Abstract
Quantum chromodynamics (QCD) rigorously predicts the existence of both nonperturbative intrinsic and perturbative extrinsic heavy quark contents of nucleons. In this article we discuss the heavy quark electroproduction on protons induced by the Fock states ∣uud + g〉 of three valence quarks in the proton and a nonperturbative gluon, and the \( \mid uud+Q\overline{Q}\Big\rangle \) non-perturbative state of three valence quarks and a heavy quark-antiquark pair. The first one gives the perturbative contribution when the gluon produces a heavy quark pair, while the second is the intrinsic part, and they produce amplitude interference. We use nonperturbative light-front wavefunctions for these Fock states, which are computed using the color-confining light-front holographic QCD theory. Due to interference of the amplitudes corresponding to the intrinsic and extrinsic heavy quark contribution to the proton a novel Q vs. \( \overline{Q} \) asymmetry emerges in the differential cross section of the electroproduction off a proton \( {d}^2{\sigma}_{e^{-}p}/\left( dxd{Q}^2\right) \). Our analysis proposed a novel asymmetry in QCD between intrinsic and extrinsic heavy quark content in nucleon and provides new insights into the physics of heavy quark phenomena in QCD at the amplitude level. This asymmetry is similar to the Brodsky-Gillespie asymmetry discovered before in QED case and confirmed at DESY.
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14 August 2023
An Erratum to this paper has been published: https://doi.org/10.1007/JHEP08(2023)061
References
I. Schmidt and M. Siddikov, Contribution of digluons to charmonia production, J. Phys. G 46 (2019) 065002 [arXiv:1801.09974] [INSPIRE].
S.J. Brodsky, I. Schmidt and J.-J. Yang, Nuclear antishadowing in neutrino deep inelastic scattering, Phys. Rev. D 70 (2004) 116003 [hep-ph/0409279] [INSPIRE].
S.J. Brodsky, D.S. Hwang and I. Schmidt, Final state interactions and single spin asymmetries in semiinclusive deep inelastic scattering, Phys. Lett. B 530 (2002) 99 [hep-ph/0201296] [INSPIRE].
V.E. Lyubovitskij, I. Schmidt and S.J. Brodsky, Predictions for the Sivers single-spin asymmetry from holographic QCD, Phys. Rev. D 105 (2022) 114032 [arXiv:2205.08986] [INSPIRE].
S.J. Brodsky, C. Peterson and N. Sakai, Intrinsic Heavy Quark States, Phys. Rev. D 23 (1981) 2745 [INSPIRE].
S.J. Brodsky, P. Hoyer, C. Peterson and N. Sakai, The Intrinsic Charm of the Proton, Phys. Lett. B 93 (1980) 451 [INSPIRE].
S.J. Brodsky, A. Kusina, F. Lyonnet, I. Schienbein, H. Spiesberger and R. Vogt, A review of the intrinsic heavy quark content of the nucleon, Adv. High Energy Phys. 2015 (2015) 231547 [arXiv:1504.06287] [INSPIRE].
R.S. Sufian et al., Constraints on charm-anticharm asymmetry in the nucleon from lattice QCD, Phys. Lett. B 808 (2020) 135633 [arXiv:2003.01078] [INSPIRE].
S.J. Brodsky, V.E. Lyubovitskij and I. Schmidt, Heavy quark contribution to the electromagnetic properties of the nucleon, Phys. Rev. D 106 (2022) 094025 [arXiv:2209.00403] [INSPIRE].
S.J. Brodsky and J. Gillespie, Second Born Corrections to Wide Angle Electron Pair Production and Bremsstrahlung, Phys. Rev. 173 (1968) 1011 [INSPIRE].
J.G. Asbury et al., Virtual compton scattering at high energies, Phys. Lett. B 25 (1967) 565 [INSPIRE].
S.J. Brodsky, G.F. de Teramond, H.G. Dosch and J. Erlich, Light-Front Holographic QCD and Emerging Confinement, Phys. Rept. 584 (2015) 1 [arXiv:1407.8131] [INSPIRE].
