics, New Mexico State University, Las Cruces, New Mexico 88003, USA

  • *adamiak.5@osu.edu
  • †kovchegov.1@osu.edu
  • ‡pitonyak@lvc.edu
  • §nsato@jlab.org
  • ∥msievert@nmsu.edu
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Phys. Rev. D 104, L031501 – Published 5 August, 2021

DOI: https://doi.org/10.1103/PhysRevD.104.L031501

Abstract

We present a Monte Carlo based analysis of the combined world data on polarized lepton-nucleon deep-inelastic scattering at small Bjorken x within the polarized quark dipole formalism. We show for the first time that double-spin asymmetries at x<0.1 can be successfully described using only small-x evolution derived from first-principles QCD, allowing predictions to be made for the g1 structure function at much smaller x. Anticipating future data from the Electron-Ion Collider, we assess the impact of electromagnetic and parity-violating polarization asymmetries on g1 and demonstrate an extraction of the individual flavor helicity parton distribution functions at small x.

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References (83)

  1. R. L. Jaffe and A. Manohar, The G(1) problem: Fact and fantasy on the spin of the proton, Nucl. Phys. B337, 509 (1990).
  2. X. Ji, Gauge-Invariant Decomposition of Nucleon Spin, Phys. Rev. Lett. 78, 610 (1997).
  3. C. A. Aidala, S. D. Bass, D. Hasch, and G. K. Mallot, The spin structure of the nucleon, Rev. Mod. Phys. 85, 655 (2013).
  4. Y. V. Kovchegov, D. Pitonyak, and M. D. Sievert, Helicity evolution at small-x, J. High Energy Phys. 01 (2016) 072; Erratum, 10 (2016) 148.
  5. Y. Hatta, Y. Nakagawa, F. Yuan, Y. Zhao, and B. Xiao, Gluon orbital angular momentum at small-x, Phys. Rev. D 95, 114032 (2017).
  6. Y. V. Kovchegov, D. Pitonyak, and M. D. Sievert, Helicity evolution at small x: Flavor singlet and non-singlet observables, Phys. Rev. D 95, 014033 (2017).
  7. Y. V. Kovchegov, D. Pitonyak, and M. D. Sievert, Small-x Asymptotics of the Quark Helicity Distribution, Phys. Rev. Lett. 118, 052001 (2017).
  8. G. A. Chirilli, Sub-eikonal corrections to scattering amplitudes at high energy, J. High Energy Phys. 01 (2019) 118.
  9. Y. V. Kovchegov, Orbital angular momentum at small x, J. High Energy Phys. 03 (2019) 174.
  10. R. Boussarie, Y. Hatta, and F. Yuan, Proton spin structure at small-x, Phys. Lett. B 797, 134817 (2019).
  11. G. A. Chirilli, High-energy operator product expansion at sub-eikonal level, J. High Energy Phys. 06 (2021) 096.
  12. R. Kirschner and L. Lipatov, Double logarithmic asymptotics and Regge singularities of quark amplitudes with flavor exchange, Nucl. Phys. B213, 122 (1983).
  13. J. Bartels, B. I. Ermolaev, and M. G. Ryskin, Nonsinglet contributions to the structure function g1 at small x, Z. Phys. C 70, 273 (1996).
  14. J. Bartels, B. Ermolaev, and M. Ryskin, Flavor singlet contribution to the structure function G(1) at small x, Z. Phys. C 72, 627 (1996).
  15. Y. V. Kovchegov, D. Pitonyak, and M. D. Sievert, Small-x asymptotics of the quark helicity distribution: Analytic results, Phys. Lett. B 772, 136 (2017).
  16. Y. V. Kovchegov, D. Pitonyak, and M. D. Sievert, Small-x asymptotics of the gluon helicity distribution, J. High Energy Phys. 10 (2017) 198.
  17. Y. V. Kovchegov and M. D. Sievert, Small-x helicity evolution: An operator treatment, Phys. Rev. D 99, 054032 (2019).
  18. F. Cougoulic and Y. V. Kovchegov, Helicity-dependent generalization of the JIMWLK evolution, Phys. Rev. D 100, 114020 (2019).
