# Mining for Gluon Saturation at Colliders

^{1}

^{2}

^{3}

^{4}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Color Glass Condensate Effective Field Theory

#### 2.1. Separation of Degrees of Freedom: Sources and Fields

- Compute the quantum expectation value/path integral $\mathcal{O}\left[\rho \right]={\langle \mathcal{O}\rangle}_{\rho}$ in the presence of sources $\rho $ drawn from ${W}_{{x}_{0}}\left[\rho \right]$.
- Average over all possible configurations given by an appropriate gauge invariant weight functional ${W}_{{x}_{0}}\left[\rho \right]$.

#### 2.2. High Energy Scattering: Light-like Wilson Lines and Correlators

#### 2.3. From DIS to Proton–Nucleus (pA) Collisions

#### 2.4. Quantum Evolution

## 3. Experimental Signatures to Date

#### 3.1. Structure Functions

#### Competing Mechanisms in Structure Functions

#### 3.2. Diffractive Reactions

#### Competing Mechanisms and Systematic Uncertainties

#### 3.3. Semi-Inclusive Reactions

#### 3.3.1. Single Inclusive Production

#### 3.3.2. Competing Mechanisms in Single Inclusive Production

#### 3.3.3. Double Inclusive Production

#### 3.3.4. Competing Mechanisms in Double Inclusive Production

#### 3.4. High Multiplicity and Small Systems

#### A Final Note on Competing Mechanisms

## 4. A New Generation of High Energy DIS Colliders

#### 4.1. Structure Functions

#### 4.2. Diffractive Measurements

#### 4.3. Semi-Inclusive Measurements

## 5. Discussion and Concluding Remarks

#### 5.1. Theoretical Advances

#### 5.2. Experimental Requirements

- Accurate description of physics- and machine-induced backgrounds. This requires an effort of open-sourced, cross-collaboration simulation packages that include theory, phenomenology studies as well as up-to-date machine background knowledge. Two principal machine backgrounds that we can learn from past experiments are synchrotron radiation and beam–gas interactions. Synchrotron radiation occurs when the trajectory of a charged particle is bent, synchrotron photons are emitted tangential to the particle’s path. More concretely, these backgrounds can affect tracking detectors and calorimeters by depositing energy leading to detector hits. Ultimately this can also lead to a large number of ghost tracks and large detector occupancy effects. Beam–gas interactions on the other hand occur when proton or ion beam particles collide with residual gas. Ion beam interactions with gas cause beam particle losses and halo, which can reach the detectors. Addition of these backgrounds in future simulations is needed for detector design or AI-based data training techniques; as such these should be included in the next generation of DIS experiments [296].
- Improved jet tagging capabilities which can disentangle jets that come from quarks, gluons, gluon-dense vs. saturated gluon signatures. Jet tagging refers to the reconstruction of streams of particles coming from the collision or displaced vertices with the flexibility of a loose event selection requirement. The classification of jets depends on the kinematic variables such as transverse momentum (${p}_{\perp}$), pseudorapidity (rapidity) $\eta $(y), azimuthal angle $\varphi $, number of tracks, and energy (E). We remind the reader that jets can be contaminated by many soft processes that are not correlated to the jet. We often rely on classification/regression tasks which give us an approximation of the background. A potential AI application which should build upon existing experiments and further developed could be to extract and study list of features using kinematic variables from simulations. The list of features could be used to form jet images or graphs in $\eta -\varphi $ plane which will be used as an input of various AI-related algorithms to classify jet events from background events [299].
- Precisely identify particles: open and hidden charm mesons, direct photons, electrons all while minimizing biases. While standard cut and slice techniques have done a excellent job when the detectors are adequate and production cross sections are large, many rare resonances or small cross sections have suffered from these same methods and have yet reached statistical significance. While machine learning techniques are currently implemented for identification of rare particles in certain physics cases of nuclear experiments at accelerators, AI is at its infancy and has not replaced or considerably complemented standard particle identification methods at high-energy nuclear experiments. Applying Machine Learning algorithms can give advantages in the signal to background ratios as strict cuts and slices on the variables are minimized or eliminated altogether. This, however, requires a dedicated computing effort to go beyond the standard ML methods used so far.

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Notes

1 | This is an oversimplified view point, as the small-x evolution will not only change the value of ${Q}_{s}$ but also the functional form of the dipole. In the most general case, the saturation scale will also depend on the impact parameter ${b}_{\perp}$ as more color charge densities are expected in the center of the nucleus than in its periphery, modulo fluctuations. |

2 | Unfortunately, the GBW model fails to describe other observables such as single hadron inclusive spectra in pA due to its exponential tail, rather than the expected power law behavior. |

3 | The factor of A in Equation (31) arises from an ${A}^{2/3}$ overall area, and ${A}^{1/3}$ from the scaling of the saturation momentum. |

4 | Note that the partons in the dilute projectile (in this case the deuteron) involved in the forward production carry large momentum fraction x close to the kinematic limit $x\sim 1$. |

5 | At the LHC one has to include the gluon initiated channels as well. |

6 | More massive vector mesons probe shorter distances where saturation effects are suppressed. |

7 | In electron–nucleus collisions there are no initial state interactions in the gauge links, in the language of TMDs, as the exchange photon is colorless. This is in contrast to proton–nucleus collisions, where the collinear quark or gluon to the proton carry color and thus initial interactions in the gauge links are present [12,32,198]. |

