Orbital angular momentum at small $x$ revisited

Kovchegov, Yuri V.; Manley, Brandon

doi:10.1007/jhep02(2024)060

Title: Orbital angular momentum at small $$x$$ revisited

Journal Article · 08 February 2024 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep02(2024)060 · OSTI ID:2322576

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The Ohio State Univ., Columbus, OH (United States)

We revisit the problem of the small Bjorken-x asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton utilizing the revised small-x helicity evolution derived recently in [1]. We relate the quark and gluon OAM distributions at small x to the polarized dipole amplitudes and their (first) impact-parameter moments. To obtain the OAM distributions, we derive novel small-x evolution equations for the impact-parameter moments of the polarized dipole amplitudes in the double-logarithmic approximation (summing powers of α_s ln²(1/x) with α_s the strong coupling constant). We solve these evolution equations numerically and extract the leading large-N_c, small-x asymptotics of the quark and gluon OAM distributions, which we determine to be $${L}_{q+\overline{q}}\left(x,{Q}^2\right)\sim {L}_G\left(x,{Q}^2\right)\sim \Delta \Sigma \left(x,{Q}^2\right)\sim \Delta G\left(x,{Q}^2\right)\sim {\left(\frac{1}{2}\right)}^{3.66\sqrt{\frac{\alpha_s{N}_c}{2_π}}}$$in agreement with [2] within the precision of our numerical evaluation. (Here N_c is the number of quark colors.) We also investigate the ratios of the quark and gluon OAM distributions to their helicity distribution counterparts in the small-x region.

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Research Organization:: The Ohio State Univ., Columbus, OH (United States). Office of Sponsored Programs

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0004286

OSTI ID:: 2322576

Journal Information:: Journal of High Energy Physics (Online), Vol. 2024, Issue 2; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

References (102)

Extraction of spin-dependent parton densities and their uncertainties de Florian, Daniel; Sassot, Rodolfo; Stratmann, Marco Physical Review D, Vol. 80, Issue 3 https://doi.org/10.1103/PhysRevD.80.034030	journal	August 2009
Polarized antimatter in the proton from a global QCD analysis Cocuzza, C.; Melnitchouk, W.; Metz, A. Physical Review D, Vol. 106, Issue 3 https://doi.org/10.1103/PhysRevD.106.L031502	journal	August 2022
Flavor singlet contribution to the structure functiong 1 at small-x Bartels, J.; Ermolaev, B. I.; Ryskin, M. G. Zeitschrift für Physik C: Particles and Fields, Vol. 72, Issue 4 https://doi.org/10.1007/s002880050285	journal	December 1996
Small- x Asymptotics of the Quark Helicity Distribution Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D. Physical Review Letters, Vol. 118, Issue 5 https://doi.org/10.1103/PhysRevLett.118.052001	journal	January 2017
The spin dependent odderon in the diquark model Szymanowski, Lech; Zhou, Jian Physics Letters B, Vol. 760 https://doi.org/10.1016/j.physletb.2016.06.055	journal	September 2016
First Simultaneous Extraction of Spin-Dependent Parton Distributions and Fragmentation Functions from a Global QCD Analysis Ethier, J. J.; Sato, N.; Melnitchouk, W. Physical Review Letters, Vol. 119, Issue 13 https://doi.org/10.1103/PhysRevLett.119.132001	journal	September 2017
