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One BK-evolved dipole amplitude plus constant per-collider K-factors fits HERA DIS and forward hadron data at RHIC and the LHC with global χ² per degree of freedom near one.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · grok-4.5

2026-07-30 21:04 UTC pith:K3S3XY7I

load-bearing objection First simultaneous LO BK fit of HERA DIS and RHIC/LHCb forward hadrons works cleanly, with honest FF/scale caveats and a public dipole grid.

arxiv 2607.23485 v1 pith:K3S3XY7I submitted 2026-07-26 hep-ph

Simultaneous Color Glass Condensate fit to deep inelastic scattering and forward hadron production at HERA, RHIC, and the LHC

Piotr Korcyl , Truong My Hau Le , Farid Salazar , Tomasz Stebel This is my paper
classification hep-ph
keywords Color Glass CondensateBalitsky-Kovchegov evolutiondipole amplitudedeep inelastic scatteringforward hadron productiongluon saturationrunning couplingK-factor
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper asks whether the same Color Glass Condensate dipole that describes deep inelastic scattering at HERA can also describe forward single-inclusive hadron production in proton-proton collisions at RHIC and the LHC. Using the leading-order Balitsky–Kovchegov equation with running coupling (with or without a kinematical constraint), and allowing only a constant normalization K-factor for each collider, the authors obtain a simultaneous fit whose global χ² per degree of freedom is close to unity. The K-factors needed at RHIC are roughly twice those at the LHC, matching the pattern expected from threshold-resummed one-loop calculations. Adding the hadron data tightens the constraint on the dipole’s evolution speed without spoiling the DIS description, so the two observables act as complementary probes of the same amplitude. The dominant remaining systematics are the choice of fragmentation functions and the factorization scale that enter the hadron cross section.

Core claim

A single MV^γ initial dipole evolved with leading-order running-coupling BK (rcBK or kcBK) plus one constant K-factor per collider simultaneously describes HERA reduced DIS cross sections and forward SIHP spectra at RHIC and LHCb, reaching global χ²/d.o.f. ≈ 0.94 for rcBK, with no tension between the two data sets and with SIHP mainly tightening the evolution-speed parameter C².

What carries the argument

The dipole scattering amplitude N(r,x) obtained from LO BK evolution of an MV^γ initial condition; both the DIS reduced cross section and the dilute-dense forward hadron cross section are built from the same amplitude (fundamental or adjoint), with overall missing higher-order strength absorbed into constant per-collider K-factors.

Load-bearing premise

All missing higher-order corrections to forward hadron production can be absorbed into one constant, rapidity- and transverse-momentum-independent K-factor per collider.

What would settle it

A simultaneous fit in which the same dipole is required to describe both data sets without free per-collider K-factors, or with K-factors forced to be equal at RHIC and the LHC, that yields a global χ²/d.o.f. substantially worse than one, or a clear deterioration of the DIS description once SIHP is included.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The same fitted dipole can be used as the proton reference for forward hadron spectra and nuclear modification factors in proton-nucleus collisions.
  • Charm reduced cross sections at HERA would give a cleaner handle on the short-distance part of the amplitude because the heavy-quark mass suppresses large dipoles.
  • Two-particle correlations (photon-hadron, dihadron, dijet) become direct tests of the transverse-momentum structure of the same target amplitude.
  • The observed RHIC-to-LHC K-factor ratio of about two supplies a quantitative benchmark for future threshold-resummed or full NLO SIHP calculations.
  • Fragmentation-function choice and factorization-scale prescription dominate the present systematic uncertainty and must be controlled before SIHP can tightly constrain the dipole.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If constant-K fits continue to work once NLO impact factors are used, the residual K-factors should drop toward unity and lose most of their collider-energy dependence, giving a sharp consistency check of the CGC factorization.
  • Tension at high pT in the 13 TeV LHCb bins already visible with constant K suggests that any successful NLO or resummed extension will have to restore the correct pT slope, not merely the overall normalization.
  • Because SIHP mainly constrains evolution speed while DIS fixes the initial shape and area, a joint fit that also includes exclusive vector-meson or diffractive data could separate impact-parameter dependence from the inclusive dipole without new free normalizations.

Editorial analysis

A structured set of objections, weighed in public.

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

Circularity Check

1 steps flagged

Standard global CGC fit with free parameters; no load-bearing circular derivation.

specific steps
  1. fitted input called prediction [Eq. (5); Introduction; Tables I–II]
    "The K-factor is introduced to account for missing higher-order corrections. ... we include different K−factors at RHIC and LHC which account for missing higher-order corrections ... a global χ²/d.o.f. close to unity is achieved in both schemes."

