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Forward parton-nucleus scattering at next-to-eikonal accuracy in the CGC

T0 review · 4 major / 3 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper derives the full next-to-eikonal gluon propagator in a boosted gluon background and the resulting forward gluon and quark production cross sections in all parton-nucleus channels.

desk verdict Genuine next step in the CGC NEik program—new gluon propagators and four forward cross sections, with the compact Wilson-line rewriting the main thing a referee should verify. read the letter →

arxiv 2411.15047 v1 pith:PVHNWBSK submitted 2024-11-22 hep-ph

Tolga Altinoluk , Guillaume Beuf , Swaleha Mulani This is my paper · ORCID
classification hep-ph
keywords next-to-eikonalcorrectionscolorglasscondensategluonpropagatorquarkforwardparticleproductiondecoratedWilsonlineshybridfactorizationdynamicalbackgroundfield
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper completes the program of next-to-eikonal (NEik) corrections in the color glass condensate for forward parton-nucleus scattering: it derives the full NEik gluon propagator through a highly boosted, dynamical gluon background, collects the companion quark and gluon propagators with endpoints inside the target, and writes down single-inclusive gluon and quark production cross sections at forward rapidity in all four parton-nucleus channels. The central claim is that these formulas constitute the complete set of building blocks for computing high-energy scattering observables beyond the eikonal approximation, organized systematically in the inverse boost parameter $1/\gamma_t$. If the claim is right, the standard leading-power hybrid-factorization results can now be upgraded to the first subleading power, with the finite-energy effects encoded in explicit decorated Wilson lines that wait for modeling and evolution. The authors deliberately stop at partonic level, leaving the convolution with parton distributions and fragmentation functions, and the numerical evaluation of the new operators, for later work.

What carries the argument

The carrying objects are the decorated Wilson lines of Eqs. (64)-(66): $U^{(1)}$ inserts a pair of transverse covariant derivatives acting in opposite directions on the two Wilson-line factors, $U^{(2)}$ inserts two covariant derivatives acting in the same direction, and $U^{(3)}$ inserts a background field-strength tensor $F_{ij}$. They convert the brute-force NEik propagator corrections into gauge-covariant operators, and every resulting cross section is an expectation value of products of these operators with ordinary Wilson lines at separated transverse positions. Two approximations carry the derivation: the gradient expansion in the minus coordinate $z^-$ around a common value, which treats the target's slow time dependence as a $1/\gamma_t$ effect beyond the static limit, and a power counting in which the finite target width $L^+ \sim 1/\gamma_t$ and the unenhanced transverse fields $A_\perp \sim (\gamma_t)^0$ supply the suppression that makes a subleading-looking object count as NEik. For the quark-background sector, the same counting is applied through the enhanced 'good' component $\Psi^{(-)} \sim (\gamma_t)^{1/2}$ of the target quark field, which is the only quark-field component that contributes at NEik order.

What would settle it

A concrete test is to carry the same before-to-after propagator expansion to next-to-next-to-eikonal order while keeping the discarded $q^+ k^+ < 0$ zero-mode cross terms (Sec. II, around Eq. (28)): if those sectors generate any contribution of order $1/\gamma_t$ to the $\delta'(q^+ - k^+)$ terms of Eqs. (120) and (137), the reported cross sections are incomplete. A second self-contained check is to verify that the full NEik gluon propagator of Eq. (55) satisfies the QCD Ward identity order by order in $1/\gamma_t$, which would fail if the decorated-Wilson-line terms were assembled inconsistently.

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Extended reading notes

Core claim

On its own terms, the paper establishes a closed expression for the before-to-after gluon propagator at full NEik accuracy: Eq. (55) sums the generalized-eikonal propagator with slow $z^-$ dependence (Eq. (38)) and two correction terms (Eqs. (68) and (69)) written through decorated Wilson lines, which are integrals over the target's longitudinal extent of Wilson lines with covariant-derivative or field-strength insertions. These corrections collect the three sources of $1/\gamma_t$ suppression in a boosted target: transverse motion and finite width beyond the shockwave limit, non-static $z^-$-dependent fields beyond the static limit, and insertions of the transverse components $A_\perp$ of the background field. The paper also supplies the before-to-inside, inside-to-inside, and inside-to-after quark and gluon propagators at (generalized) eikonal order, which enter observables only at NEik order because one or both endpoints sit inside the target, and it adds the contributions from t-channel quark exchange with a quark background field. Assembling these pieces gives the forward gluon production cross sections in gluon-nucleus (Eq. (119)) and quark-nucleus (Eq. (151)) scattering and the forward quark production cross sections in quark-nucleus (Eq. (136)) and gluon-nucleus (Eq. (161)) scattering at NEik accuracy, with the beyond-static effects appearing as $\delta'(q^+ - k^+)$ terms that encode longitudinal momentum transfer from the target.