S.J. Brodsky and G.F. de Teramond, Light-Front Dynamics and AdS/QCD Correspondence: The Pion Form Factor in the Space- and Time-Like Regions, Phys. Rev. D 77 (2008) 056007 [arXiv:0707.3859] [INSPIRE].
T. Gutsche, V.E. Lyubovitskij and I. Schmidt, Nucleon parton distributions in a light-front quark model, Eur. Phys. J. C 77 (2017) 86 [arXiv:1610.03526] [INSPIRE].
T. Gutsche, V.E. Lyubovitskij, I. Schmidt and A. Vega, Light-front quark model consistent with Drell-Yan-West duality and quark counting rules, Phys. Rev. D 89 (2014) 054033 [arXiv:1306.0366] [Erratum ibid. 92 (2015) 019902] [INSPIRE].
T. Gutsche, V.E. Lyubovitskij, I. Schmidt and A. Vega, Nucleon structure in a light-front quark model consistent with quark counting rules and data, Phys. Rev. D 91 (2015) 054028 [arXiv:1411.1710] [INSPIRE].
V.E. Lyubovitskij and I. Schmidt, Scaling of PDFs, TMDs, and GPDs in soft-wall AdS/QCD, Phys. Rev. D 102 (2020) 034011 [arXiv:2005.10163] [INSPIRE].
V.E. Lyubovitskij and I. Schmidt, Gluon parton densities in soft-wall AdS/QCD, Phys. Rev. D 103 (2021) 094017 [arXiv:2012.01334] [INSPIRE].
NNPDF collaboration, Evidence for intrinsic charm quarks in the proton, Nature 608 (2022) 483 [arXiv:2208.08372] [INSPIRE].
J.F. Donoghue and E. Golowich, The Quark Sea and Quantum Chromodynamics, Phys. Rev. D 15 (1977) 3421 [INSPIRE].
S.J. Brodsky and I.A. Schmidt, Polarized and Unpolarized Intrinsic Gluon Distributions, Phys. Lett. B 234 (1990) 144 [INSPIRE].
C. Alexandrou et al., Complete flavor decomposition of the spin and momentum fraction of the proton using lattice QCD simulations at physical pion mass, Phys. Rev. D 101 (2020) 094513 [arXiv:2003.08486] [INSPIRE].
J.D. Bjorken, Inelastic Scattering of Polarized Leptons from Polarized Nucleons, Phys. Rev. D 1 (1970) 1376 [INSPIRE].
V.N. Gribov and L.N. Lipatov, Deep inelastic e p scattering in perturbation theory, Sov. J. Nucl. Phys. 15 (1972) 438 [INSPIRE].
S.J. Brodsky, J.R. Ellis and M. Karliner, Chiral Symmetry and the Spin of the Proton, Phys. Lett. B 206 (1988) 309 [INSPIRE].
H1 collaboration, Inelastic photoproduction of J/ψ mesons at HERA, Eur. Phys. J. C 25 (2002) 25 [hep-ex/0205064] [INSPIRE].
Acknowledgments
We thank Stan Brodsky for useful discussions. This work was funded by BMBF (Germany) “Verbundprojekt 05P2021 (ErUM-FSP T01) — Run 3 von ALICE am LHC: Perturbative Berechnungen von Wirkungsquerschnitten für ALICE” (Förderkennzeichen: 05P21VTCAA), by ANID PIA/APOYO AFB180002 and AFB220004 (Chile), by FONDECYT (Chile) under Grants No. 1191103, No. 1230160 and No. 1230391 and by ANID−Millennium Program−ICN2019_044 (Chile).
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Lyubovitskij, V.E., Schmidt, I. QCD at the amplitude level: Fock state interference in heavy quark electroproduction. J. High Energ. Phys. 2023, 54 (2023). https://doi.org/10.1007/JHEP05(2023)054
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DOI: https://doi.org/10.1007/JHEP05(2023)054