    Absolute SIHP rates are normalized by free per-collider K-factors fitted to the same SIHP data whose description is then reported as successful. This is only a mild, openly declared fit degree of freedom: shapes in pT and rapidity, DIS, and the K_RHIC/K_LHC ratio vs external theory remain non-circular tests. Not load-bearing for the complementarity or evolution claims.

full rationale

The paper is a phenomenological simultaneous fit of MV^γ initial-condition parameters (Q²_s0, γ), running-coupling scale C², proton area σ0/2, and two constant per-collider K-factors to HERA DIS plus RHIC/LHCb SIHP, using LO BK evolution. Good global χ²/d.o.f. is the expected outcome of a multi-parameter fit to the same data, not a first-principles prediction claimed as such. The authors explicitly introduce K-factors as proxies for missing higher-order corrections and quantify their dependence on FF set and scale; they do not smuggle the absolute SIHP normalization in as a derived result. Non-circular content includes: (i) a single rapidity-independent K per collider still describing multi-rapidity, multi-energy SIHP shapes via BK evolution; (ii) DIS-only vs global comparison showing SIHP tightens C² without degrading χ²_DIS; (iii) K_RHIC/K_LHC ≈ 1.9 compared to an external threshold-resummation calculation (Ref. [31]). No self-definitional loop, uniqueness theorem from overlapping authors, or ansatz smuggled as theorem. Score 1 only for the trivial fact that free K-factors absorb SIHP overall normalization by construction—an openly stated modeling choice, not a hidden circular claim.

Axiom & Free-Parameter Ledger

9 free parameters · 6 axioms · 0 invented entities

The central claim rests on the standard LO CGC dilute-dense and DIS dipole formulas, MV^γ initial conditions, rcBK/kcBK evolution with a chosen IR-frozen coupling, collinear PDFs/FFs, and—most critically—free overall K-factors per collider plus several hand-fixed scales (x0, quark mass, µ prescription). No new dynamical entity is postulated; the ledger is dominated by fit parameters and domain modeling choices.

free parameters (9)
  • Q²_s0 = 0.1483(34) GeV² (rcBK global)
    Initial saturation scale squared in the MV^γ dipole at x0; fitted.
  • γ (anomalous dimension) = 1.1661(74) (rcBK global)
    Controls UV steepness of the initial dipole; fitted and strongly correlated with Q²_s0.
  • C² (running-coupling scale factor) = 8.69(85) (rcBK global); 1.133(54) (kcBK global)
    Sets the argument of αs in Balitsky’s prescription and thereby the evolution speed; fitted.
  • σ0/2 = 16.79(24) mb (rcBK global)
    Effective proton transverse area replacing b-integral; overall DIS/SIHP normalization parameter.
  • K_RHIC = 5.61(48) (rcBK)
    Constant multiplier for LO SIHP at RHIC energies, proxy for missing higher orders.
  • K_LHCb = 2.990(93) (rcBK)
    Constant multiplier for LO SIHP at LHC energies.
  • x0 = 0.015 (fixed)
    Starting rapidity for BK evolution; fixed by hand to cover all datasets.
  • Λ_QCD, IR freeze of αs, quark mass m = fixed as stated in Numerical Setup
    Λ_QCD=0.241 GeV, αs frozen ≈0.76, m=0.140 GeV for three light flavors; fixed inputs affecting low-Q² DIS and IR dipole.
  • Factorization scale prescription µ²=(pT/z)²+Q_s²(x) = GBW Q0²=1 GeV², x0=3.04e-4, λ=0.288
    Hand-chosen scale with GBW Q_s parameters; SM shows K-factors and χ² change under alternatives.
axioms (6)
  • domain assumption LO CGC expressions: DIS reduced cross section from dipole convolution with photon wave function (Eq. 2–3); forward SIHP from dilute-dense hybrid formula (Eq. 5).
    Entire fit uses LO impact factors only; NLO SIHP known to be problematic is replaced by K-factors.
  • domain assumption Dipole evolves with LO BK plus running coupling (Balitsky prescription), optionally with kinematical constraint shifts (rcBK/kcBK).
    Evolution engine of the universal dipole; two schemes compared in Tables I–II.
  • domain assumption Initial condition is the MV^γ model with translational invariance (no b-dependence) and adjoint dipole DA=DF² at large Nc.
    Standard CGC phenomenology ansatz; σ0/2 absorbs impact-parameter integral.
  • ad hoc to paper Higher-order corrections to SIHP factor into one constant K per collider, independent of pT and rapidity.
    Explicit modeling choice justified by expected dominance of energy-dependent threshold corrections; load-bearing for claiming shape-only SIHP constraints.
  • domain assumption Collinear cteq6l PDFs and NNFF1.0 FFs (baseline) with DGLAP evolution to µ are adequate external inputs.
    SIHP normalization and shape inherit FF/PDF systematics quantified in SM.
  • domain assumption Kinematic applicability cuts Q²≤45 GeV² and pT≥1 GeV select the CGC-valid region.
    Follows prior DIS fits; defines the 532+172 point sample.