On the small-x behavior of the orbital angular momentum distributions in QCD Hatta, Yoshitaka; Yang, Dong-Jing Physics Letters B, Vol. 781 https://doi.org/10.1016/j.physletb.2018.03.081	journal	June 2018
Science Requirements and Detector Concepts for the Electron-Ion Collider Abdul Khalek, R.; Accardi, A.; Adam, J. Nuclear Physics A, Vol. 1026 https://doi.org/10.1016/j.nuclphysa.2022.122447	journal	October 2022
Small-x asymptotics of the gluon helicity distribution Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D. Journal of High Energy Physics, Vol. 2017, Issue 10 https://doi.org/10.1007/JHEP10(2017)198	journal	October 2017
Semihard processes in QCD Gribov, L. Physics Reports, Vol. 100, Issue 1-2 https://doi.org/10.1016/0370-1573(83)90022-4	journal	November 1983
The Color Glass Condensate Gelis, Francois; Iancu, Edmond; Jalilian-Marian, Jamal Annual Review of Nuclear and Particle Science, Vol. 60, Issue 1 https://doi.org/10.1146/annurev.nucl.010909.083629	journal	November 2010
Evolution at small : The color glass condensate Weigert, H. Progress in Particle and Nuclear Physics, Vol. 55, Issue 2 https://doi.org/10.1016/j.ppnp.2005.01.029	journal	October 2005
Signature of the Gluon Orbital Angular Momentum Bhattacharya, Shohini; Boussarie, Renaud; Hatta, Yoshitaka Physical Review Letters, Vol. 128, Issue 18 https://doi.org/10.1103/PhysRevLett.128.182002	journal	May 2022
Gauge-Invariant Decomposition of Nucleon Spin Ji, Xiangdong Physical Review Letters, Vol. 78, Issue 4 https://doi.org/10.1103/PhysRevLett.78.610	journal	January 1997
Longitudinal polarized parton densities updated Leader, Elliot; Sidorov, Aleksander V.; Stamenov, Dimiter B. Physical Review D, Vol. 73, Issue 3 https://doi.org/10.1103/PhysRevD.73.034023	journal	February 2006
Quark jets scattering from a gluon field: From saturation to high p t Jalilian-Marian, Jamal Physical Review D, Vol. 99, Issue 1 https://doi.org/10.1103/PhysRevD.99.014043	journal	January 2019
The g1 problem: Deep inelastic electron scattering and the spin of the proton Jaffe, R. L.; Manohar, Aneesh Nuclear Physics B, Vol. 337, Issue 3 https://doi.org/10.1016/0550-3213(90)90506-9	journal	June 1990
Helicity evolution at small x: the single-logarithmic contribution Kovchegov, Yuri V.; Tarasov, Andrey; Tawabutr, Yossathorn Journal of High Energy Physics, Vol. 2022, Issue 3 https://doi.org/10.1007/JHEP03(2022)184	journal	March 2022
Erratum to: Helicity evolution at small x Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D. Journal of High Energy Physics, Vol. 2016, Issue 10 https://doi.org/10.1007/JHEP10(2016)148	journal	October 2016
Sea quark Sivers distribution Dong, Hui; Zheng, Du-xin; Zhou, Jian Physics Letters B, Vol. 788 https://doi.org/10.1016/j.physletb.2018.11.010	journal	January 2019
Determination of polarized parton densities from a QCD analysis of inclusive and semi-inclusive deep inelastic scattering data Leader, Elliot; Sidorov, Aleksander V.; Stamenov, Dimiter B. Physical Review D, Vol. 82, Issue 11 https://doi.org/10.1103/PhysRevD.82.114018	journal	December 2010
Probing parton orbital angular momentum in longitudinally polarized nucleon Ji, Xiangdong; Xiong, Xiaonu; Yuan, Feng Physical Review D, Vol. 88, Issue 1 https://doi.org/10.1103/PhysRevD.88.014041	journal	July 2013