## References

- Gross, D.J.; Wilczek, F. Ultraviolet Behavior of Nonabelian Gauge Theories. Phys. Rev. Lett.
**1973**, 30, 1343–1346. [Google Scholar] [CrossRef][Green Version] - Politzer, H.D. Reliable Perturbative Results for Strong Interactions? Phys. Rev. Lett.
**1973**, 30, 1346–1349. [Google Scholar] [CrossRef][Green Version] - Hanada, M.; Jevicki, A.; Peng, C.; Wintergerst, N. Anatomy of Deconfinement. J. High Energy Phys.
**2019**, 12, 167. [Google Scholar] [CrossRef][Green Version] - Bjorken, J.D. Asymptotic Sum Rules at Infinite Momentum. Phys. Rev.
**1969**, 179, 1547–1553. [Google Scholar] [CrossRef] - Bjorken, J.D.; Paschos, E.A. Inelastic Electron Proton and gamma Proton Scattering, and the Structure of the Nucleon. Phys. Rev.
**1969**, 185, 1975–1982. [Google Scholar] [CrossRef] - Feynman, R.P. Very high-energy collisions of hadrons. Phys. Rev. Lett.
**1969**, 23, 1415–1417. [Google Scholar] [CrossRef][Green Version] - Gribov, V.N.; Lipatov, L.N. Deep inelastic e p scattering in perturbation theory. Sov. J. Nucl. Phys.
**1972**, 15, 438–450. [Google Scholar] - Lipatov, L.N. The parton model and perturbation theory. Sov. J. Nucl. Phys.
**1975**, 20, 94–102. [Google Scholar] - Altarelli, G.; Parisi, G. Asymptotic Freedom in Parton Language. Nucl. Phys.
**1977**, B126, 298–318. [Google Scholar] [CrossRef] - Dokshitzer, Y.L. Calculation of the Structure Functions for Deep Inelastic Scattering and e+ e- Annihilation by Perturbation Theory in Quantum Chromodynamics. Sov. Phys. JETP
**1977**, 46, 641–653. [Google Scholar] - Collins, J.C.; Soper, D.E. Parton Distribution and Decay Functions. Nucl. Phys.
**1982**, B194, 445–492. [Google Scholar] [CrossRef] - Mulders, P.J.; Rodrigues, J. Transverse momentum dependence in gluon distribution and fragmentation functions. Phys. Rev. D
**2001**, 63, 094021. [Google Scholar] [CrossRef][Green Version] - Meissner, S.; Metz, A.; Goeke, K. Relations between generalized and transverse momentum dependent parton distributions. Phys. Rev. D
**2007**, 76, 034002. [Google Scholar] [CrossRef][Green Version] - Ji, X.D. Gauge-Invariant Decomposition of Nucleon Spin. Phys. Rev. Lett.
**1997**, 78, 610–613. [Google Scholar] [CrossRef] - Radyushkin, A. Nonforward parton distributions. Phys. Rev. D
**1997**, 56, 5524–5557. [Google Scholar] [CrossRef][Green Version] - Müller, D.; Robaschik, D.; Geyer, B.; Dittes, F.M.; Hořejši, J. Wave functions, evolution equations and evolution kernels from light ray operators of QCD. Fortsch. Phys.
**1994**, 42, 101–141. [Google Scholar] [CrossRef][Green Version] - Gribov, L.; Levin, E.; Ryskin, M. Semihard Processes in QCD. Phys. Rept.
**1983**, 100, 1–150. [Google Scholar] [CrossRef] - Mueller, A.H.; Qiu, J.W. Gluon Recombination and Shadowing at Small Values of x. Nucl. Phys. B
**1986**, 268, 427–452. [Google Scholar] [CrossRef] - McLerran, L.D.; Venugopalan, R. Computing quark and gluon distribution functions for very large nuclei. Phys. Rev. D
**1994**, 49, 2233–2241. [Google Scholar] [CrossRef][Green Version] - McLerran, L.D.; Venugopalan, R. Gluon distribution functions for very large nuclei at small transverse momentum. Phys. Rev. D
**1994**, 49, 3352–3355. [Google Scholar] [CrossRef][Green Version] - McLerran, L.D.; Venugopalan, R. Green’s functions in the color field of a large nucleus. Phys. Rev. D
**1994**, 50, 2225–2233. [Google Scholar] [CrossRef] [PubMed][Green Version] - Ayala, A.; Jalilian-Marian, J.; McLerran, L.D.; Venugopalan, R. The Gluon propagator in nonAbelian Weizsacker-Williams fields. Phys. Rev. D
**1995**, 52, 2935–2943. [Google Scholar] [CrossRef] [PubMed][Green Version] - Ayala, A.; Jalilian-Marian, J.; McLerran, L.D.; Venugopalan, R. Quantum corrections to the Weizsacker-Williams gluon distribution function at small x. Phys. Rev. D
**1996**, 53, 458–475. [Google Scholar] [CrossRef] [PubMed][Green Version] - Iancu, E.; Venugopalan, R. The Color glass condensate and high-energy scattering in QCD. In Quark-Gluon Plasma 4; Hwa, R.C., Wang, X.N., Eds.; World Scientific: Singapore, 2003. [Google Scholar] [CrossRef][Green Version]
- Gelis, F.; Iancu, E.; Jalilian-Marian, J.; Venugopalan, R. The Color Glass Condensate. Ann. Rev. Nucl. Part. Sci.
**2010**, 60, 463–489. [Google Scholar] [CrossRef][Green Version] - Kovchegov, Y.V.; Levin, E. Quantum chromodynamics at high energy. Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol.
**2012**, 33, 1–350. [Google Scholar] [CrossRef][Green Version] - Albacete, J.L.; Marquet, C. Gluon saturation and initial conditions for relativistic heavy ion collisions. Prog. Part. Nucl. Phys.
**2014**, 76, 1–42. [Google Scholar] [CrossRef][Green Version] - Blaizot, J.P. High gluon densities in heavy ion collisions. Rep. Prog. Phys.
**2017**, 80, 032301. [Google Scholar] [CrossRef] [PubMed][Green Version] - Jeon, S.; Venugopalan, R. Random walks of partons in SU(N(c)) and classical representations of color charges in QCD at small x. Phys. Rev. D
**2004**, 70, 105012. [Google Scholar] [CrossRef][Green Version] - Gotsman, E.; Levin, E.; Maor, U. CGC/saturation approach for soft interactions at high energy: A two channel model. Eur. Phys. J. C
**2015**, 75, 179. [Google Scholar] [CrossRef] - Gelis, F.; Jalilian-Marian, J. From DIS to proton nucleus collisions in the color glass condensate model. Phys. Rev. D
**2003**, 67, 074019. [Google Scholar] [CrossRef][Green Version] - Dominguez, F.; Marquet, C.; Xiao, B.W.; Yuan, F. Universality of Unintegrated Gluon Distributions at small x. Phys. Rev. D
**2011**, 83, 105005. [Google Scholar] [CrossRef][Green Version] - Balitsky, I. Operator expansion for high-energy scattering. Nucl. Phys. B
**1996**, 463, 99–160. [Google Scholar] [CrossRef][Green Version] - Kovchegov, Y.V. Small x F(2) structure function of a nucleus including multiple pomeron exchanges. Phys. Rev. D
**1999**, 60, 034008. [Google Scholar] [CrossRef][Green Version] - Lipatov, L.N. Reggeization of the Vector Meson and the Vacuum Singularity in Nonabelian Gauge Theories. Sov. J. Nucl. Phys.
**1976**, 23, 338–345. [Google Scholar] - Kuraev, E.A.; Lipatov, L.N.; Fadin, V.S. The Pomeranchuk Singularity in Nonabelian Gauge Theories. Sov. Phys. JETP
**1977**, 45, 199–204. [Google Scholar] - Balitsky, I.I.; Lipatov, L.N. The Pomeranchuk Singularity in Quantum Chromodynamics. Sov. J. Nucl. Phys.