  19. V. N. Gribov and L. N. Lipatov, Deep inelastic e p scattering in perturbation theory, Sov. J. Nucl. Phys. 15, 438 (1972).
  20. G. Altarelli and G. Parisi, Asymptotic freedom in parton language, Nucl. Phys. B126, 298 (1977).
  21. Y. L. Dokshitzer, Calculation of the structure functions for deep inelastic scattering and e+e− annihilation by perturbation theory in quantum chromodynamics, Sov. Phys. JETP 46, 641 (1977).
  22. I. Balitsky, Operator expansion for high-energy scattering, Nucl. Phys. B463, 99 (1996).
  23. I. Balitsky, Factorization and high-energy effective action, Phys. Rev. D 60, 014020 (1999).
  24. Y. V. Kovchegov, Small x F(2) structure function of a nucleus including multiple pomeron exchanges, Phys. Rev. D 60, 034008 (1999).
  25. Y. V. Kovchegov, Unitarization of the BFKL Pomeron on a nucleus, Phys. Rev. D 61, 074018 (2000).
  26. Y. V. Kovchegov and H. Weigert, Triumvirate of running couplings in small-x evolution, Nucl. Phys. A784, 188 (2007).
  27. I. Balitsky, Quark contribution to the small-x evolution of color dipole, Phys. Rev. D 75, 014001 (2007).
  28. J. L. Albacete, N. Armesto, J. G. Milhano, P. Quiroga-Arias, and C. A. Salgado, AAMQS: A non-linear QCD analysis of new HERA data at small-x including heavy quarks, Eur. Phys. J. C 71, 1705 (2011).
  29. J. L. Albacete, N. Armesto, J. G. Milhano, and C. A. Salgado, Non-linear QCD meets data: A global analysis of lepton-proton scattering with running coupling BK evolution, Phys. Rev. D 80, 034031 (2009).
  30. G. Beuf, H. Hänninen, T. Lappi, and H. Mäntysaari, Color glass condensate at next-to-leading order meets HERA data, Phys. Rev. D 102, 074028 (2020).
  31. J. Blümlein and A. Vogt, The singlet contribution to the structure function g1 (x, Q2) at small x, Phys. Lett. B 386, 350 (1996).
  32. Y. V. Kovchegov and Y. Tawabutr, Helicity at small x: Oscillations generated by bringing back the quarks, J. High Energy Phys. 08 (2020) 014.
  33. C. Cocuzza, J. J. Ethier, W. Melnitchouk, A. Metz, and N. Sato, Parton distributions functions from JLab to LHC (to be published).
  34. N. Sato, C. Andres, J. J. Ethier, and W. Melnitchouk (JAM Collaboration), Strange quark suppression from a simultaneous Monte Carlo analysis of parton distributions and fragmentation functions, Phys. Rev. D 101, 074020 (2020).
  35. P. Jimenez-Delgado, A. Accardi, and W. Melnitchouk, Impact of hadronic and nuclear corrections on global analysis of spin-dependent parton distributions, Phys. Rev. D 89, 034025 (2014).
  36. N. Sato, W. Melnitchouk, S. Kuhn, J. Ethier, and A. Accardi, Iterative Monte Carlo analysis of spin-dependent parton distributions, Phys. Rev. D 93, 074005 (2016).
  37. J. J. Ethier, N. Sato, and W. Melnitchouk, First Simultaneous Extraction of Spin-Dependent Parton Distributions and Fragmentation Functions from a Global QCD Analysis, Phys. Rev. Lett. 119, 132001 (2017).
  38. E. Moffat, W. Melnitchouk, T. Rogers, and N. Sato, Simultaneous Monte Carlo analysis of parton densities and fragmentation functions, Phys. Rev. D 104, 016015 (2021).
  39. T. Hobbs and W. Melnitchouk, Finite-Q2 corrections to parity-violating DIS, Phys. Rev. D 77, 114023 (2008).
  40. Y. Zhao, A. Deshpande, J. Huang, K. Kumar, and S. Riordan, Neutral-current weak interactions at an EIC, Eur. Phys. J. A 53, 55 (2017).
  41. P. L. Anthony et al. (E142 Collaboration), Deep inelastic scattering of polarized electrons by polarized He-3 and the study of the neutron spin structure, Phys. Rev. D 54, 6620 (1996).