A first unbiased global determination of polarized PDFs and their uncertainties Nocera, Emanuele R.; Ball, Richard D.; Forte, Stefano Nuclear Physics B, Vol. 887 https://doi.org/10.1016/j.nuclphysb.2014.08.008	journal	October 2014
Iterative Monte Carlo analysis of spin-dependent parton distributions Sato, Nobuo; Melnitchouk, W.; Kuhn, S. E. Physical Review D, Vol. 93, Issue 7 https://doi.org/10.1103/PhysRevD.93.074005	journal	April 2016
-Broadening and production processes versus dipole/quadrupole amplitudes at next-to-leading order Mueller, A. H.; Munier, S. Nuclear Physics A, Vol. 893 https://doi.org/10.1016/j.nuclphysa.2012.08.005	journal	November 2012
Helicity evolution at small x : Flavor singlet and nonsinglet observables Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D. Physical Review D, Vol. 95, Issue 1 https://doi.org/10.1103/PhysRevD.95.014033	journal	January 2017
Sub-eikonal corrections to scattering amplitudes at high energy Chirilli, Giovanni Antonio Journal of High Energy Physics, Vol. 2019, Issue 1 https://doi.org/10.1007/JHEP01(2019)118	journal	January 2019
Single-spin production asymmetries from the hard scattering of pointlike constituents Sivers, Dennis Physical Review D, Vol. 41, Issue 1 https://doi.org/10.1103/PhysRevD.41.83	journal	January 1990
Gluon TMD in particle production from low to moderate x Balitsky, I.; Tarasov, A. Journal of High Energy Physics, Vol. 2016, Issue 6 https://doi.org/10.1007/JHEP06(2016)164	journal	June 2016
Orbital angular momentum in deep inelastic scattering Harindranath, A.; Kundu, Rajen Physical Review D, Vol. 59, Issue 11 https://doi.org/10.1103/PhysRevD.59.116013	journal	May 1999
Perturbative odderon in the dipole model Kovchegov, Yuri V.; Szymanowski, Lech; Wallon, Samuel Physics Letters B, Vol. 586, Issue 3-4 https://doi.org/10.1016/j.physletb.2004.02.036	journal	April 2004
Monte Carlo sampling variant of the DSSV14 set of helicity parton densities de Florian, Daniel; Lucero, Gonzalo Agustín; Sassot, Rodolfo Physical Review D, Vol. 100, Issue 11 https://doi.org/10.1103/PhysRevD.100.114027	journal	December 2019
Orbital angular momentum at small x Kovchegov, Yuri V. Journal of High Energy Physics, Vol. 2019, Issue 3 https://doi.org/10.1007/JHEP03(2019)174	journal	March 2019
Quantum Chromodynamics at High Energy Kovchegov, Yuri V.; Levin, Eugene Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology https://doi.org/10.1017/CBO9781139022187	book	September 2012
Helicity-dependent generalization of the JIMWLK evolution Cougoulic, Florian; Kovchegov, Yuri V. Physical Review D, Vol. 100, Issue 11 https://doi.org/10.1103/PhysRevD.100.114020	journal	December 2019
The renormalization group equation for the color glass condensate Iancu, Edmond; Leonidov, Andrei; McLerran, Larry Physics Letters B, Vol. 510, Issue 1-4 https://doi.org/10.1016/S0370-2693(01)00524-X	journal	June 2001
Mining for Gluon Saturation at Colliders Morreale, Astrid; Salazar, Farid Universe, Vol. 7, Issue 8 https://doi.org/10.3390/universe7080312	journal	August 2021
Proton spin structure at small-x Boussarie, Renaud; Hatta, Yoshitaka; Yuan, Feng Physics Letters B, Vol. 797 https://doi.org/10.1016/j.physletb.2019.134817	journal	October 2019