pith-pipeline@v1.2.0-grok45-kimik3 · 30282 in / 3892 out tokens · 76447 ms · 2026-07-30T21:04:23.008593+00:00 · methodology

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read the original abstract

We present the first simultaneous fit to deep inelastic scattering (DIS) reduced cross sections from HERA and forward single inclusive hadron production (SIHP) from RHIC and the LHC in which the dipole amplitude is obtained from Balitsky--Kovchegov (BK) evolution within the Color Glass Condensate effective theory. We demonstrate that, using the LO BK equation with running coupling (with or without kinematical constraint) and a constant per-collider $K$-factor accounting for higher-order corrections, a global $\chi^2/\mathrm{d.o.f.}$ close to unity is achieved in both schemes. The required $K$-factors are about a factor of two larger at RHIC than at the LHC, remarkably in agreement with threshold-resummed one-loop studies of forward production. In our setup and with the data available, we find the two observables to be complementary: the SIHP data tighten the constraint on the evolution speed of the dipole amplitude without introducing tension with the DIS description. We further quantify the dependence of the $K$-factors on the fragmentation-function set and the factorization scale, identifying these as the dominant systematic uncertainties to be addressed in future precision analyses of forward hadron production. We perform a full uncertainty analysis using the Hessian method, validated against a Monte Carlo Bayesian inference study.

Figures

Figures reproduced from arXiv: 2607.23485 by Farid Salazar, Piotr Korcyl, Tomasz Stebel, Truong My Hau Le.

Figure 2
Figure 2. Figure 2: Comparison of HERA data with CGC calculations [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of RHIC data with CGC calculations [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of LHCb data with CGC calculations [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Parameter correlations from the global and DIS-only fits using rcBK evolution. The off-diagonal panels display 1 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) Comparison of FF contributions under various factorization scale choices, demonstrating the regularization [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Results for different sets of fragmentation functions (FFs) using the CTEQ PDF based on the best fit. Panel (a): [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Validation of the Monte Carlo Markov chain. The histogram of the accepted [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The comparison of the MCMC and Hessian methods. The result is calculated based on the global best fit. We see [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Unbiased Data-Driven Determination of the Nuclear Dipole Amplitude in the Color Glass Condensate

    hep-ph 2026-07 conditional novelty 6.0

    The 208Pb dipole amplitude is learned from R_pPb and coherent J/ψ photoproduction data with the BK equation embedded in training, giving Q²_s0(Pb)/Q²_s0(p) = 3.17 and an MV-type initial condition.

Reference graph

Works this paper leans on

116 extracted references · 70 linked inside Pith · cited by 1 Pith paper

  1. [1]

    R. P. Feynman, Very high-energy collisions of hadrons, Phys. Rev. Lett.23, 1415 (1969)

    1969

  2. [2]

    J. D. Bjorken and E. A. Paschos, Inelastic Electron Pro- ton and gamma Proton Scattering, and the Structure of the Nucleon, Phys. Rev.185, 1975 (1969)

    1975

  3. [3]

    V. N. Gribov and L. N. Lipatov, Deep inelastic e p scat- tering in perturbation theory, Sov. J. Nucl. Phys.15, 438 (1972), [Yad. Fiz.15,781(1972)]

    1972

  4. [4]

    Altarelli and G

    G. Altarelli and G. Parisi, Asymptotic Freedom in Par- ton Language, Nucl. Phys.B126, 298 (1977)

    1977

  5. [5]

    Y. L. Dokshitzer, Calculation of the Structure Func- tions for Deep Inelastic Scattering and e+ e- Annihila- tion by Perturbation Theory in Quantum Chromody- namics., Sov. Phys. JETP46, 641 (1977), [Zh. Eksp. Teor. Fiz.73,1216(1977)]