**1978**, 28, 822–829. [Google Scholar] - Jalilian-Marian, J.; Kovner, A.; McLerran, L.D.; Weigert, H. The Intrinsic glue distribution at very small x. Phys. Rev. D
**1997**, 55, 5414–5428. [Google Scholar] [CrossRef][Green Version] - Jalilian-Marian, J.; Kovner, A.; Weigert, H. The Wilson renormalization group for low x physics: Gluon evolution at finite parton density. Phys. Rev. D
**1998**, 59, 014015. [Google Scholar] [CrossRef][Green Version] - Kovner, A.; Milhano, J.G.; Weigert, H. Relating different approaches to nonlinear QCD evolution at finite gluon density. Phys. Rev. D
**2000**, 62, 114005. [Google Scholar] [CrossRef][Green Version] - Iancu, E.; Leonidov, A.; McLerran, L.D. Nonlinear gluon evolution in the color glass condensate. 1. Nucl. Phys. A
**2001**, 692, 583–645. [Google Scholar] [CrossRef][Green Version] - Iancu, E.; Leonidov, A.; McLerran, L.D. The Renormalization group equation for the color glass condensate. Phys. Lett. B
**2001**, 510, 133–144. [Google Scholar] [CrossRef][Green Version] - Ferreiro, E.; Iancu, E.; Leonidov, A.; McLerran, L. Nonlinear gluon evolution in the color glass condensate. 2. Nucl. Phys. A
**2002**, 703, 489–538. [Google Scholar] [CrossRef][Green Version] - Weigert, H. Unitarity at small Bjorken x. Nucl. Phys. A
**2002**, 703, 823–860. [Google Scholar] [CrossRef][Green Version] - Derrick, M.; Krakauer, D.; Magill, S.; Musgrave, B.; Repond, J.; Repond, S.; Stanek, R.; Talaga, R.L.; Thron, J.; Arzarello, F.; et al. Measurement of the proton structure function F2 in e p scattering at HERA. Phys. Lett. B
**1993**, 316, 412–426. [Google Scholar] [CrossRef] - Ball, R.D.; Bertone, V.; Bonvini, M.; Marzani, S.; Rojo, J.; Rottoli, L. Parton distributions with small-x resummation: Evidence for BFKL dynamics in HERA data. Eur. Phys. J. C
**2018**, 78, 321. [Google Scholar] [CrossRef] - Hentschinski, M.; Sabio Vera, A.; Salas, C. F
_{2}and F_{L}at small x using a collinearly improved BFKL resummation. Phys. Rev. D**2013**, 87, 076005. [Google Scholar] [CrossRef][Green Version] - Golec-Biernat, K.J.; Wusthoff, M. Saturation effects in deep inelastic scattering at low Q**2 and its implications on diffraction. Phys. Rev. D
**1998**, 59, 014017. [Google Scholar] [CrossRef][Green Version] - Stasto, A.M.; Golec-Biernat, K.J.; Kwiecinski, J. Geometric scaling for the total gamma* p cross-section in the low x region. Phys. Rev. Lett.
**2001**, 86, 596–599. [Google Scholar] [CrossRef][Green Version] - Kowalski, H.; Lappi, T.; Venugopalan, R. Nuclear enhancement of universal dynamics of high parton densities. Phys. Rev. Lett.
**2008**, 100, 022303. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kowalski, H.; Teaney, D. An Impact parameter dipole saturation model. Phys. Rev. D
**2003**, 68, 114005. [Google Scholar] [CrossRef][Green Version] - Watt, G.; Kowalski, H. Impact parameter dependent colour glass condensate dipole model. Phys. Rev. D
**2008**, 78, 014016. [Google Scholar] [CrossRef][Green Version] - Rezaeian, A.H.; Siddikov, M.; Van de Klundert, M.; Venugopalan, R. Analysis of combined HERA data in the Impact-Parameter dependent Saturation model. Phys. Rev. D
**2013**, 87, 034002. [Google Scholar] [CrossRef][Green Version] - Rezaeian, A.H.; Schmidt, I. Impact-parameter dependent Color Glass Condensate dipole model and new combined HERA data. Phys. Rev. D
**2013**, 88, 074016. [Google Scholar] [CrossRef][Green Version] - Berger, J.; Stasto, A.M. Small x nonlinear evolution with impact parameter and the structure function data. Phys. Rev. D
**2011**, 84, 094022. [Google Scholar] [CrossRef][Green Version] - Bendova, D.; Cepila, J.; Contreras, J.G.; Matas, M. Solution to the Balitsky-Kovchegov equation with the collinearly improved kernel including impact-parameter dependence. Phys. Rev. D
**2019**, 100, 054015. [Google Scholar] [CrossRef][Green Version] - Albacete, J.L.; Armesto, N.; Milhano, J.G.; Quiroga-Arias, P.; Salgado, C.A. AAMQS: A non-linear QCD analysis of new HERA data at small-x including heavy quarks. Eur. Phys. J. C
**2011**, 71, 1705. [Google Scholar] [CrossRef][Green Version] - Albacete, J.L. Resummation of double collinear logs in BK evolution versus HERA data. Nucl. Phys. A
**2017**, 957, 71–84. [Google Scholar] [CrossRef][Green Version] - Iancu, E.; Madrigal, J.D.; Mueller, A.H.; Soyez, G.; Triantafyllopoulos, D.N. Collinearly-improved BK evolution meets the HERA data. Phys. Lett. B
**2015**, 750, 643–652. [Google Scholar] [CrossRef] - Ducloué, B.; Iancu, E.; Soyez, G.; Triantafyllopoulos, D.N. HERA data and collinearly-improved BK dynamics. Phys. Lett. B
**2020**, 803, 135305. [Google Scholar] [CrossRef] - Beuf, G.; Hänninen, H.; Lappi, T.; Mäntysaari, H. Color Glass Condensate at next-to-leading order meets HERA data. Phys. Rev. D
**2020**, 102, 074028. [Google Scholar] [CrossRef] - Beuf, G.; Lappi, T.; Paatelainen, R. Massive quarks in NLO dipole factorization for DIS: Longitudinal photon. arXiv
**2021**, arXiv:2103.14549. [Google Scholar] - Mäntysaari, H.; Zurita, P. In depth analysis of the combined HERA data in the dipole models with and without saturation. Phys. Rev. D
**2018**, 98, 036002. [Google Scholar] [CrossRef][Green Version] - Mäntysaari, H.; Schenke, B. Confronting impact parameter dependent JIMWLK evolution with HERA data. Phys. Rev. D
**2018**, 98, 034013. [Google Scholar] [CrossRef][Green Version] - Golec-Biernat, K.J.; Wusthoff, M. Saturation in diffractive deep inelastic scattering. Phys. Rev. D
**1999**, 60, 114023. [Google Scholar] [CrossRef][Green Version] - Bartels, J.; Golec-Biernat, K.J.; Kowalski, H. A modification of the saturation model: DGLAP evolution. Phys. Rev. D
**2002**, 66, 014001. [Google Scholar] [CrossRef][Green Version] - Marquet, C. A Unified description of diffractive deep inelastic scattering with saturation. Phys. Rev. D
**2007**, 76, 094017. [Google Scholar] [CrossRef][Green Version] - Kowalski, H.; Lappi, T.; Marquet, C.; Venugopalan, R. Nuclear enhancement and suppression of diffractive structure functions at high energies. Phys. Rev. C