A new look at the statistical model identification Akaike, H. IEEE Transactions on Automatic Control, Vol. 19, Issue 6 https://doi.org/10.1109/TAC.1974.1100705	journal	December 1974
What we know and what we don’t know about the proton spin after 30 years Ji, Xiangdong; Yuan, Feng; Zhao, Yong Nature Reviews Physics, Vol. 3, Issue 1 https://doi.org/10.1038/s42254-020-00248-4	journal	November 2020
Reggeon interactions in perturbative QCD Kirschner, R. Zeitschrift für Physik C Particles and Fields, Vol. 65, Issue 3 https://doi.org/10.1007/BF01556138	journal	September 1995
DIS dijet production at next-to-eikonal accuracy in the CGC Altinoluk, Tolga; Beuf, Guillaume; Czajka, Alina Physical Review D, Vol. 107, Issue 7 https://doi.org/10.1103/PhysRevD.107.074016	journal	April 2023
Models for the polarized parton distributions of the nucleon Glück, M.; Reya, E.; Stratmann, M. Physical Review D, Vol. 63, Issue 9 https://doi.org/10.1103/PhysRevD.63.094005	journal	March 2001
Asymptotic freedom in parton language Altarelli, G.; Parisi, G. Nuclear Physics B, Vol. 126, Issue 2 https://doi.org/10.1016/0550-3213(77)90384-4	journal	August 1977
Wilson renormalization group for low x physics: Gluon evolution at finite parton density Jalilian-Marian, Jamal; Kovner, Alex; Weigert, Heribert Physical Review D, Vol. 59, Issue 1 https://doi.org/10.1103/PhysRevD.59.014015	journal	November 1998
Helicity-dependent extension of the McLerran–Venugopalan model Cougoulic, Florian; Kovchegov, Yuri V. Nuclear Physics A, Vol. 1004 https://doi.org/10.1016/j.nuclphysa.2020.122051	journal	December 2020
Soft gluons in the infinite-momentum wave function and the BFKL pomeron Mueller, A. H. Nuclear Physics B, Vol. 415, Issue 2 https://doi.org/10.1016/0550-3213(94)90116-3	journal	March 1994
Impact of hadronic and nuclear corrections on global analysis of spin-dependent parton distributions Jimenez-Delgado, P.; Accardi, A.; Melnitchouk, W. Physical Review D, Vol. 89, Issue 3 https://doi.org/10.1103/PhysRevD.89.034025	journal	February 2014
Electron-Ion Collider: The next QCD frontier: Understanding the glue that binds us all Accardi, A.; Albacete, J. L.; Anselmino, M. The European Physical Journal A, Vol. 52, Issue 9 https://doi.org/10.1140/epja/i2016-16268-9	journal	September 2016
Odderon in the color glass condensate Hatta, Y.; Iancu, E.; Itakura, K. Nuclear Physics A, Vol. 760, Issue 1-2 https://doi.org/10.1016/j.nuclphysa.2005.05.163	journal	October 2005
Running coupling evolution for diffractive dissociation and the NLO odderon intercept Kovchegov, Yuri V. DIFFRACTION 2012: International Workshop on Diffraction in High Energy Physics, AIP Conference Proceedings https://doi.org/10.1063/1.4802180	conference	January 2013
How well do we know the gluon polarization in the proton? Zhou, Y.; Sato, N.; Melnitchouk, W. Physical Review D, Vol. 105, Issue 7 https://doi.org/10.1103/PhysRevD.105.074022	journal	April 2022
The three-loop splitting functions in QCD: The helicity-dependent case Moch, S.; Vermaseren, J. A. M.; Vogt, A. Nuclear Physics B, Vol. 889 https://doi.org/10.1016/j.nuclphysb.2014.10.016	journal	December 2014
Saturation physics and deuteron–gold collisions at RHIC Jalilianmarian, J.; Kovchegov, Y. Progress in Particle and Nuclear Physics, Vol. 56, Issue 1 https://doi.org/10.1016/j.ppnp.2005.07.002	journal	January 2006