    1977

  6. [6]

    L. N. Lipatov, Reggeization of the Vector Meson and the Vacuum Singularity in Nonabelian Gauge Theories, Sov. J. Nucl. Phys.23, 338 (1976)

    1976

  7. [7]

    E. A. Kuraev, L. N. Lipatov, and V. S. Fadin, The Pomeranchuk Singularity in Nonabelian Gauge Theo- ries, Sov. Phys. JETP45, 199 (1977)

    1977

  8. [8]

    I. I. Balitsky and L. N. Lipatov, The Pomeranchuk Sin- gularity in Quantum Chromodynamics, Sov. J. Nucl. Phys.28, 822 (1978)

    1978

  9. [9]

    L. V. Gribov, E. M. Levin, and M. G. Ryskin, Semihard Processes in QCD, Phys. Rept.100, 1 (1983)

    1983

  10. [10]

    A. H. Mueller and J.-w. Qiu, Gluon Recombination and Shadowing at Small Values of x, Nucl. Phys. B268, 427 (1986)

    1986

  11. [11]

    L. D. McLerran and R. Venugopalan, Computing quark and gluon distribution functions for very large nuclei, Phys. Rev. D49, 2233 (1994), arXiv:hep-ph/9309289

    Pith/arXiv arXiv 1994

  12. [12]

    Morreale and F

    A. Morreale and F. Salazar, Mining for Gluon Saturation at Colliders, Universe7, 312 (2021), arXiv:2108.08254 [hep-ph]

    Pith/arXiv arXiv 2021

  13. [13]

    Abdul Khalek et al., Science Requirements and De- tector Concepts for the Electron-Ion Collider: EIC Yellow Report, Nucl

    R. Abdul Khalek et al., Science Requirements and De- tector Concepts for the Electron-Ion Collider: EIC Yellow Report, Nucl. Phys. A1026, 122447 (2022), arXiv:2103.05419 [physics.ins-det]

    Pith/arXiv arXiv 2022

  14. [14]

    Gelis, E

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

    Pith/arXiv arXiv 2010

  15. [15]

    Balitsky, Operator expansion for high-energy scat- tering, Nucl

    I. Balitsky, Operator expansion for high-energy scat- tering, Nucl. Phys. B463, 99 (1996), arXiv:hep- ph/9509348

    arXiv 1996

  16. [16]

    Y. V. Kovchegov, Small x F(2) structure function of a nucleus including multiple pomeron exchanges, Phys. Rev. D60, 034008 (1999), arXiv:hep-ph/9901281

    Pith/arXiv arXiv 1999

  17. [17]

    Jalilian-Marian, A

    J. Jalilian-Marian, A. Kovner, A. Leonidov, and H. Weigert, The BFKL equation from the Wilson renormalization group, Nucl. Phys. B504, 415 (1997), arXiv:hep-ph/9701284

    Pith/arXiv arXiv 1997

  18. [18]

    Jalilian-Marian, A

    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. D59, 014014 (1998), arXiv:hep-ph/9706377

    Pith/arXiv arXiv 1998

  19. [19]

    Kovner, J

    A. Kovner, J. G. Milhano, and H. Weigert, Relating different approaches to nonlinear QCD evolution at fi- nite gluon density, Phys. Rev. D62, 114005 (2000), arXiv:hep-ph/0004014

    Pith/arXiv arXiv 2000

  20. [20]

    Iancu, A

    E. Iancu, A. Leonidov, and L. D. McLerran, Nonlinear gluon evolution in the color glass condensate. 1., Nucl. Phys. A692, 583 (2001), arXiv:hep-ph/0011241

    Pith/arXiv arXiv 2001

  21. [21]

    Iancu, A

    E. Iancu, A. Leonidov, and L. D. McLerran, The Renormalization group equation for the color glass con- densate, Phys. Lett. B510, 133 (2001), arXiv:hep- ph/0102009

    arXiv 2001

  22. [22]

    Ferreiro, E

    E. Ferreiro, E. Iancu, A. Leonidov, and L. McLerran, Nonlinear gluon evolution in the color glass conden- sate. 2., Nucl. Phys. A703, 489 (2002), arXiv:hep- ph/0109115

    arXiv 2002

  23. [23]

    J. L. Albacete and C. Marquet, Gluon saturation and initial conditions for relativistic heavy ion collisions, Prog. Part. Nucl. Phys.76, 1 (2014), arXiv:1401.4866 [hep-ph]