Load-bearing premise

The ordering of the whole calculation rests on a prescribed boost hierarchy — the target's $A^-$ component grows with the boost while transverse components stay fixed and the $+$ component shrinks, and the slow $z^-$ dependence of the fields can be captured by a gradient expansion around one common value — together with the assumption that zero-mode cross terms with $q^+ k^+ < 0$ can be discarded and that the finite target width $L^+$ is the only source of $1/\gamma_t$ suppression. If a physical target violates this hierarchy, or the gradient expansion is not controlled, the claimed NEik cross sections — in particular the $\delta'(q^+ - k^+)$ terms of Eqs. (120) and (137) — would be incomplete or misordered.

Editorial extensions

If this is right

  • The four NEik cross sections (Eqs. (119), (136), (151), (161)) give the first complete set of forward single-inclusive parton-nucleus results beyond the eikonal approximation, covering both gluon and quark projectiles and targets.
  • The $\delta'(q^+ - k^+)$ terms mean the target can exchange longitudinal momentum with the projectile; at hadron level the partonic cross sections must be folded with $k^+$-dependent parton densities rather than evaluated at $q^+ = k^+$, which changes how forward RHIC and LHC data would be interpreted.
  • The decorated Wilson lines $U^{(1)}, U^{(2)}, U^{(3)}$ become the objects that any NEik computation must supply with small-$x$ evolution and a phenomenological model, a step the paper explicitly leaves open.
  • The before-to-inside, inside-to-inside, and inside-to-after propagators are reusable building blocks; the paper names forward dijet production in pA collisions, SIDIS at NEik order, and photon+jet production as immediate applications.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The decorated-Wilson-line operators, not the individual cross sections, are likely the durable output: any future NEik calculation of dijets, jets+photon, or SIDIS will probably reorganize into the same $U^{(1)}, U^{(2)}, U^{(3)}$ structures, so building their evolution equations first would let several observables be computed at once.
  • Because the quark-background channels enter through the enhanced component $\Psi^{(-)}$ of the target quark field, the $q \to g$ and $g \to q$ cross sections give a direct route to quark TMDs of nuclei from CGC-type calculations; taking the back-to-back limit of these cross sections and matching to TMD factorization would test that connection explicitly.
  • A cheap consistency check is available before any new modeling: setting $q^+ = k^+$ in Eqs. (119) and (136) should reproduce the standard dipole cross sections, and the $\delta'$ terms should act as derivatives of those dipole expressions with respect to $k^+$; existing dipole-model fits could test this immediately.
  • The beyond-static and beyond-shockwave corrections are both $1/\gamma_t$ effects but enter with different signatures — $\delta'$ terms versus integrals over $z^+$ — so a measurement of the $q^+$ dependence of forward production might separate the two classes of corrections experimentally.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 3 minor

Summary. The paper derives the full next-to-eikonal (NEik) corrections to the before-to-after gluon propagator in a dynamical gluon background, beyond both the shockwave and static limits, and compiles the before-to-inside, inside-to-inside, and inside-to-after quark and gluon propagators. These building blocks are then used to compute partonic forward single-inclusive cross sections for gluon production in gluon-nucleus scattering (Eq. (119)), quark production in quark-nucleus scattering (Eq. (136)), gluon production in quark-nucleus scattering (Eq. (151)), and quark production in gluon-nucleus scattering (Eq. (161)), including contributions from t-channel quark exchanges. The central claimed result is the compact before-to-after gluon propagator of Eqs. (55), (68), and (69), expressed through decorated Wilson lines.

Significance. If the derivation is correct, the paper provides a complete and systematic set of NEik parton propagators and cross sections that can serve as building blocks for higher-accuracy CGC phenomenology. The derivations are detailed, the algebra is organized, and the results are parameter-free in the sense of containing no fitted constants; the final cross sections are explicit operator expressions that can in principle be tested or evolved. The main uncertainties are concentrated in a few algebraic identities and power-counting steps rather than in the overall framework.