Double logarithmic asymptotics and regge singularities of quark amplitudes with flavour exchange Kirschner, R.; Lipatov, L. N. Nuclear Physics B, Vol. 213, Issue 1 https://doi.org/10.1016/0550-3213(83)90178-5	journal	March 1983
Wigner distributions for gluons More, Jai; Mukherjee, Asmita; Nair, Sreeraj The European Physical Journal C, Vol. 78, Issue 5 https://doi.org/10.1140/epjc/s10052-018-5858-1	journal	May 2018
Evolution equations for higher moments of angular momentum distributions Hägler, P.; Schäfer, A. Physics Letters B, Vol. 430, Issue 1-2 https://doi.org/10.1016/S0370-2693(98)00414-6	journal	June 1998
Studying the perturbative Reggeon Griffiths, S.; Ross, D. A. The European Physical Journal C, Vol. 12, Issue 2 https://doi.org/10.1007/s100529900240	journal	January 2000
The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements Blümlein, J.; Marquard, P.; Schneider, C. Journal of High Energy Physics, Vol. 2022, Issue 1 https://doi.org/10.1007/JHEP01(2022)193	journal	January 2022
Small x physics beyond eikonal approximation: an effective Hamiltonian approach Li, Ming Journal of High Energy Physics, Vol. 2023, Issue 7 https://doi.org/10.1007/JHEP07(2023)158	journal	July 2023
Gluon saturation and initial conditions for relativistic heavy ion collisions Albacete, J. L.; Marquet, C. Progress in Particle and Nuclear Physics, Vol. 76 https://doi.org/10.1016/j.ppnp.2014.01.004	journal	May 2014
Probing quark transverse momentum distributions in the color glass condensate: Quark-gluon dijets in deep inelastic scattering at next-to-eikonal accuracy Altinoluk, Tolga; Armesto, Néstor; Beuf, Guillaume Physical Review D, Vol. 108, Issue 7 https://doi.org/10.1103/PhysRevD.108.074023	journal	October 2023
High-energy operator product expansion at sub-eikonal level Chirilli, Giovanni Antonio Journal of High Energy Physics, Vol. 2021, Issue 6 https://doi.org/10.1007/JHEP06(2021)096	journal	June 2021
Operator expansion for high-energy scattering Balitsky, I. Nuclear Physics B, Vol. 463, Issue 1 https://doi.org/10.1016/0550-3213(95)00638-9	journal	March 1996
Wilson renormalization group for low x physics: Towards the high density regime Jalilian-Marian, Jamal; Kovner, Alex; Leonidov, Andrei Physical Review D, Vol. 59, Issue 1 https://doi.org/10.1103/PhysRevD.59.014014	journal	November 1998
Quark orbital-angular-momentum distribution in the nucleon Hoodbhoy, Pervez; Ji, Xiangdong; Lu, Wei Physical Review D, Vol. 59, Issue 1 https://doi.org/10.1103/PhysRevD.59.014013	journal	November 1998
Quark and scalar propagators at next-to-eikonal accuracy in the CGC through a dynamical background gluon field Altinoluk, Tolga; Beuf, Guillaume Physical Review D, Vol. 105, Issue 7 https://doi.org/10.1103/PhysRevD.105.074026	journal	April 2022
On the behaviour of non-singlet structure functions at small x Blümlein, J.; Vogt, A. Physics Letters B, Vol. 370, Issue 1-2 https://doi.org/10.1016/0370-2693(95)01568-X	journal	March 1996
Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution Kovchegov, Yuri V.; Santiago, M. Gabriel Journal of High Energy Physics, Vol. 2021, Issue 11 https://doi.org/10.1007/JHEP11(2021)200	journal	November 2021
Rapidity loss, spin, and angular asymmetries in the scattering of a quark from the color field of a proton or nucleus Jalilian-Marian, Jamal Physical Review D, Vol. 102, Issue 1 https://doi.org/10.1103/PhysRevD.102.014008	journal	July 2020