    Pith/arXiv arXiv 2014

  24. [24]

    Dumitru, A

    A. Dumitru, A. Hayashigaki, and J. Jalilian-Marian, The Color glass condensate and hadron production in the forward region, Nucl. Phys. A765, 464 (2006), 8 arXiv:hep-ph/0506308

    Pith/arXiv arXiv 2006

  25. [25]

    Gelis and J

    F. Gelis and J. Jalilian-Marian, From DIS to proton nucleus collisions in the color glass condensate model, Phys. Rev. D67, 074019 (2003), arXiv:hep-ph/0211363

    Pith/arXiv arXiv 2003

  26. [26]

    G. Beuf, H. H¨ anninen, T. Lappi, and H. M¨ antysaari, Color Glass Condensate at next-to-leading order meets HERA data, Phys. Rev. D102, 074028 (2020), arXiv:2007.01645 [hep-ph]

    Pith/arXiv arXiv 2020

  27. [27]

    G. A. Chirilli, B.-W. Xiao, and F. Yuan, Inclusive Hadron Productions in pA Collisions, Phys. Rev. D86, 054005 (2012), arXiv:1203.6139 [hep-ph]

    Pith/arXiv arXiv 2012

  28. [28]

    Liu, Y.-Q

    H.-Y. Liu, Y.-Q. Ma, and K.-T. Chao, Improvement for Color Glass Condensate factorization: single hadron production in pA collisions at next-to-leading order, Phys. Rev. D100, 071503 (2019), arXiv:1909.02370 [nucl-th]

    Pith/arXiv arXiv 2019

  29. [29]

    H¨ anninen, H

    H. H¨ anninen, H. M¨ antysaari, R. Paatelainen, and J. Penttala, Proton Structure Functions at Next- to-Leading Order in the Dipole Picture with Mas- sive Quarks, Phys. Rev. Lett.130, 192301 (2023), arXiv:2211.03504 [hep-ph]

    Pith/arXiv arXiv 2023

  30. [30]

    Casuga and H

    C. Casuga and H. Mantysaari, Confronting Color Glass Condensate at next-to-leading order with HERA data, (2026), arXiv:2604.22332 [hep-ph]

    Pith/arXiv arXiv 2026

  31. [31]

    Y. Shi, L. Wang, S.-Y. Wei, and B.-W. Xiao, Pursuing the Precision Study for Color Glass Condensate in For- ward Hadron Productions, Phys. Rev. Lett.128, 202302 (2022), arXiv:2112.06975 [hep-ph]

    Pith/arXiv arXiv 2022

  32. [32]

    M¨ antysaari and Y

    H. M¨ antysaari and Y. Tawabutr, Complete next-to- leading order calculation of single inclusiveπ0 produc- tion in forward proton-nucleus collisions, Phys. Rev. D 109, 034018 (2024), arXiv:2310.06640 [hep-ph]

    Pith/arXiv arXiv 2024

  33. [33]

    J. L. Albacete, N. Armesto, J. G. Milhano, and C. A. Salgado, Non-linear QCD meets data: A Global anal- ysis of lepton-proton scattering with running cou- pling BK evolution, Phys. Rev. D80, 034031 (2009), arXiv:0902.1112 [hep-ph]

    Pith/arXiv arXiv 2009

  34. [34]

    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 includ- ing heavy quarks, Eur. Phys. J. C71, 1705 (2011), arXiv:1012.4408 [hep-ph]

    Pith/arXiv arXiv 2011

  35. [35]

    A. H. Rezaeian and I. Schmidt, Impact-parameter de- pendent Color Glass Condensate dipole model and new combined HERA data, Phys. Rev. D88, 074016 (2013), arXiv:1307.0825 [hep-ph]

    Pith/arXiv arXiv 2013

  36. [36]

    J. L. Albacete and C. Marquet, Single Inclusive Hadron Production at RHIC and the LHC from the Color Glass Condensate, Phys. Lett. B687, 174 (2010), arXiv:1001.1378 [hep-ph]

    Pith/arXiv arXiv 2010

  37. [37]

    Lappi and H

    T. Lappi and H. M¨ antysaari, Single inclusive particle production at high energy from HERA data to proton- nucleus collisions, Phys. Rev. D88, 114020 (2013), arXiv:1309.6963 [hep-ph]

    Pith/arXiv arXiv 2013

  38. [38]