major comments (4)
  1. [Section II.C, Eqs. (64)–(66)] The compact NEik gluon propagator rests on the identities that rewrite sums of A_perp insertions and finite-width corrections as the decorated Wilson lines U^(1), U^(2), and U^(3). These identities are stated without proof, with only a reference to a quark analogue in Ref. [41]. Since a sign or factor error in Eq. (64) or Eq. (65) would propagate directly into the S-matrix element (87) and into all four final cross sections (119), (136), (151), and (161), this is a load-bearing step. Please provide the derivation, or at least an appendix containing the complete algebra, including the cancellation of the endpoint A_j terms that relies on the boundary condition (63).
  2. [Section II.A, Eqs. (27)–(28)] The evaluation of the p_n^+ and z_n^- integrals discards the cross terms with θ(q^+)θ(−k^+) and θ(−q^+)θ(k^+), stating that they correspond to zero modes with q^+ = k^+ = 0 and are not relevant for the eikonal expansion. This step is not demonstrated within the stated power counting. The final cross sections contain both δ(q^+−k^+) and δ'(q^+−k^+) terms, so even a subleading contribution from q^+ k^+ < 0 could alter the coefficient of the derivative-of-delta terms in Eqs. (120) and (137). Please quantify the suppression of these cross terms or provide an explicit argument that they are beyond NEik accuracy.
  3. [Section II.C, after Eq. (66)] The manuscript replaces the finite target width L^+ by ±∞ in the decorated Wilson lines and Wilson-line endpoints, asserting that faster-than-power decay of the background makes L^+ redundant. However, the finite width L^+ is used earlier to assign the NEik order of A_perp insertions and of the beyond-shockwave corrections. The equivalence requires that boundary terms at x^+ = ±L^+/2 cancel, but the identities (64) and (65) contain explicit endpoint contributions whose cancellation is not shown. Please justify the infinite-width replacement more rigorously, or retain finite integration limits and display the L^+-dependent terms that are dropped at the claimed accuracy.
  4. [Section IV.A, Eq. (95)] The identity (2k^+)(2q^+)/(q^+ + k^+)^2 = 1 + NNEik is justified by saying that q^+−k^+ is the conjugate of r^−, but q^+−k^+ is not parametrically small in the NEik power counting; the final expressions retain δ(q^+−k^+) and δ'(q^+−k^+) dependence, so q^+−k^+ offsets are not uniformly suppressed. Please clarify the precise sense in which the square term is NNEik, or derive the cross section without this step, since this affects the normalization of the NEik terms in Eqs. (119) and (120).
minor comments (3)
  1. [Eq. (64)] There is an evident typo in the displayed argument of the second Wilson line: “z′+, −L+/2” appears where a consistent integration variable should appear, and the notation “− −L+/2” should be cleaned up.
  2. [Eq. (65)] The argument “F^−_j(z+ z, z−)” is missing a comma and should read “F^−_j(z^+, z, z^−)” or similar; please make the z^+ dependence explicit.
  3. [Eq. (84)] The displayed inside-to-inside gluon propagator looks unbalanced: the instantaneous term is multiplied by one transverse projector and the Wilson-line term by another, but the closing parenthesis suggests a different grouping. Please check and correct the tensor structure, since this expression is quoted as input in Section V.B.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation found: the NEik gluon propagator and all four cross sections are obtained by explicit background-field Feynman-rule calculations, not by fitting or by importing the target result.

full rationale

The paper's central claim is the before-to-after gluon propagator at NEik accuracy, assembled from the explicit medium corrections in Eqs. (42), (47), (52) and (54), and organized in Eqs. (55)-(57) and then Eqs. (68)-(69). These pieces are computed from background-field Feynman diagrams (three-gluon and four-gluon vertices, instantaneous propagator insertions), not from the cross sections they later produce. The cross sections in Eqs. (119), (136), (151) and (161) are obtained by LSZ reduction from those propagators and by interference of eikonal and NEik amplitudes; no parameter is fitted and no data set is used, so there is no fitted-input-called-prediction pattern. The paper does rely on prior same-group results: the quark propagator results of Refs. [41,43,44], the z- gradient-expansion treatment of Appendix D of [43], and in Appendix A the statement that a gluon result 'can be read off from Eq. (A14) of [41]'. These are self-citations, but they supply previously computed building blocks and mathematical techniques, not the present NEik gluon propagator or the cross-section claims. The decorated-Wilson-line identities (64)-(66) are stated without proof and are the main correctness risk; however, they are not circular because they are not assumed as the definition of the final propagator, and an error there would break the derivation rather than make it tautologically valid. The zero-mode neglect and the power-counting hierarchy are stated assumptions, not circular reductions. Overall, the central derivation is self-contained and the self-citations are not load-bearing in the circularity sense.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

All quantities are analytic; there are no numbers fitted to data. The free-parameter list is empty because L+ and gamma_t are bookkeeping scales, not fit parameters. The axioms are the standard light-cone gauge framework plus the boosted-target power counting and slow-z- assumptions that define NEik order. The decorated Wilson lines introduced in the paper are composite operators, not new physical entities.