  42. K. Abe et al. (E154 Collaboration), Precision Determination of the Neutron Spin Structure Function g1(n), Phys. Rev. Lett. 79, 26 (1997).
  43. K. Abe et al. (E143 Collaboration), Measurements of the proton and deuteron spin structure functions g(1) and g(2), Phys. Rev. D 58, 112003 (1998).
  44. P. L. Anthony et al. (E155 Collaboration), Measurement of the deuteron spin structure function g1(d)(x) for 1−(GeV/c)2<Q2<40 (GeV/c)2, Phys. Lett. B 463, 339 (1999).
  45. P. L. Anthony et al. (E155 Collaboration), Measurements of the Q2 dependence of the proton and neutron spin structure functions g1p andg1n, Phys. Lett. B 493, 19 (2000).
  46. J. Ashman et al. (European Muon Collaboration), An investigation of the spin structure of the proton in deep inelastic scattering of polarized muons on polarized protons, Nucl. Phys. B328, 1 (1989).
  47. B. Adeva et al. (Spin Muon Collaboration), Spin asymmetries A(1) and structure functions g1 of the proton and the deuteron from polarized high-energy muon scattering, Phys. Rev. D 58, 112001 (1998).
  48. B. Adeva et al. (Spin Muon Collaboration), Spin asymmetries A(1) of the proton and the deuteron in the low x and low Q2 region from polarized high-energy muon scattering, Phys. Rev. D 60, 072004 (1999); Erratum, 62, 079902 (2000).
  49. M. G. Alekseev et al. (COMPASS Collaboration), The spin-dependent structure function of the proton g1p and a test of the Bjorken sum rule, Phys. Lett. B 690, 466 (2010).
  50. C. Adolph et al. (COMPASS Collaboration), The spin structure function g1p of the proton and a test of the Bjorken sum rule, Phys. Lett. B 753, 18 (2016).
  51. C. Adolph et al. (COMPASS), Final COMPASS results on the deuteron spin-dependent structure function g1d and the Bjorken sum rule, Phys. Lett. B 769, 34 (2017).
  52. K. Ackerstaff et al. (HERMES Collaboration), Measurement of the neutron spin structure function g1(n) with a polarized He-3 internal target, Phys. Lett. B 404, 383 (1997).
  53. A. Airapetian et al. (HERMES Collaboration), Precise determination of the spin structure function g(1) of the proton, deuteron and neutron, Phys. Rev. D 75, 012007 (2007).
  54. D. de Florian, R. Sassot, M. Stratmann, and W. Vogelsang, Evidence for Polarization of Gluons in the Proton, Phys. Rev. Lett. 113, 012001 (2014).
  55. D. De Florian, G. A. Lucero, R. Sassot, M. Stratmann, and W. Vogelsang, Monte Carlo sampling variant of the DSSV14 set of helicity parton densities, Phys. Rev. D 100, 114027 (2019).
  56. I. Borsa, G. Lucero, R. Sassot, E. C. Aschenauer, and A. S. Nunes, Revisiting helicity parton distributions at a future electron-ion collider, Phys. Rev. D 102, 094018 (2020).
  57. G. Baum et al., A New Measurement of Deep Inelastic e−p Asymmetries, Phys. Rev. Lett. 51, 1135 (1983).
  58. Y. Prok et al. (CLAS), Precision measurements of g1 of the proton and the deuteron with 6 GeV electrons, Phys. Rev. C 90, 025212 (2014).
  59. D. S. Parno et al. (Jefferson Lab Hall A Collaboration), Precision measurements of A1n in the deep inelastic regime, Phys. Lett. B 744, 309 (2015).
  60. N. Guler et al. (CLAS Collaboration), Precise determination of the deuteron spin structure at low to moderate Q2 with CLAS and extraction of the neutron contribution, Phys. Rev. C 92, 055201 (2015).
  61. R. Fersch et al. (CLAS Collaboration), Determination of the proton spin structure functions for 0.05<Q2<5  GeV2 using CLAS, Phys. Rev. C 96, 065208 (2017).