**2008**, 78, 045201. [Google Scholar] [CrossRef][Green Version] - Kowalski, H.; Motyka, L.; Watt, G. Exclusive diffractive processes at HERA within the dipole picture. Phys. Rev. D
**2006**, 74, 074016. [Google Scholar] [CrossRef][Green Version] - Goncalves, V.P.; Moreira, B.D.; Navarra, F.S. Investigation of diffractive photoproduction of J/Ψ in hadronic collisions. Phys. Rev. C
**2014**, 90, 015203. [Google Scholar] [CrossRef][Green Version] - Schlichting, S.; Schenke, B. The shape of the proton at high energies. Phys. Lett. B
**2014**, 739, 313–319. [Google Scholar] [CrossRef][Green Version] - Armesto, N.; Rezaeian, A.H. Exclusive vector meson production at high energies and gluon saturation. Phys. Rev. D
**2014**, 90, 054003. [Google Scholar] [CrossRef][Green Version] - Gonçalves, V.P.; Moreira, B.D.; Navarra, F.S. Exclusive Υ photoproduction in hadronic collisions at CERN LHC energies. Phys. Lett. B
**2015**, 742, 172–177. [Google Scholar] [CrossRef][Green Version] - Arroyo Garcia, A.; Hentschinski, M.; Kutak, K. QCD evolution based evidence for the onset of gluon saturation in exclusive photo-production of vector mesons. Phys. Lett. B
**2019**, 795, 569–575. [Google Scholar] [CrossRef] - Klein, S.R.; Nystrand, J.; Seger, J.; Gorbunov, Y.; Butterworth, J. STARlight: A Monte Carlo simulation program for ultra-peripheral collisions of relativistic ions. Comput. Phys. Commun.
**2017**, 212, 258–268. [Google Scholar] [CrossRef][Green Version] - Lappi, T. Ultraperipheral collisions and low-x physics. In Proceedings of the 28th International Workshop on Deep Inelastic Scattering and Related Subjects, Brooklyn, NY, USA, 23–27 March 2020. [Google Scholar]
- Acharya, S. et al. [ALICE Collaboration] First measurement of the |t|-dependence of coherent J/ψ photonuclear production. Phys. Lett. B
**2021**, 817, 136280. [Google Scholar] [CrossRef] - Bendova, D.; Cepila, J.; Contreras, J.G.; Matas, M. Photonuclear J/ψ production at the LHC: Proton-based versus nuclear dipole scattering amplitudes. Phys. Lett. B
**2021**, 817, 136306. [Google Scholar] [CrossRef] - Guzey, V.; Strikman, M.; Zhalov, M. Accessing transverse nucleon and gluon distributions in heavy nuclei using coherent vector meson photoproduction at high energies in ion ultraperipheral collisions. Phys. Rev. C
**2017**, 95, 025204. [Google Scholar] [CrossRef] - Frankfurt, L.; Miller, G.A.; Strikman, M. Evidence for color fluctuations in hadrons from coherent nuclear diffraction. Phys. Rev. Lett.
**1993**, 71, 2859–2862. [Google Scholar] [CrossRef] [PubMed][Green Version] - Frankfurt, L.; Strikman, M.; Treleani, D.; Weiss, C. Evidence for color fluctuations in the nucleon in high-energy scattering. Phys. Rev. Lett.
**2008**, 101, 202003. [Google Scholar] [CrossRef][Green Version] - Dominguez, F.; Marquet, C.; Wu, B. On multiple scatterings of mesons in hot and cold QCD matter. Nucl. Phys. A
**2009**, 823, 99–119. [Google Scholar] [CrossRef][Green Version] - Lappi, T.; Mäntysaari, H. Incoherent diffractive J/ψ production in high energy nuclear DIS. Phys. Rev. C
**2011**, 83, 065202. [Google Scholar] [CrossRef][Green Version] - Mäntysaari, H.; Schenke, B. Evidence of strong proton shape fluctuations from incoherent diffraction. Phys. Rev. Lett.
**2016**, 117, 052301. [Google Scholar] [CrossRef] [PubMed] - Mäntysaari, H.; Schenke, B. Revealing proton shape fluctuations with incoherent diffraction at high energy. Phys. Rev. D
**2016**, 94, 034042. [Google Scholar] [CrossRef][Green Version] - Mäntysaari, H.; Schenke, B. Probing subnucleon scale fluctuations in ultraperipheral heavy ion collisions. Phys. Lett. B
**2017**, 772, 832–838. [Google Scholar] [CrossRef] - Cepila, J.; Contreras, J.; Tapia Takaki, J.D. Energy dependence of dissociative J/ψ photoproduction as a signature of gluon saturation at the LHC. Phys. Lett. B
**2017**, 766, 186–191. [Google Scholar] [CrossRef] - Cepila, J.; Contreras, J.; Krelina, M.; Tapia Takaki, J. Mass dependence of vector meson photoproduction off protons and nuclei within the energy-dependent hot-spot model. Nucl. Phys. B
**2018**, 934, 330–340. [Google Scholar] [CrossRef] - Mäntysaari, H. Review of proton and nuclear shape fluctuations at high energy. Rep. Prog. Phys.
**2020**, 83, 082201. [Google Scholar] [CrossRef] - Altinoluk, T.; Armesto, N.; Beuf, G.; Rezaeian, A.H. Diffractive Dijet Production in Deep Inelastic Scattering and Photon-Hadron Collisions in the Color Glass Condensate. Phys. Lett. B
**2016**, 758, 373–383. [Google Scholar] [CrossRef][Green Version] - Mäntysaari, H.; Mueller, N.; Schenke, B. Diffractive Dijet Production and Wigner Distributions from the Color Glass Condensate. Phys. Rev. D
**2019**, 99, 074004. [Google Scholar] [CrossRef][Green Version] - Salazar, F.; Schenke, B. Diffractive dijet production in impact parameter dependent saturation models. Phys. Rev. D
**2019**, 100, 034007. [Google Scholar] [CrossRef][Green Version] - Shi, Y.; Wang, L.; Wei, S.Y.; Xiao, B.W.; Zheng, L. Exploring collective phenomena at the electron-ion collider. Phys. Rev. D
**2021**, 103, 054017. [Google Scholar] [CrossRef] - Boer, D.; Setyadi, C. GTMD model predictions for diffractive dijet production at EIC. arXiv
**2021**, arXiv:2106.15148. [Google Scholar] - Aad, G. et al. [ATLAS Collaboration] Two-particle azimuthal correlations in photonuclear ultraperipheral Pb+Pb collisions at 5.02 TeV with ATLAS. Phys. Rev. C
**2021**, 104, 014903. [Google Scholar] [CrossRef] - Gonçalves, V.P.; Machado, M.V.T.; Moreira, B.D.; Navarra, F.S.; dos Santos, G.S. Color dipole predictions for the exclusive vector meson photoproduction in pp, pPb, and PbPb collisions at run 2 LHC energies. Phys. Rev. D
**2017**, 96, 094027. [Google Scholar] [CrossRef][Green Version] - Lappi, T.; Mäntysaari, H.; Penttala, J. Relativistic corrections to the vector meson light front wave function. Phys. Rev. D
**2020**, 102, 054020. [Google Scholar] [CrossRef] - Frankfurt, L.; Guzey, V.; Strikman, M. Leading Twist Nuclear Shadowing Phenomena in Hard Processes with Nuclei. Phys. Rep.