assumptions (5)
  • standard math Light-cone gauge A+ = 0, with the gluon vacuum propagator Eqs. (15)-(16) and standard Feynman rules in a background field.
    Used from the start of Sec. II; the gauge choice makes A- insertions the only surviving eikonal terms.
  • domain assumption Boosted target field hierarchy: A- proportional to gamma_t, A_j of order 1, A+ proportional to 1/gamma_t, with coordinates scaled as in Eqs. (1)-(4).
    Defines the eikonal expansion and fixes which background components enter at NEik order; if this hierarchy is wrong, the classification of corrections collapses.
  • domain assumption The target has finite support in x+ of width L+ of order 1/gamma_t and fields vanish outside it (Sec. II, around Eq. (27) and Eq. (63)).
    Justifies the shockwave limit and the counting of single A_perp insertions as NEik; also justifies replacing L+ by infinity in Wilson lines.
  • domain assumption The z- dependence of target fields is slow, so a gradient expansion around a common z- is valid, and zero modes with q+ = k+ = 0 are neglected (Sec. II.A, Eqs. (25)-(28)).
    This converts longitudinal momentum transfer into derivative terms such as delta'(q+ - k+) at NEik; the expansion is uncontrolled if z- dependence is not slow.
  • domain assumption Quark background field scaling: good component Psi(-) proportional to gamma_t^{1/2}, bad component Psi(+) proportional to gamma_t^{-1/2}; only Psi(-) contributes at NEik (Sec. I, Eq. (13)).
    Basis for t-channel quark exchange contributions; if the scaling is modified, quark background terms appear at different order.

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Pith. "Pith review of Forward parton-nucleus scattering at next-to-eikonal accuracy in the CGC." pith.science (2026). https://pith.science/paper/PVHNWBSK

@misc{pith2026241115047,
  author       = {Pith},
  title        = {Pith review of: Forward parton-nucleus scattering at next-to-eikonal accuracy in the CGC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PVHNWBSK}},
  note         = {Machine review of arXiv:2411.15047}
}
read the original abstract

We derive the full next-to-eikonal (NEik) corrections to the gluon propagator from before to after traversing a highly boosted gluon background field, including corrections both beyond the shockwave limit and beyond the static limit in particular. After summarizing the results of the full NEik corrections to the before-to-after quark propagator computed in our earlier works, we also derive the before-to-inside, inside-to-inside and inside-to-after quark and gluon propagators, which are building blocks to calculate high-energy scattering processes at NEik order. Using these results and also including the NEik corrections that stem from interactions with the target via t-channel quark exchanges, we compute inclusive cross sections for quark and gluon production at forward rapidities in quark-nucleus and gluon-nucleus scatterings at NEik accuracy.

Figures

Figures reproduced from arXiv: 2411.15047 by the authors.

Figure 1
Figure 1. FIG. 1. Contribution to the gluon propagator in background field, with insertions of the [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Contribution to the gluon propagator in background field, with a single transverse component of the background field [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Contribution to the gluon propagator in background field, with a local insertion of two transverse components of the [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Contribution to the gluon propagator in background field, with an instantaneous non-local insertion of two transverse [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Diagram for quark production from an incoming quark temporarily converted into a gluon, via two interactions with [PITH_FULL_IMAGE:figures/full_fig_p028_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Diagram for quark to gluon conversion due to the quark background field of the target [PITH_FULL_IMAGE:figures/full_fig_p032_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Diagram for quark to gluon conversion due to the quark background field of the target [PITH_FULL_IMAGE:figures/full_fig_p034_8.png]

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Reference graph

Works this paper leans on

89 extracted references · 5 canonical work pages · cited by 4 Pith papers

  1. [41]

    Agostini, T

    P. Agostini, T. Altinoluk, and N. Armesto, Eur. Phys. J. C 79, 790 (2019), arXiv:1907.03668 [hep-ph]

    arXiv 2019

  2. [1]

    In that regime, x+ and y+ are of order L+ which is power suppressed in the shockwave limit

    Inside-to-inside quark propagator in a pure A− background at eikonal order Our starting point for the computation of this contribution is the quark propagator at generalized eikonal order, in a background field containing only a A− component, which is computed in [44] as SF (x, y)|Eik, A− = δ3(x − y)γ+ Z dk+ 2π i 2k+ e−ik+(x−−y−) + Z d3p (2π)3 Z d3k (2π)3...

  3. [2]

    Eikonal contribution to inside-to-inside quark propagator from A⊥ insertions Even though, the interaction with the transverse component of the background field is of order ( γt)0, and thus suppressed with respect to the A− component, this suppression can be compensated. At eikonal order, the integration 41 over the longitudinal coordinate gives a factor o...