  62. E. A. Kuraev, L. N. Lipatov, and V. S. Fadin, The Pomeranchuk singularity in nonabelian gauge theories, Sov. Phys. JETP 45, 199 (1977).
  63. I. I. Balitsky and L. N. Lipatov, The Pomeranchuk singularity in quantum chromodynamics, Sov. J. Nucl. Phys. 28, 822 (1978).
  64. J. Jalilian-Marian, A. Kovner, and H. Weigert, The Wilson renormalization group for low x physics: Gluon evolution at finite parton density, Phys. Rev. D 59, 014015 (1998).
  65. J. Jalilian-Marian, A. Kovner, A. Leonidov, and H. Weigert, The Wilson renormalization group for low x physics: Towards the high density regime, Phys. Rev. D 59, 014014 (1998).
  66. H. Weigert, Unitarity at small Bjorken x, Nucl. Phys. A703, 823 (2002).
  67. E. Iancu, A. Leonidov, and L. D. McLerran, The renormalization group equation for the color glass condensate, Phys. Lett. B 510, 133 (2001).
  68. E. Iancu, A. Leonidov, and L. D. McLerran, Nonlinear gluon evolution in the color glass condensate: I, Nucl. Phys. A692, 583 (2001).
  69. E. Ferreiro, E. Iancu, A. Leonidov, and L. McLerran, Nonlinear gluon evolution in the color glass condensate: II, Nucl. Phys. A703, 489 (2002).
  70. D. Kharzeev, Y. V. Kovchegov, and K. Tuchin, Cronin effect and high p(T) suppression in pA collisions, Phys. Rev. D 68, 094013 (2003).
  71. J. L. Albacete, N. Armesto, A. Kovner, C. A. Salgado, and U. A. Wiedemann, Energy Dependence of the Cronin Effect from Nonlinear QCD Evolution, Phys. Rev. Lett. 92, 082001 (2004).
  72. D. Kharzeev, Y. V. Kovchegov, and K. Tuchin, Nuclear modification factor in d+Au collisions: Onset of suppression in the color glass condensate, Phys. Lett. B 599, 23 (2004).
  73. J. Albacete, N. Armesto, J. Milhano, C. Salgado, and U. Wiedemann, Numerical analysis of the Balitsky-Kovchegov equation with running coupling: Dependence of the saturation scale on nuclear size and rapidity, Phys. Rev. D 71, 014003 (2005).
  74. R. Kirschner, Regge asymptotics of scattering amplitudes in the logarithmic approximation of QCD, Z. Phys. C 31, 135 (1986).
  75. R. Kirschner, Regge asymptotics of scattering with flavor exchange in QCD, Z. Phys. C 67, 459 (1995).
  76. R. Kirschner, Reggeon interactions in perturbative QCD, Z. Phys. C 65, 505 (1995).
  77. S. Griffiths and D. A. Ross, Studying the perturbative Reggeon, Eur. Phys. J. C 12, 277 (2000).
  78. B. I. Ermolaev, S. I. Manaenkov, and M. G. Ryskin, Nonsinglet structure functions at small x, Z. Phys. C 69, 259 (1995).
  79. J. Bartels and M. Lublinsky, Quark anti-quark exchange in γ* γ* scattering, J. High Energy Phys. 09 (2003) 076.
  80. A. Donnachie and P. V. Landshoff, Total cross-sections, Phys. Lett. B 296, 227 (1992).
  81. K. Itakura, Y. V. Kovchegov, L. McLerran, and D. Teaney, Baryon stopping and valence quark distribution at small x, Nucl. Phys. A730, 160 (2004).
  82. R. Abdul Khalek et al., Science requirements and detector concepts for the electron-ion collider: EIC Yellow Report, arXiv:2103.05419.
  83. Y. V. Kovchegov, A. Tarasov, and Y. Tawabutr, Helicity evolution at small x: The single-logarithmic contribution, arXiv:2104.11765.

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Phys. Rev. D 104, L031501– Published 5 August, 2021
  • Received 17 February 2021
  • Accepted 5 July 2021
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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.

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