**2012**, 512, 255–393. [Google Scholar] [CrossRef][Green Version] - Guzey, V.; Kryshen, E.; Strikman, M.; Zhalov, M. Evidence for nuclear gluon shadowing from the ALICE measurements of PbPb ultraperipheral exclusive J/ψ production. Phys. Lett. B
**2013**, 726, 290–295. [Google Scholar] [CrossRef][Green Version] - Guzey, V.; Zhalov, M. Exclusive J/ψ production in ultraperipheral collisions at the LHC: Constrains on the gluon distributions in the proton and nuclei. J. High Energy Phys.
**2013**, 10, 207. [Google Scholar] [CrossRef][Green Version] - Guzey, V.; Kryshen, E.; Zhalov, M. Coherent photoproduction of vector mesons in ultraperipheral heavy ion collisions: Update for run 2 at the CERN Large Hadron Collider. Phys. Rev. C
**2016**, 93, 055206. [Google Scholar] [CrossRef][Green Version] - Guzey, V.; Klasen, M. Diffractive dijet photoproduction in ultraperipheral collisions at the LHC in next-to-leading order QCD. J. High Energy Phys.
**2016**, 4, 158. [Google Scholar] [CrossRef][Green Version] - Kharzeev, D.; Levin, E.; McLerran, L. Jet azimuthal correlations and parton saturation in the color glass condensate. Nucl. Phys. A
**2005**, 748, 627–640. [Google Scholar] [CrossRef][Green Version] - Kovchegov, Y.V.; Mueller, A.H. Gluon production in current nucleus and nucleon - nucleus collisions in a quasiclassical approximation. Nucl. Phys. B
**1998**, 529, 451–479. [Google Scholar] [CrossRef][Green Version] - Dumitru, A.; Jalilian-Marian, J. Scattering of gluons from the color glass condensate. Phys. Lett. B
**2002**, 547, 15–20. [Google Scholar] [CrossRef][Green Version] - Kovner, A.; Wiedemann, U.A. Eikonal evolution and gluon radiation. Phys. Rev. D
**2001**, 64, 114002. [Google Scholar] [CrossRef][Green Version] - Dumitru, A.; Jalilian-Marian, J. Forward quark jets from protons shattering the colored glass. Phys. Rev. Lett.
**2002**, 89, 022301. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kharzeev, D.; Levin, E.; McLerran, L. Parton saturation and N(part) scaling of semihard processes in QCD. Phys. Lett. B
**2003**, 561, 93–101. [Google Scholar] [CrossRef][Green Version] - Kharzeev, D.; Kovchegov, Y.V.; Tuchin, K. Cronin effect and high p(T) suppression in pA collisions. Phys. Rev. D
**2003**, 68, 094013. [Google Scholar] [CrossRef][Green Version] - Arsene, I. et al. [BRAHMS Collaboration] 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.
**2004**, 93, 242303. [Google Scholar] [CrossRef][Green Version] - Cronin, J.W.; Frisch, H.J.; Shochet, M.J.; Boymond, J.P.; Mermod, R.; Piroue, P.A.; Sumner, R.L. Production of hadrons with large transverse momentum at 200, 300, and 400 GeV. Phys. Rev. D
**1975**, 11, 3105–3123. [Google Scholar] [CrossRef][Green Version] - Albacete, J.L.; Armesto, N.; Kovner, A.; Salgado, C.A.; Wiedemann, U.A. Energy dependence of the Cronin effect from nonlinear QCD evolution. Phys. Rev. Lett.
**2004**, 92, 082001. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kharzeev, D.; Kovchegov, Y.V.; Tuchin, K. Nuclear modification factor in d+Au collisions: Onset of suppression in the color glass condensate. Phys. Lett. B
**2004**, 599, 23–31. [Google Scholar] [CrossRef][Green Version] - Rezaeian, A.H. CGC predictions for p+A collisions at the LHC and signature of QCD saturation. Phys. Lett. B
**2013**, 718, 1058–1069. [Google Scholar] [CrossRef][Green Version] - Albacete, J.L.; Dumitru, A.; Fujii, H.; Nara, Y. CGC predictions for p + Pb collisions at the LHC. Nucl. Phys. A
**2013**, 897, 1–27. [Google Scholar] [CrossRef][Green Version] - Lappi, T.; Mäntysaari, H. Single inclusive particle production at high energy from HERA data to proton-nucleus collisions. Phys. Rev. D
**2013**, 88, 114020. [Google Scholar] [CrossRef][Green Version] - Ducloué, B.; Lappi, T.; Mäntysaari, H. Forward J/ψ and D meson nuclear suppression at the LHC. Nucl. Part. Phys. Proc.
**2017**, 289–290, 309–312. [Google Scholar] [CrossRef] - Mäntysaari, H.; Paukkunen, H. Saturation and forward jets in proton-lead collisions at the LHC. Phys. Rev. D
**2019**, 100, 114029. [Google Scholar] [CrossRef][Green Version] - Acharya, S. et al. [ALICE Collaboration] Neutral pion and η meson production in p-Pb collisions at $\sqrt{{s}_{\mathrm{NN}}}$ = 5.02 TeV. Eur. Phys. J. C
**2018**, 78, 624. [Google Scholar] [CrossRef][Green Version] - Eskola, K.J.; Helenius, I.; Paakkinen, P.; Paukkunen, H. A QCD analysis of LHCb D-meson data in p+Pb collisions. J. High Energy Phys.
**2020**, 5, 037. [Google Scholar] [CrossRef] - Gelis, F.; Jalilian-Marian, J. Photon production in high-energy proton nucleus collisions. Phys. Rev. D
**2002**, 66, 014021. [Google Scholar] [CrossRef][Green Version] - Jalilian-Marian, J. Photon + hadron production in high energy deuteron (proton)-nucleus collisions. Nucl. Phys. A
**2006**, 770, 210–220. [Google Scholar] [CrossRef][Green Version] - Helenius, I.; Eskola, K.J.; Paukkunen, H. Probing the small-x nuclear gluon distributions with isolated photons at forward rapidities in p+Pb collisions at the LHC. J. High Energy Phys.
**2014**, 9, 138. [Google Scholar] [CrossRef][Green Version] - Jalilian-Marian, J.; Rezaeian, A.H. Prompt photon production and photon-hadron correlations at RHIC and the LHC from the Color Glass Condensate. Phys. Rev. D
**2012**, 86, 034016. [Google Scholar] [CrossRef][Green Version] - Benic, S.; Fukushima, K.; Garcia-Montero, O.; Venugopalan, R. Probing gluon saturation with next-to-leading order photon production at central rapidities in proton-nucleus collisions. J. High Energy Phys.
**2017**, 1, 115. [Google Scholar] [CrossRef][Green Version] - Ducloue, B.; Lappi, T.; Mäntysaari, H. Isolated photon production in proton-nucleus collisions at forward rapidity. Phys. Rev. D
**2018**, 97, 054023. [Google Scholar] [CrossRef][Green Version] - Golec-Biernat, K.; Motyka, L.; Stebel, T. Prompt photon production in proton collisions as a probe of parton scattering in high energy limit. Phys. Rev. D
**2021**, 103, 034013. [Google Scholar] [CrossRef] - Sampaio dos Santos, G.; Gil da Silveira, G.; Machado, M.V.T. Prompt photon production in high-energy pA collisions at forward rapidity. Phys. Rev. C
**2020**, 102, 054901. [Google Scholar] [CrossRef] - Acharya, S. et al. [ALICE Collaboration] Direct photon production at low transverse momentum in proton-proton collisions at $\sqrt{\mathbf{s}}$ =
**2.76**and 8 TeV. Phys. Rev. C**2019**, 99, 024912. [Google Scholar] [CrossRef][Green Version] - Letter of Intent: A Forward Calorimeter (FoCal) in the ALICE Experiment. Available online: https://cds.cern.ch/record/2719928 (accessed on 20 August 2021).
- Boettcher, T. Direct photon production at LHCb. Nucl. Phys. A