  4. [3]

    T otal inside-to-inside quark propagator in a gluon background field at eikonal order The total inside-to-inside quark propagator at eikonal order for x+ > y+ can be written as sum of the contributions computed above. Schematically, it reads SF (x, y) II,q Eik = SF (x, y) II,q Eik, A− + SF (x, y) II,q Eik, A⊥x + SF (x, y) II,q Eik,A⊥y + SF (x, y) II,q Eik...

  5. [4]

    Gelis, E

    F. Gelis, E. Iancu, J. Jalilian-Marian, and R. Venugopalan, Ann. Rev. Nucl. Part. Sci. 60, 463 (2010), arXiv:1002.0333 [hep-ph]

    arXiv 2010

  6. [5]

    J. L. Albacete and C. Marquet, Prog. Part. Nucl. Phys. 76, 1 (2014), arXiv:1401.4866 [hep-ph]

    arXiv 2014

  7. [6]

    Blaizot, Rept

    J.-P. Blaizot, Rept. Prog. Phys. 80, 032301 (2017), arXiv:1607.04448 [hep-ph]

    arXiv 2017

  8. [7]

    Balitsky, Nucl

    I. Balitsky, Nucl. Phys. B 463, 99 (1996), arXiv:hep-ph/9509348

    arXiv 1996

Show all 89 references
  1. [8]

    Y. V. Kovchegov, Phys. Rev. D 60, 034008 (1999), arXiv:hep-ph/9901281

    1999 arXiv

  2. [9]

    Y. V. Kovchegov, Phys. Rev. D 61, 074018 (2000), arXiv:hep-ph/9905214

    2000 arXiv

  3. [10]

    Jalilian-Marian, A

    J. Jalilian-Marian, A. Kovner, L. D. McLerran, and H. Weigert, Phys. Rev. D 55, 5414 (1997), arXiv:hep-ph/9606337

    1997 arXiv

  4. [11]

    Jalilian-Marian, A

    J. Jalilian-Marian, A. Kovner, A. Leonidov, and H. Weigert, Nucl. Phys. B 504, 415 (1997), arXiv:hep-ph/9701284

    1997 arXiv

  5. [12]

    Jalilian-Marian, A

    J. Jalilian-Marian, A. Kovner, A. Leonidov, and H. Weigert, Phys. Rev. D 59, 014014 (1998), arXiv:hep-ph/9706377. 45

    1998 arXiv

  6. [13]

    Jalilian-Marian, A

    J. Jalilian-Marian, A. Kovner, and H. Weigert, Phys. Rev. D 59, 014015 (1998), arXiv:hep-ph/9709432

    1998 arXiv

  7. [14]

    Kovner, J

    A. Kovner, J. G. Milhano, and H. Weigert, Phys. Rev. D 62, 114005 (2000), arXiv:hep-ph/0004014

    2000 arXiv

  8. [15]

    Weigert, Nucl

    H. Weigert, Nucl. Phys. A 703, 823 (2002), arXiv:hep-ph/0004044

    2002 arXiv

  9. [16]

    Iancu, A

    E. Iancu, A. Leonidov, and L. D. McLerran, Nucl. Phys. A 692, 583 (2001), arXiv:hep-ph/0011241

    2001 arXiv

  10. [17]

    Iancu, A

    E. Iancu, A. Leonidov, and L. D. McLerran, Phys. Lett. B 510, 133 (2001), arXiv:hep-ph/0102009

    2001 arXiv

  11. [18]

    Ferreiro, E

    E. Ferreiro, E. Iancu, A. Leonidov, and L. McLerran, Nucl. Phys. A 703, 489 (2002), arXiv:hep-ph/0109115

    2002 arXiv

  12. [19]

    Dumitru, A

    A. Dumitru, A. Hayashigaki, and J. Jalilian-Marian, Nucl. Phys. A 765, 464 (2006), arXiv:hep-ph/0506308

    2006 arXiv

  13. [20]

    Altinoluk and A

    T. Altinoluk and A. Kovner, Phys. Rev. D 83, 105004 (2011), arXiv:1102.5327 [hep-ph]

    2011 arXiv

  14. [21]

    G. A. Chirilli, B.-W. Xiao, and F. Yuan, Phys. Rev. Lett. 108, 122301 (2012), arXiv:1112.1061 [hep-ph]

    2012 arXiv

  15. [22]

    G. A. Chirilli, B.-W. Xiao, and F. Yuan, Phys. Rev. D 86, 054005 (2012), arXiv:1203.6139 [hep-ph]

    2012 arXiv

  16. [23]