New analysis concerning the strange quark polarization puzzle Leader, Elliot; Sidorov, Alexander V.; Stamenov, Dimiter B. Physical Review D, Vol. 91, Issue 5 https://doi.org/10.1103/PhysRevD.91.054017	journal	March 2015
Unitarity and the BFKL pomeron Mueller, A. H. Nuclear Physics B, Vol. 437, Issue 1 https://doi.org/10.1016/0550-3213(94)00480-3	journal	March 1995
Analytic solution for the revised helicity evolution at small x and large Nc : New resummed gluon-gluon polarized anomalous dimension and intercept Borden, Jeremy; Kovchegov, Yuri V. Physical Review D, Vol. 108, Issue 1 https://doi.org/10.1103/PhysRevD.108.014001	journal	July 2023
Next-to-eikonal corrections in the CGC: gluon production and spin asymmetries in pA collisions Altinoluk, Tolga; Armesto, Néstor; Beuf, Guillaume Journal of High Energy Physics, Vol. 2014, Issue 7 https://doi.org/10.1007/JHEP07(2014)068	journal	July 2014
Single Spin Asymmetries from a Single Wilson Loop Boer, Daniël; Echevarria, Miguel G.; Mulders, Piet J. Physical Review Letters, Vol. 116, Issue 12 https://doi.org/10.1103/PhysRevLett.116.122001	journal	March 2016
Quark and gluon orbital angular momentum and spin in hard processes Bashinsky, S. V.; Jaffe, R. L. Nuclear Physics B, Vol. 536, Issue 1-2 https://doi.org/10.1016/S0550-3213(98)00559-8	journal	December 1998
Evidence for Polarization of Gluons in the Proton de Florian, Daniel; Sassot, Rodolfo; Stratmann, Marco Physical Review Letters, Vol. 113, Issue 1 https://doi.org/10.1103/PhysRevLett.113.012001	journal	July 2014
Exclusive processes in perturbative quantum chromodynamics Lepage, G. Peter; Brodsky, Stanley J. Physical Review D, Vol. 22, Issue 9 https://doi.org/10.1103/PhysRevD.22.2157	journal	November 1980
Gluon orbital angular momentum at small x Hatta, Yoshitaka; Nakagawa, Yuya; Xiao, Bowen Physical Review D, Vol. 95, Issue 11 https://doi.org/10.1103/PhysRevD.95.114032	journal	June 2017
Unbiased determination of polarized parton distributions and their uncertainties Ball, Richard D.; Forte, Stefano; Guffanti, Alberto Nuclear Physics B, Vol. 874, Issue 1 https://doi.org/10.1016/j.nuclphysb.2013.05.007	journal	September 2013
Probing Nucleons and Nuclei in High Energy Collisions Prokudin, Alexei; Hatta, Yoshitaka; Kovchegov, Yuri Proceedings of INT Program INT-18-3 https://doi.org/10.1142/11684	conference	November 2019
Unitarity at small Bjorken x Weigert, Heribert Nuclear Physics A, Vol. 703, Issue 3-4 https://doi.org/10.1016/S0375-9474(01)01668-2	journal	June 2002
Quark and gluon helicity evolution at small x: revised and updated Cougoulic, Florian; Kovchegov, Yuri V.; Tarasov, Andrey Journal of High Energy Physics, Vol. 2022, Issue 7 https://doi.org/10.1007/JHEP07(2022)095	journal	July 2022
Small- x asymptotics of the quark helicity distribution: Analytic results Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D. Physics Letters B, Vol. 772 https://doi.org/10.1016/j.physletb.2017.06.032	journal	September 2017
Quarks at next-to-eikonal accuracy in the CGC: Forward quark-nucleus scattering Altinoluk, Tolga; Beuf, Guillaume; Czajka, Alina Physical Review D, Vol. 104, Issue 1 https://doi.org/10.1103/PhysRevD.104.014019	journal	July 2021