**2019**, 982, 251–254. [Google Scholar] [CrossRef] - Watanabe, K. Quarkonium production at collider energies in Small-x formalism. Few Body Syst.
**2017**, 58, 134. [Google Scholar] [CrossRef][Green Version] - Kharzeev, D.; Tuchin, K. Signatures of the color glass condensate in J/psi production off nuclear targets. Nucl. Phys. A
**2006**, 770, 40–56. [Google Scholar] [CrossRef][Green Version] - Kharzeev, D.; Thews, R.L. Quarkonium formation time in a model independent approach. Phys. Rev. C
**1999**, 60, 041901. [Google Scholar] [CrossRef][Green Version] - Bodwin, G.T.; Braaten, E.; Lepage, G.P. Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium. Phys. Rev. D
**1995**, 51, 1125–1171. [Google Scholar] [CrossRef] [PubMed][Green Version] - Ma, Y.Q.; Wang, K.; Chao, K.T. A complete NLO calculation of the J/ψ and ψ′ production at hadron colliders. Phys. Rev. D
**2011**, 84, 114001. [Google Scholar] [CrossRef][Green Version] - Ma, Y.Q.; Venugopalan, R. Comprehensive Description of J/ψ Production in Proton-Proton Collisions at Collider Energies. Phys. Rev. Lett.
**2014**, 113, 192301. [Google Scholar] [CrossRef][Green Version] - Butenschoen, M.; Kniehl, B.A. Reconciling J/ψ production at HERA, RHIC, Tevatron, and LHC with NRQCD factorization at next-to-leading order. Phys. Rev. Lett.
**2011**, 106, 022003. [Google Scholar] [CrossRef][Green Version] - Acharya, S. et al. [ALCE Collaboration] Energy dependence of forward-rapidity J/ψ and ψ(2S) production in pp collisions at the LHC. Eur. Phys. J. C
**2017**, 77, 392. [Google Scholar] [CrossRef][Green Version] - Bodwin, G.T.; Braaten, E.; Lee, J. Comparison of the color-evaporation model and the NRQCD factorization approach in charmonium production. Phys. Rev. D
**2005**, 72, 014004. [Google Scholar] [CrossRef][Green Version] - Adam, J. et al. [STAR Collaboration] Measurements of the transverse-momentum-dependent cross sections of J/ψ production at mid-rapidity in proton+proton collisions at $\sqrt{s}$ = 510 and 500 GeV with the STAR detector. Phys. Rev. D
**2019**, 100, 052009. [Google Scholar] [CrossRef][Green Version] - Eskola, K.J.; Paukkunen, H.; Salgado, C.A. EPS09: A New Generation of NLO and LO Nuclear Parton Distribution Functions. J. High Energy Phys.
**2009**, 4, 065. [Google Scholar] [CrossRef][Green Version] - Accardi, A.; Gyulassy, M. Cronin effect versus geometrical shadowing in d + Au collisions at RHIC. Phys. Lett. B
**2004**, 586, 244–253. [Google Scholar] [CrossRef][Green Version] - Kopeliovich, B.Z.; Nemchik, J.; Potashnikova, I.K.; Johnson, M.B.; Schmidt, I. Breakdown of QCD factorization at large Feynman x. Phys. Rev. C
**2005**, 72, 054606. [Google Scholar] [CrossRef][Green Version] - Armesto, N. Small collision systems: Theory overview on cold nuclear matter effects. Eur. Phys. J. Web Conf.
**2018**, 171, 11001. [Google Scholar] [CrossRef][Green Version] - Marquet, C. Forward inclusive dijet production and azimuthal correlations in p(A) collisions. Nucl. Phys. A
**2007**, 796, 41–60. [Google Scholar] [CrossRef][Green Version] - Albacete, J.L.; Marquet, C. Azimuthal correlations of forward di-hadrons in d+Au collisions at RHIC in the Color Glass Condensate. Phys. Rev. Lett.
**2010**, 105, 162301. [Google Scholar] [CrossRef] [PubMed][Green Version] - Lappi, T.; Mäntysaari, H. Forward dihadron correlations in deuteron-gold collisions with the Gaussian approximation of JIMWLK. Nucl. Phys. A
**2013**, 908, 51–72. [Google Scholar] [CrossRef][Green Version] - Strikman, M.; Vogelsang, W. Multiple parton interactions and forward double pion production in pp and dA scattering. Phys. Rev. D
**2011**, 83, 034029. [Google Scholar] [CrossRef][Green Version] - Chu, X. Di-Hadron Correlations in p+p, p+Au and p+Al Collisions at STAR. Initial Stages 2021. Available online: http://cds.cern.ch/record/2749297 (accessed on 20 August 2021).
- Adare, A. et al. [PHENIX Collaboration] Suppression of back-to-back hadron pairs at forward rapidity in d+Au Collisions at $\sqrt{{s}_{\mathrm{NN}}}$ = 200 GeV. Phys. Rev. Lett.
**2011**, 107, 172301. [Google Scholar] [CrossRef][Green Version] - Lappi, T.; Mantysaari, H. Forward dihadron correlations in the Gaussian approximation of JIMWLK. Nucl. Phys. A
**2013**, 910–911, 498–501. [Google Scholar] [CrossRef][Green Version] - Mueller, A.H.; Xiao, B.W.; Yuan, F. Sudakov double logarithms resummation in hard processes in the small-x saturation formalism. Phys. Rev. D
**2013**, 88, 114010. [Google Scholar] [CrossRef][Green Version] - Albacete, J.L.; Giacalone, G.; Marquet, C.; Matas, M. Forward dihadron back-to-back correlations in pA collisions. Phys. Rev. D
**2019**, 99, 014002. [Google Scholar] [CrossRef][Green Version] - Stasto, A.; Wei, S.Y.; Xiao, B.W.; Yuan, F. On the Dihadron Angular Correlations in Forward pA collisions. Phys. Lett. B
**2018**, 784, 301–306. [Google Scholar] [CrossRef] - Kutak, K.; Sapeta, S. Gluon saturation in dijet production in p-Pb collisions at Large Hadron Collider. Phys. Rev. D
**2012**, 86, 094043. [Google Scholar] [CrossRef][Green Version] - van Hameren, A.; Kotko, P.; Kutak, K.; Marquet, C.; Sapeta, S. Saturation effects in forward-forward dijet production in p+Pb collisions. Phys. Rev. D
**2014**, 89, 094014. [Google Scholar] [CrossRef][Green Version] - van Hameren, A.; Kotko, P.; Kutak, K.; Sapeta, S. Small-x dynamics in forward-central dijet decorrelations at the LHC. Phys. Lett. B
**2014**, 737, 335–340. [Google Scholar] [CrossRef] - Kotko, P.; Kutak, K.; Marquet, C.; Petreska, E.; Sapeta, S.; van Hameren, A. Improved TMD factorization for forward dijet production in dilute-dense hadronic collisions. J. High Energy Phys.
**2015**, 9, 106. [Google Scholar] [CrossRef][Green Version] - van Hameren, A.; Kotko, P.; Kutak, K.; Marquet, C.; Petreska, E.; Sapeta, S. Forward di-jet production in p+Pb collisions in the small-x improved TMD factorization framework. J. High Energy Phys.