    A. M. Sta´ sto, B.-W. Xiao, F. Yuan, and D. Zaslavsky, Phys. Rev. D 90, 014047 (2014), arXiv:1405.6311 [hep-ph]

    2014 arXiv

  17. [24]

    Z.-B. Kang, I. Vitev, and H. Xing, Phys. Rev. Lett. 113, 062002 (2014), arXiv:1403.5221 [hep-ph]

    2014 arXiv

  18. [25]

    Altinoluk, N

    T. Altinoluk, N. Armesto, G. Beuf, A. Kovner, and M. Lublinsky, Phys. Rev. D 91, 094016 (2015), arXiv:1411.2869 [hep-ph]

    2015 arXiv

  19. [26]

    Altinoluk, N

    T. Altinoluk, N. Armesto, G. Beuf, A. Kovner, and M. Lublinsky, Phys. Rev. D 93, 054049 (2016), arXiv:1511.09415 [hep-ph]

    2016 arXiv

  20. [27]

    Iancu, A

    E. Iancu, A. H. Mueller, and D. N. Triantafyllopoulos, JHEP 12, 041, arXiv:1608.05293 [hep-ph]

    arXiv

  21. [28]

    Liu, Z.-B

    H.-Y. Liu, Z.-B. Kang, and X. Liu, Phys. Rev. D 102, 051502 (2020), arXiv:2004.11990 [hep-ph]

    2020 arXiv

  22. [29]

    Duclou´ e, T

    B. Duclou´ e, T. Lappi, and Y. Zhu, Phys. Rev. D 93, 114016 (2016), arXiv:1604.00225 [hep-ph]

    2016 arXiv

  23. [30]

    Y. Shi, L. Wang, S.-Y. Wei, and B.-W. Xiao, Phys. Rev. Lett. 128, 202302 (2022), arXiv:2112.06975 [hep-ph]

    2022 arXiv

  24. [31]

    L. Wang, L. Chen, Z. Gao, Y. Shi, S.-Y. Wei, and B.-W. Xiao, Phys. Rev. D107, 016016 (2023), arXiv:2211.08322 [hep-ph]

    2023 arXiv

  25. [32]

    Altinoluk, N

    T. Altinoluk, N. Armesto, A. Kovner, and M. Lublinsky, Phys. Rev. D 108, 074003 (2023), arXiv:2307.14922 [hep-ph]

    2023 arXiv

  26. [33]

    A. M. Stasto, B.-W. Xiao, and D. Zaslavsky, Phys. Rev. Lett. 112, 012302 (2014), arXiv:1307.4057 [hep-ph]

    2014 arXiv

  27. [34]

    Watanabe, B.-W

    K. Watanabe, B.-W. Xiao, F. Yuan, and D. Zaslavsky, Phys. Rev. D 92, 034026 (2015), arXiv:1505.05183 [hep-ph]

    2015 arXiv

  28. [35]

    Duclou´ e, E

    B. Duclou´ e, E. Iancu, T. Lappi, A. H. Mueller, G. Soyez, D. N. Triantafyllopoulos, and Y. Zhu, Phys. Rev. D 97, 054020 (2018), arXiv:1712.07480 [hep-ph]

    2018 arXiv

  29. [36]

    Duclou´ e, T

    B. Duclou´ e, T. Lappi, and Y. Zhu, Phys. Rev. D 95, 114007 (2017), arXiv:1703.04962 [hep-ph]

    2017 arXiv

  30. [37]

    Altinoluk, N

    T. Altinoluk, N. Armesto, G. Beuf, M. Mart ´ ınez, and C. A. Salgado, JHEP 07, 068, arXiv:1404.2219 [hep-ph]

    arXiv

  31. [38]

    Altinoluk, N

    T. Altinoluk, N. Armesto, G. Beuf, and A. Moscoso, JHEP 01, 114, arXiv:1505.01400 [hep-ph]

    arXiv

  32. [39]

    Altinoluk and A

    T. Altinoluk and A. Dumitru, Phys. Rev. D 94, 074032 (2016), arXiv:1512.00279 [hep-ph]

    2016 arXiv

  33. [40]

    Agostini, T

    P. Agostini, T. Altinoluk, and N. Armesto, Eur. Phys. J. C 79, 600 (2019), arXiv:1902.04483 [hep-ph]

    2019 arXiv

  34. [42]

    Agostini, T

    P. Agostini, T. Altinoluk, N. Armesto, F. Dominguez, and J. G. Milhano, Eur. Phys. J. C82, 1001 (2022), arXiv:2207.10472 [hep-ph]

    2022 arXiv

  35. [43]

    Agostini, T

    P. Agostini, T. Altinoluk, and N. Armesto, Phys. Lett. B 840, 137892 (2023), arXiv:2212.03633 [hep-ph]

    2023 arXiv

  36. [44]