    Kutak and S

    K. Kutak and S. Sapeta, Gluon saturation in dijet pro- duction in p-Pb collisions at Large Hadron Collider, Phys. Rev. D86, 094043 (2012), arXiv:1205.5035 [hep- ph]

    Pith/arXiv arXiv 2012

  39. [39]

    Salazar, B

    F. Salazar, B. Schenke, and A. Soto-Ontoso, Accessing subnuclear fluctuations and saturation with multiplicity dependent J/ψproduction in p+p and p+Pb collisions, Phys. Lett. B827, 136952 (2022), arXiv:2112.04611 [hep-ph]

    Pith/arXiv arXiv 2022

  40. [40]

    Beni´ c, O

    S. Beni´ c, O. Garcia-Montero, and A. Perkov, Isolated photon-hadron production in high energy pp and pA collisions at RHIC and LHC, Phys. Rev. D105, 114052 (2022), arXiv:2203.01685 [hep-ph]

    Pith/arXiv arXiv 2022

  41. [41]

    Caucal, Z.-B

    P. Caucal, Z.-B. Kang, P. Korcyl, F. Salazar, B. Schenke, T. Stebel, R. Venugopalan, and W. Zhao, Probing gluon saturation with forward di-hadron corre- lations in proton-nucleus collisions, Phys. Lett. B879, 140599 (2026), arXiv:2512.21466 [hep-ph]

    arXiv 2026

  42. [42]

    Fujii, T

    H. Fujii, T. Hirano, K. Itakura, Y. Nara, and S. Zhao, Forward hadron production in pp collisions at LHC en- ergies from an event generator based on the color glass condensate framework, (2026), arXiv:2605.15494 [hep- ph]

    Pith/arXiv arXiv 2026

  43. [43]

    Kowalski, L

    H. Kowalski, L. Motyka, and G. Watt, Exclusive diffrac- tive processes at HERA within the dipole picture, Phys. Rev. D74, 074016 (2006), arXiv:hep-ph/0606272

    Pith/arXiv arXiv 2006

  44. [44]

    Bendova, J

    D. Bendova, J. Cepila, J. G. Contreras, and M. Matas, Solution to the Balitsky-Kovchegov equation with the collinearly improved kernel including impact- parameter dependence, Phys. Rev. D100, 054015 (2019), arXiv:1907.12123 [hep-ph]

    Pith/arXiv arXiv 2019

  45. [45]

    Dai, F.-P

    S.-W. Dai, F.-P. Li, L.-G. Pang, G.-Y. Qin, S.-Y. Wei, H.-Z. Zhang, and W. Zhao, Physics-Informed Global Extraction of the Universal Small-xDipole Amplitude, (2026), arXiv:2603.08008 [hep-ph]

    Pith/arXiv arXiv 2026

  46. [46]

    Kou and X

    W. Kou and X. Chen, Extraction of the color dipole amplitude with physics-informed neural networks, Phys. Lett. B877, 140507 (2026), arXiv:2601.16391 [hep-ph]

    Pith/arXiv arXiv 2026

  47. [47]

    M¨ antysaari, H

    H. M¨ antysaari, H. Roch, F. Salazar, B. Schenke, C. Shen, and W. Zhao, Global Bayesian analysis of J/ψ photoproduction on proton and lead targets, Phys. Rev. D113, 014038 (2026), arXiv:2507.14087 [hep-ph]

    arXiv 2026

  48. [48]

    M¨ antysaari, H

    H. M¨ antysaari, H. Roch, B. Schenke, C. Shen, and W. Zhao, Revisiting the role of saturation in diffrac- tive vector meson production, (2026), arXiv:2606.20362 [hep-ph]

    Pith/arXiv arXiv 2026

  49. [49]

    A. M. Stasto, B.-W. Xiao, and D. Zaslavsky, To- wards the Test of Saturation Physics Beyond Lead- ing Logarithm, Phys. Rev. Lett.112, 012302 (2014), arXiv:1307.4057 [hep-ph]

    Pith/arXiv arXiv 2014

  50. [50]

    A. M. Sta´ sto, B.-W. Xiao, F. Yuan, and D. Zaslavsky, Matching collinear and smallxfactorization calcula- tions for inclusive hadron production inpAcollisions, Phys. Rev. D90, 014047 (2014), arXiv:1405.6311 [hep- ph]

    Pith/arXiv arXiv 2014

  51. [51]

    Altinoluk, N

    T. Altinoluk, N. Armesto, G. Beuf, A. Kovner, and M. Lublinsky, Single-inclusive particle production in proton-nucleus collisions at next-to-leading order in the hybrid formalism, Phys. Rev. D91, 094016 (2015), arXiv:1411.2869 [hep-ph]