**2016**, 12, 034, Erratum in**2019**, 2, 158. [Google Scholar] [CrossRef][Green Version] - van Hameren, A.; Kotko, P.; Kutak, K.; Sapeta, S. Broadening and saturation effects in dijet azimuthal correlations in p-p and p-Pb collisions at $\sqrt{\mathbf{s}}$ = 5.02 TeV. Phys. Lett. B
**2019**, 795, 511–515. [Google Scholar] [CrossRef] - Kotko, P.; Kutak, K.; Sapeta, S.; Stasto, A.M.; Strikman, M. Estimating nonlinear effects in forward dijet production in ultra-peripheral heavy ion collisions at the LHC. Eur. Phys. J. C
**2017**, 77, 353. [Google Scholar] [CrossRef][Green Version] - Rezaeian, A.H. Semi-inclusive photon-hadron production in pp and pA collisions at RHIC and LHC. Phys. Rev. D
**2012**, 86, 094016. [Google Scholar] [CrossRef][Green Version] - Rezaeian, A.H. Photon-jet ridge at RHIC and the LHC. Phys. Rev. D
**2016**, 93, 094030. [Google Scholar] [CrossRef][Green Version] - Benic, S.; Dumitru, A. Prompt photon—Jet angular correlations at central rapidities in p+A collisions. Phys. Rev. D
**2018**, 97, 014012. [Google Scholar] [CrossRef][Green Version] - Goncalves, V.P.; Lima, Y.; Pasechnik, R.; Šumbera, M. Isolated photon production and pion-photon correlations in high-energy pp and pA collisions. Phys. Rev. D
**2020**, 101, 094019. [Google Scholar] [CrossRef] - Mueller, A.H.; Xiao, B.W.; Yuan, F. Sudakov Resummation in Small-x Saturation Formalism. Phys. Rev. Lett.
**2013**, 110, 082301. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kang, Z.B.; Vitev, I.; Xing, H. Dihadron momentum imbalance and correlations in d+Au collisions. Phys. Rev. D
**2012**, 85, 054024. [Google Scholar] [CrossRef][Green Version] - Xing, H.; Kang, Z.B.; Vitev, I.; Wang, E. Transverse momentum imbalance of back-to-back particle production in p+A and e+A collisions. Phys. Rev. D
**2012**, 86, 094010. [Google Scholar] [CrossRef][Green Version] - Armesto, N.; Gülhan, D.C.; Milhano, J.G. Kinematic bias on centrality selection of jet events in pPb collisions at the LHC. Phys. Lett. B
**2015**, 747, 441–445. [Google Scholar] [CrossRef] - Acharya, S. et al. [ALICE Collaboration] Constraints on jet quenching in p-Pb collisions at $\sqrt{{s}_{\mathrm{NN}}}$ = 5.02 TeV measured by the event-activity dependence of semi-inclusive hadron-jet distributions. Phys. Lett. B
**2018**, 783, 95–113. [Google Scholar] [CrossRef] - Connors, M.; Nattrass, C.; Reed, R.; Salur, S. Jet measurements in heavy ion physics. Rev. Mod. Phys.
**2018**, 90, 025005. [Google Scholar] [CrossRef][Green Version] - Albacete, J.L.; Arleo, F.; Barnaföldi, G.G.; Bíró, G.; Enterria, D.D.; Ducloué, B.; Eskola, K.J.; Ferreiro, E.G.; Gyulassy, M.; Harangozó, S.M.; et al. Predictions for Cold Nuclear Matter Effects in p+Pb Collisions at $\sqrt{{s}_{\mathrm{NN}}}$ =8.16 TeV. Nucl. Phys. A
**2018**, 972, 18–85. [Google Scholar] [CrossRef][Green Version] - Aamodt, K. et al. [The ALICE Collaboration] Charged-particle multiplicity measurement in proton-proton collisions at $\sqrt{s}$ = 7 TeV with ALICE at LHC. Eur. Phys. J. C
**2010**, 68, 345–354. [Google Scholar] [CrossRef][Green Version] - Chatrchyan, S. et al. [The CMS Collaboration] Study of the Inclusive Production of Charged Pions, Kaons, and Protons in pp Collisions at $\sqrt{s}$ = 0.9, 2.76, and 7 TeV. Eur. Phys. J. C
**2012**, 72, 2164. [Google Scholar] [CrossRef][Green Version] - Schenke, B.; Tribedy, P.; Venugopalan, R. Fluctuating Glasma initial conditions and flow in heavy ion collisions. Phys. Rev. Lett.
**2012**, 108, 252301. [Google Scholar] [CrossRef] [PubMed] - Schenke, B.; Schlichting, S.; Tribedy, P.; Venugopalan, R. Mass ordering of spectra from fragmentation of saturated gluon states in high multiplicity proton-proton collisions. Phys. Rev. Lett.
**2016**, 117, 162301. [Google Scholar] [CrossRef] [PubMed] - Khatun, A. J/ψ production as a function of charged-particle multiplicity in pp collisions at $\sqrt{s}$ = 5.02 TeV with ALICE. Springer Proc. Phys.
**2021**, 261, 599–603. [Google Scholar] [CrossRef] - Abelev, B. et al. [ALICE Collaboration] J/ψ Production as a Function of Charged Particle Multiplicity in pp Collisions at $\sqrt{s}$ = 7 TeV. Phys. Lett. B
**2012**, 712, 165–175. [Google Scholar] [CrossRef] - Thakur, D. J/ψ production as a function of charged-particle multiplicity with ALICE at the LHC. In Conference on Flavor Physics and CP Violation; Springer: Cham, Switzerland, 2018; pp. 217–221. [Google Scholar] [CrossRef][Green Version]
- Acharya, S. et al. [ALICE Collaboration] Multiplicity dependence of J/ψ production at midrapidity in pp collisions at $\sqrt{s}$ = 13 TeV. Phys. Lett. B
**2020**, 810, 135758. [Google Scholar] [CrossRef] - Levin, E.; Schmidt, I.; Siddikov, M. Multiplicity dependence of quarkonia production in the CGC approach. Eur. Phys. J. C
**2020**, 80, 560. [Google Scholar] [CrossRef] - Department of Energy (USA). U.S. Department of Energy Selects Brookhaven National Laboratory to Host Major New Nuclear Physics Facility. Available online: https://www.energy.gov/articles/us-department-energy-selects-brookhaven-national-laboratory-host-major-new-nuclear-physics (accessed on 22 April 2020).
- Boer, D.; Diehl, M.; Milner, R.; Venugopalan, R.; Vogelsang, W.; Accardi, A.; Aschenauer, E.; Burkardt, M.; Ent, R.; Guzey, V.; et al. Gluons and the quark sea at high energies: Distributions, polarization, tomography. arXiv