    Altinoluk, G

    T. Altinoluk, G. Beuf, A. Czajka, and A. Tymowska, Phys. Rev. D 104, 014019 (2021), arXiv:2012.03886 [hep-ph]

    2021 arXiv

  37. [45]

    Agostini, JHEP 11, 099, arXiv:2307.13573 [hep-ph]

    P. Agostini, JHEP 11, 099, arXiv:2307.13573 [hep-ph]

    arXiv

  38. [46]

    Altinoluk and G

    T. Altinoluk and G. Beuf, Phys. Rev. D 105, 074026 (2022), arXiv:2109.01620 [hep-ph]

    2022 arXiv

  39. [47]

    Altinoluk, G

    T. Altinoluk, G. Beuf, A. Czajka, and A. Tymowska, Phys. Rev. D 107, 074016 (2023), arXiv:2212.10484 [hep-ph]

    2023 arXiv

  40. [48]

    Agostini, T

    P. Agostini, T. Altinoluk, and N. Armesto, JHEP 07, 137, arXiv:2403.04603 [hep-ph]

    arXiv

  41. [49]

    Altinoluk, N

    T. Altinoluk, N. Armesto, and G. Beuf, Phys. Rev. D 108, 074023 (2023), arXiv:2303.12691 [hep-ph]

    2023 arXiv

  42. [50]

    Altinoluk, G

    T. Altinoluk, G. Beuf, A. Czajka, and C. Marquet, (2024), arXiv:2410.00612 [hep-ph]

    2024 arXiv

  43. [51]

    Y. V. Kovchegov, D. Pitonyak, and M. D. Sievert, JHEP 01, 072, [Erratum: JHEP 10, 148 (2016)], arXiv:1511.06737 [hep-ph]

    2016 arXiv

  44. [52]

    Y. V. Kovchegov, D. Pitonyak, and M. D. Sievert, Phys. Rev. D 95, 014033 (2017), arXiv:1610.06197 [hep-ph]

    2017 arXiv

  45. [53]

    Y. V. Kovchegov, D. Pitonyak, and M. D. Sievert, Phys. Rev. Lett. 118, 052001 (2017), arXiv:1610.06188 [hep-ph]

    2017 arXiv

  46. [54]

    Y. V. Kovchegov, D. Pitonyak, and M. D. Sievert, Phys. Lett. B 772, 136 (2017), arXiv:1703.05809 [hep-ph]

    2017 arXiv

  47. [55]

    Y. V. Kovchegov, D. Pitonyak, and M. D. Sievert, JHEP 10, 198, arXiv:1706.04236 [nucl-th]

    arXiv

  48. [56]

    Y. V. Kovchegov and M. D. Sievert, Phys. Rev. D 99, 054032 (2019), arXiv:1808.09010 [hep-ph]

    2019 arXiv

  49. [57]

    Y. V. Kovchegov and M. D. Sievert, Phys. Rev. D 99, 054033 (2019), arXiv:1808.10354 [hep-ph]

    2019 arXiv

  50. [58]

    Y. V. Kovchegov and M. G. Santiago, Phys. Rev. D 102, 014022 (2020), arXiv:2003.12650 [hep-ph]

    2020 arXiv

  51. [59]

    Y. V. Kovchegov and Y. Tawabutr, JHEP 08, 014, arXiv:2005.07285 [hep-ph]

    2005 arXiv

  52. [60]

    Adamiak, Y

    D. Adamiak, Y. V. Kovchegov, W. Melnitchouk, D. Pitonyak, N. Sato, and M. D. Sievert (Jefferson Lab Angular Momen- tum), Phys. Rev. D 104, L031501 (2021), arXiv:2102.06159 [hep-ph]

    2021 arXiv

  53. [61]

    Y. V. Kovchegov, A. Tarasov, and Y. Tawabutr, JHEP 03, 184, arXiv:2104.11765 [hep-ph]

    arXiv

  54. [62]

    Y. V. Kovchegov and M. G. Santiago, JHEP 11, 200, [Erratum: JHEP 09, 186 (2022)], arXiv:2108.03667 [hep-ph]

    2022 arXiv

  55. [63]

    Cougoulic, Y

    F. Cougoulic, Y. V. Kovchegov, A. Tarasov, and Y. Tawabutr, JHEP 07, 095, arXiv:2204.11898 [hep-ph]

    arXiv

  56. [64]

    Y. V. Kovchegov and M. G. Santiago, JHEP 11, 098, arXiv:2209.03538 [hep-ph]

    arXiv

  57. [65]