Twist analysis of the nucleon spin in QCD Hatta, Yoshitaka; Yoshida, Shinsuke Journal of High Energy Physics, Vol. 2012, Issue 10 https://doi.org/10.1007/JHEP10(2012)080	journal	October 2012
The spin structure of the nucleon Aidala, Christine A.; Bass, Steven D.; Hasch, Delia Reviews of Modern Physics, Vol. 85, Issue 2 https://doi.org/10.1103/RevModPhys.85.655	journal	April 2013
Regge asymptotics of scattering with flavour exchange in QCD Kirschner, R. Zeitschrift für Physik C Particles and Fields, Vol. 67, Issue 3 https://doi.org/10.1007/BF01624588	journal	September 1995
Helicity at small x: oscillations generated by bringing back the quarks Kovchegov, Yuri V.; Tawabutr, Yossathorn Journal of High Energy Physics, Vol. 2020, Issue 8 https://doi.org/10.1007/JHEP08(2020)014	journal	August 2020
Revisiting helicity parton distributions at a future electron-ion collider Borsa, Ignacio; Lucero, Gonzalo; Sassot, Rodolfo Physical Review D, Vol. 102, Issue 9 https://doi.org/10.1103/PhysRevD.102.094018	journal	November 2020
Unitarization of the BFKL Pomeron on a nucleus Kovchegov, Yuri V. Physical Review D, Vol. 61, Issue 7 https://doi.org/10.1103/PhysRevD.61.074018	journal	March 2000
The color glass condensate and high energy scattering in QCD Iancu, Edmond; Venugopalan, Raju Quark–Gluon Plasma 3 https://doi.org/10.1142/9789812795533_0005	book	January 2004
The angular momentum controversy: What’s it all about and does it matter? Leader, Elliot; Lorcé, Cédric Physics Reports, Vol. 541, Issue 3 https://doi.org/10.1016/j.physrep.2014.02.010	journal	August 2014
Valence quark transversity at small x Kovchegov, Yuri V.; Sievert, Matthew D. Physical Review D, Vol. 99, Issue 5 https://doi.org/10.1103/PhysRevD.99.054033	journal	March 2019
Single and double BFKL pomeron exchange and a dipole picture of high energy hard processes Mueller, A. H.; Patel, Bimal Nuclear Physics B, Vol. 425, Issue 3 https://doi.org/10.1016/0550-3213(94)90284-4	journal	August 1994
A new odderon solution in perturbative QCD Bartels, J.; Lipatov, L. N.; Vacca, G. P. Physics Letters B, Vol. 477, Issue 1-3 https://doi.org/10.1016/S0370-2693(00)00221-5	journal	March 2000
Small- x helicity evolution: An operator treatment Kovchegov, Yuri V.; Sievert, Matthew D. Physical Review D, Vol. 99, Issue 5 https://doi.org/10.1103/PhysRevD.99.054032	journal	March 2019
Rapidity evolution of gluon TMD from low to moderate x Balitsky, I.; Tarasov, A. Journal of High Energy Physics, Vol. 2015, Issue 10 https://doi.org/10.1007/JHEP10(2015)017	journal	October 2015
T-odd leading-twist quark TMDs at small x Kovchegov, Yuri V.; Santiago, M. Gabriel Journal of High Energy Physics, Vol. 2022, Issue 11 https://doi.org/10.1007/JHEP11(2022)098	journal	November 2022
Helicity evolution at small x : Revised asymptotic results at large Nc and Nf Adamiak, Daniel; Kovchegov, Yuri V.; Tawabutr, Yossathorn Physical Review D, Vol. 108, Issue 5 https://doi.org/10.1103/PhysRevD.108.054005	journal	September 2023
Factorization and high-energy effective action Balitsky, Ian Physical Review D, Vol. 60, Issue 1 https://doi.org/10.1103/PhysRevD.60.014020	journal	June 1999
Orbital angular momentum small-x evolution: exact results in the large-Nc limit Manley, Brandon Journal of High Energy Physics, Vol. 2024, Issue 4 https://doi.org/10.1007/JHEP04(2024)055	journal	April 2024