    Pith/arXiv arXiv 2015

  52. [52]

    Watanabe, B.-W

    K. Watanabe, B.-W. Xiao, F. Yuan, and D. Zaslavsky, Implementing the exact kinematical constraint in the saturation formalism, Phys. Rev. D92, 034026 (2015), arXiv:1505.05183 [hep-ph]

    Pith/arXiv arXiv 2015

  53. [53]

    Duclou´ e, T

    B. Duclou´ e, T. Lappi, and Y. Zhu, Single inclusive for- ward hadron production at next-to-leading order, Phys. Rev. D93, 114016 (2016), arXiv:1604.00225 [hep-ph]

    Pith/arXiv arXiv 2016

  54. [54]

    Iancu, A

    E. Iancu, A. H. Mueller, and D. N. Triantafyllopoulos, CGC factorization for forward particle production in proton-nucleus collisions at next-to-leading order, JHEP 12, 041, arXiv:1608.05293 [hep-ph]

    Pith/arXiv arXiv

  55. [55]

    Duclou´ e, T

    B. Duclou´ e, T. Lappi, and Y. Zhu, Implementation of NLO high energy factorization in single inclusive forward hadron production, Phys. Rev. D95, 114007 9 (2017), arXiv:1703.04962 [hep-ph]

    Pith/arXiv arXiv 2017

  56. [56]

    Liu, Z.-B

    H.-Y. Liu, Z.-B. Kang, and X. Liu, Threshold resumma- tion for hadron production in the small-xregion, Phys. Rev. D102, 051502 (2020), arXiv:2004.11990 [hep-ph]

    Pith/arXiv arXiv 2020

  57. [57]

    J. P. Blaizot, F. Gelis, and R. Venugopalan, High-energy pA collisions in the color glass condensate approach. 1. Gluon production and the Cronin effect, Nucl. Phys. A 743, 13 (2004), arXiv:hep-ph/0402256

    Pith/arXiv arXiv 2004

  58. [58]

    J. P. Blaizot, F. Gelis, and R. Venugopalan, High-energy pA collisions in the color glass condensate approach

  59. [59]

    Quark production, Nucl. Phys. A743, 57 (2004), arXiv:hep-ph/0402257

    Pith/arXiv arXiv 2004

  60. [60]

    L. D. McLerran and R. Venugopalan, Boost covariant gluon distributions in large nuclei, Phys. Lett. B424, 15 (1998), arXiv:nucl-th/9705055

    Pith/arXiv arXiv 1998

  61. [61]

    Balitsky, Quark contribution to the small-x evolu- tion of color dipole, Phys

    I. Balitsky, Quark contribution to the small-x evolu- tion of color dipole, Phys. Rev. D75, 014001 (2007), arXiv:hep-ph/0609105

    Pith/arXiv arXiv 2007

  62. [62]

    Motyka and A

    L. Motyka and A. M. Stasto, Exact kinematics in the small x evolution of the color dipole and gluon cascade, Phys. Rev. D79, 085016 (2009), arXiv:0901.4949 [hep- ph]

    Pith/arXiv arXiv 2009

  63. [63]

    Beuf, Improving the kinematics for low-xQCD evo- lution equations in coordinate space, Phys

    G. Beuf, Improving the kinematics for low-xQCD evo- lution equations in coordinate space, Phys. Rev. D89, 074039 (2014), arXiv:1401.0313 [hep-ph]

    Pith/arXiv arXiv 2014

  64. [64]

    Pumplin, D

    J. Pumplin, D. R. Stump, J. Huston, H.-L. Lai, P. Nadolsky, and W.-K. Tung, New generation of parton distributions with uncertainties from global qcd anal- ysis, Journal of High Energy Physics2002, 012–012 (2002)

    2002

  65. [65]

    Bertone, S

    V. Bertone, S. Carrazza, N. P. Hartland, E. R. Nocera, and J. Rojo (NNPDF), A determination of the frag- mentation functions of pions, kaons, and protons with faithful uncertainties, Eur. Phys. J. C77, 516 (2017), arXiv:1706.07049 [hep-ph]

    Pith/arXiv arXiv 2017

  66. [66]

    G. A. Chirilli, B.-W. Xiao, and F. Yuan, One-loop Fac- torization for Inclusive Hadron Production inpACol- lisions in the Saturation Formalism, Phys. Rev. Lett. 108, 122301 (2012), arXiv:1112.1061 [hep-ph]