    Borden and Y

    J. Borden and Y. V. Kovchegov, Phys. Rev. D 108, 014001 (2023), arXiv:2304.06161 [hep-ph]

    2023 arXiv

  58. [66]

    Y. V. Kovchegov and M. Li, JHEP 05, 177, arXiv:2403.06959 [hep-ph]

    arXiv

  59. [67]

    Cougoulic and Y

    F. Cougoulic and Y. V. Kovchegov, Phys. Rev. D 100, 114020 (2019), arXiv:1910.04268 [hep-ph]

    2019 arXiv

  60. [68]

    Cougoulic and Y

    F. Cougoulic and Y. V. Kovchegov, Nucl. Phys. A 1004, 122051 (2020), arXiv:2005.14688 [hep-ph]

    2020 arXiv

  61. [69]

    Balitsky and A

    I. Balitsky and A. Tarasov, JHEP 10, 017, arXiv:1505.02151 [hep-ph]

    arXiv

  62. [70]

    Balitsky and A

    I. Balitsky and A. Tarasov, JHEP 06, 164, arXiv:1603.06548 [hep-ph]. 46

    arXiv

  63. [71]

    Balitsky and A

    I. Balitsky and A. Tarasov, JHEP 07, 095, arXiv:1706.01415 [hep-ph]

    arXiv

  64. [72]

    Boussarie and Y

    R. Boussarie and Y. Mehtar-Tani, Phys. Lett. B 831, 137125 (2022), arXiv:2006.14569 [hep-ph]

    2022 arXiv

  65. [73]

    Boussarie and Y

    R. Boussarie and Y. Mehtar-Tani, JHEP 07, 080, arXiv:2112.01412 [hep-ph]

    arXiv

  66. [74]

    Boussarie and Y

    R. Boussarie and Y. Mehtar-Tani, JHEP 10, 056, arXiv:2309.16576 [hep-ph]

    arXiv

  67. [75]

    G. A. Chirilli, JHEP 01, 118, arXiv:1807.11435 [hep-ph]

    arXiv

  68. [76]

    G. A. Chirilli, JHEP 06, 096, arXiv:2101.12744 [hep-ph]

    arXiv

  69. [77]

    Li, JHEP 07, 158, arXiv:2304.12842 [hep-ph]

    M. Li, JHEP 07, 158, arXiv:2304.12842 [hep-ph]

    arXiv

  70. [78]

    Li, Phys

    M. Li, Phys. Rev. Lett. 133, 021902 (2024), arXiv:2402.17568 [hep-ph]

    2024 arXiv

  71. [79]

    Li, (2024), arXiv:2411.13431 [hep-ph]

    M. Li, (2024), arXiv:2411.13431 [hep-ph]

    2024 arXiv

  72. [80]

    Jalilian-Marian, Phys

    J. Jalilian-Marian, Phys. Rev. D 96, 074020 (2017), arXiv:1708.07533 [hep-ph]

    2017 arXiv

  73. [81]

    Jalilian-Marian, Phys

    J. Jalilian-Marian, Phys. Rev. D 99, 014043 (2019), arXiv:1809.04625 [hep-ph]

    2019 arXiv

  74. [82]

    Jalilian-Marian, Phys

    J. Jalilian-Marian, Phys. Rev. D 102, 014008 (2020), arXiv:1912.08878 [hep-ph]

    2020 arXiv

  75. [83]

    Hatta, Y

    Y. Hatta, Y. Nakagawa, F. Yuan, Y. Zhao, and B. Xiao, Phys. Rev. D 95, 114032 (2017), arXiv:1612.02445 [hep-ph]

    2017 arXiv

  76. [84]

    Y. V. Kovchegov, JHEP 03, 174, arXiv:1901.07453 [hep-ph]

    1901 arXiv

  77. [85]

    Boussarie, Y

    R. Boussarie, Y. Hatta, and F. Yuan, Phys. Lett. B 797, 134817 (2019), arXiv:1904.02693 [hep-ph]

    2019 arXiv

  78. [86]

    Y. V. Kovchegov and B. Manley, JHEP 02, 060, arXiv:2310.18404 [hep-ph]

    arXiv

  79. [87]

    Y. V. Kovchegov and B. Manley, (2024), arXiv:2410.21260 [hep-ph]

    2024 arXiv

  80. [88]

    Altinoluk, J

    T. Altinoluk, J. Jalilian-Marian, and C. Marquet, (2024), arXiv:2406.08277 [hep-ph]

    2024 arXiv

  81. [89]

    Dominguez, C

    F. Dominguez, C. Marquet, B.-W. Xiao, and F. Yuan, Phys. Rev. D 83, 105005 (2011), arXiv:1101.0715 [hep-ph]

    2011 arXiv

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