    Pith/arXiv arXiv 2012

  67. [67]

    K. J. Golec-Biernat and M. Wusthoff, Saturation effects in deep inelastic scattering at low Q**2 and its impli- cations on diffraction, Phys. Rev. D59, 014017 (1998), arXiv:hep-ph/9807513

    Pith/arXiv arXiv 1998

  68. [68]

    Pumplin, D

    J. Pumplin, D. R. Stump, and W. K. Tung, Multivariate fitting and the error matrix in global analysis of data, Phys. Rev. D65, 014011 (2001), arXiv:hep-ph/0008191

    Pith/arXiv arXiv 2001

  69. [69]

    Pumplin, D

    J. Pumplin, D. Stump, R. Brock, D. Casey, J. Hus- ton, J. Kalk, H. L. Lai, and W. K. Tung, Uncertain- ties of predictions from parton distribution functions. 2. The Hessian method, Phys. Rev. D65, 014013 (2001), arXiv:hep-ph/0101032

    Pith/arXiv arXiv 2001

  70. [70]

    Casuga, M

    C. Casuga, M. Karhunen, and H. M¨ antysaari, Inferring the initial condition for the Balitsky- Kovchegov equation, Phys. Rev. D109, 054018 (2024), arXiv:2311.10491 [hep-ph]

    Pith/arXiv arXiv 2024

  71. [71]

    Gelman, J

    A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin, Bayesian Data Analysis, 3rd ed. (Chapman and Hall/CRC, Boca Raton, FL, 2013)

    2013

  72. [72]

    Abramowicz et al

    H. Abramowicz et al. (H1, ZEUS), Combination of mea- surements of inclusive deep inelastice±pscattering cross sections and QCD analysis of HERA data, Eur. Phys. J. C75, 580 (2015), arXiv:1506.06042 [hep-ex]

    Pith/arXiv arXiv 2015

  73. [73]

    Arsene et al

    I. Arsene et al. (BRAHMS), On the evolution of the nuclear modification factors with rapidity and centrality in d + Au collisions at s(NN)**(1/2) = 200-GeV, Phys. Rev. Lett.93, 242303 (2004), arXiv:nucl-ex/0403005

    Pith/arXiv arXiv 2004

  74. [74]

    Adams et al

    J. Adams et al. (STAR), Forward neutral pion produc- tion in p+p and d+Au collisions at s(NN)**(1/2) = 200- GeV, Phys. Rev. Lett.97, 152302 (2006), arXiv:nucl- ex/0602011

    arXiv 2006

  75. [75]

    Aaij et al

    R. Aaij et al. (LHCb), Measurement of the Nuclear Modification Factor and Prompt Charged Particle Pro- duction inp−P bandppCollisions at √sN N=5 TeV, Phys. Rev. Lett.128, 142004 (2022), arXiv:2108.13115 [hep-ex]

    arXiv 2022

  76. [76]

    Aaij et al

    R. Aaij et al. (LHCb), Measurement of prompt charged- particle production in pp collisions at √s = 13 TeV, JHEP01, 166, arXiv:2107.10090 [hep-ex]

    arXiv

  77. [77]

    Duclou´ e, E

    B. Duclou´ e, E. Iancu, A. H. Mueller, G. Soyez, and D. N. Triantafyllopoulos, Non-linear evolution in QCD at high-energy beyond leading order, JHEP04, 081, arXiv:1902.06637 [hep-ph]

    Pith/arXiv arXiv 1902

  78. [78]

    Casuga, H

    C. Casuga, H. H¨ anninen, and H. M¨ antysaari, Initial condition for the Balitsky-Kovchegov equation at next- to-leading order, Phys. Rev. D112, 034003 (2025), arXiv:2506.00487 [hep-ph]

    Pith/arXiv arXiv 2025

  79. [79]

    K. J. Eskola and H. Honkanen, A Perturbative QCD analysis of charged particle distributions in hadronic and nuclear collisions, Nucl. Phys. A713, 167 (2003), arXiv:hep-ph/0205048

    Pith/arXiv arXiv 2003

  80. [80]

    E. A. F. Basso, M. B. Gay Ducati, and E. G. de Oliveira, Momentum space saturation model for deep inelastic scattering and single inclusive hadron production, Phys. Rev. D84, 034024 (2011), arXiv:1103.2145 [hep-ph]

    Pith/arXiv arXiv 2011

Showing first 80 references.