**2011**, arXiv:1108.1713. [Google Scholar] - Accardi, A.; Albacete, J.L.; Anselmino, M.; Armesto, N.; Aschenauer, E.C.; Bacchetta, A.; Boer, D.; Brooks, W.K.; Burton, T.; Chang, N.-B.; et al. Electron Ion Collider: The Next QCD Frontier: Understanding the glue that binds us all. Eur. Phys. J. A
**2016**, 52, 268. [Google Scholar] [CrossRef][Green Version] - Aschenauer, E.C.; Fazio, S.; Lee, J.H.; Mäntysaari, H.; Page, B.S.; Schenke, B.; Ullrich, T.; Venugopalan, R.; Zurita, P. The electron–ion collider: Assessing the energy dependence of key measurements. Rep. Prog. Phys.
**2019**, 82, 024301. [Google Scholar] [CrossRef][Green Version] - Abdul Khalek, R.; Accardi, A.; Adam, J.; Adamiak, D.; Akers, W.; Albaladejo, M.; Al-bataineh, A.; Alexeev, M.G.; Ameli, F.; Antonioli, P.; et al. Science Requirements and Detector Concepts for the Electron-Ion Collider: EIC Yellow Report. arXiv
**2021**, arXiv:2103.05419. [Google Scholar] - Agostini, P.; Aksakal, H.; Alan, H.; Alekhin, S.; Allport, P.P.; Andari, N.; Andre, K.D.J.; Angal-Kalinin, D.; Antusch, S.; Aperio Bella, L.; et al. The Large Hadron-Electron Collider at the HL-LHC. arXiv
**2020**, arXiv:2007.14491. [Google Scholar] - Goncalves, V.P.; Martins, D.E.; Sena, C.R. Exclusive vector meson production in electron—Ion collisions at the EIC, LHeC and FCC–eh. Nucl. Phys. A
**2020**, 1004, 122055. [Google Scholar] [CrossRef] - Bartels, J.; Golec-Biernat, K.; Motyka, L. Twist expansion of the nucleon structure functions, F(2) and F(L), in the DGLAP improved saturation model. Phys. Rev. D
**2010**, 81, 054017. [Google Scholar] [CrossRef][Green Version] - Marquet, C.; Moldes, M.R.; Zurita, P. Unveiling saturation effects from nuclear structure function measurements at the EIC. Phys. Lett. B
**2017**, 772, 607–614. [Google Scholar] [CrossRef] - Toll, T.; Ullrich, T. Exclusive diffractive processes in electron-ion collisions. Phys. Rev. C
**2013**, 87, 024913. [Google Scholar] [CrossRef][Green Version] - Toll, T.; Ullrich, T. The dipole model Monte Carlo generator Sartre 1. Comput. Phys. Commun.
**2014**, 185, 1835–1853. [Google Scholar] [CrossRef][Green Version] - Miller, G.A.; Sievert, M.D.; Venugopalan, R. Probing short-range nucleon-nucleon interactions with an Electron-Ion Collider. Phys. Rev. C
**2016**, 93, 045202. [Google Scholar] [CrossRef][Green Version] - Mäntysaari, H.; Schenke, B. Accessing the gluonic structure of light nuclei at a future electron-ion collider. Phys. Rev. C
**2020**, 101, 015203. [Google Scholar] [CrossRef][Green Version] - Tu, Z.; Jentsch, A.; Baker, M.; Zheng, L.; Lee, J.H.; Venugopalan, R.; Hen, O.; Higinbotham, D.; Aschenauer, E.C.; Ullrich, T. Probing short-range correlations in the deuteron via incoherent diffractive J/ψ production with spectator tagging at the EIC. Phys. Lett. B
**2020**, 811, 135877. [Google Scholar] [CrossRef] - Kolbé, I.; Roy, K.; Salazar, F.; Schenke, B.; Venugopalan, R. Inclusive prompt photon-jet correlations as a probe of gluon saturation in electron-nucleus scattering at small x. J. High Energy Phys.
**2021**, 1, 52. [Google Scholar] [CrossRef] - Petreska, E. TMD gluon distributions at small x in the CGC theory. Int. J. Mod. Phys. E
**2018**, 27, 1830003. [Google Scholar] [CrossRef][Green Version] - Zheng, L.; Aschenauer, E.C.; Lee, J.H.; Xiao, B.W. Probing Gluon Saturation through Dihadron Correlations at an Electron-Ion Collider. Phys. Rev. D
**2014**, 89, 074037. [Google Scholar] [CrossRef][Green Version] - van Hameren, A.; Kotko, P.; Kutak, K.; Sapeta, S.; Żarów, E. Probing gluon number density with electron-dijet correlations at EIC. Eur. Phys. J. C
**2021**, 81, 741. [Google Scholar] [CrossRef] - Altinoluk, T.; Boussarie, R.; Kotko, P. Interplay of the CGC and TMD frameworks to all orders in kinematic twist. J. High Energy Phys.
**2019**, 5, 156. [Google Scholar] [CrossRef][Green Version] - Altinoluk, T.; Marquet, C.; Taels, P. Low-x improved TMD approach to the lepto- and hadroproduction of a heavy-quark pair. arXiv
**2021**, arXiv:2103.14495v1. [Google Scholar] - Boussarie, R.; Mäntysaari, H.; Salazar, F.; Schenke, B. The importance of kinematic twists and genuine saturation effects in dijet production at the Electron-Ion Collider. arXiv
**2021**, arXiv:2106.11301. [Google Scholar] - Marquet, C.; Xiao, B.W.; Yuan, F. Semi-inclusive Deep Inelastic Scattering at small x. Phys. Lett. B
**2009**, 682, 207–211. [Google Scholar] [CrossRef][Green Version] - Iancu, E.; Mueller, A.H.; Triantafyllopoulos, D.N.; Wei, S.Y. Saturation effects in SIDIS at very forward rapidities. J. High Energy Phys.
**2021**, 2021, 196. [Google Scholar] [CrossRef] - Kovchegov, Y.V.; Weigert, H. Triumvirate of Running Couplings in Small-x Evolution. Nucl. Phys.
**2007**, A784, 188–226. [Google Scholar] [CrossRef][Green Version] - Balitsky, I. Quark contribution to the small-x evolution of color dipole. Phys. Rev. D
**2007**, 75, 014001. [Google Scholar] [CrossRef][Green Version] - Albacete, J.L.; Kovchegov, Y.V. Solving high energy evolution equation including running coupling corrections. Phys. Rev. D
**2007**, 75, 125021. [Google Scholar] [CrossRef][Green Version] - Lappi, T.; Mäntysaari, H. On the running coupling in the JIMWLK equation. Eur. Phys. J. C
**2013**, 73, 2307. [Google Scholar] [CrossRef][Green Version] - Balitsky, I.; Chirilli, G.A. Next-to-leading order evolution of color dipoles. Phys. Rev. D
**2008**, 77, 014019. [Google Scholar] [CrossRef][Green Version] - Balitsky, I.; Chirilli, G.A. Rapidity evolution of Wilson lines at the next-to-leading order. Phys. Rev. D
**2013**, 88, 111501. [Google Scholar] [CrossRef][Green Version] - Kovner, A.; Lublinsky, M.; Mulian, Y. Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner evolution at next to leading order. Phys. Rev. D
**2014**, 89, 061704. [Google Scholar] [CrossRef][Green Version] - Kovner, A.; Lublinsky, M.; Mulian, Y. NLO JIMWLK evolution unabridged. J. High Energy Phys.
**2014**, 8, 114. [Google Scholar] [CrossRef][Green Version] - Lublinsky, M.; Mulian, Y. High Energy QCD at NLO: From light-cone wave function to JIMWLK evolution. J. High Energy Phys.
**2017**, 5, 097. [Google Scholar] [CrossRef][Green Version] - Lappi, T.; Mäntysaari, H. Direct numerical solution of the coordinate space Balitsky-Kovchegov equation at next to leading order. Phys. Rev. D
**2015**, 91, 074016. [Google Scholar] [CrossRef][Green Version] - Beuf, G. Improving the kinematics for low-x QCD evolution equations in coordinate space. Phys. Rev. D
**2014**, 89, 074039. [Google Scholar] [CrossRef][Green Version] - Iancu, E.; Madrigal, J.; Mueller, A.; Soyez, G.; Triantafyllopoulos, D. Resumming double logarithms in the QCD evolution of color dipoles. Phys. Lett. B
**2015**, 744, 293–302. [Google Scholar] [CrossRef] - Ducloué, B.; Iancu, E.; Mueller, A.; Soyez, G.; Triantafyllopoulos, D. Non-linear evolution in QCD at high-energy beyond leading order. J. High Energy Phys.
**2019**, 4, 081. [Google Scholar] [CrossRef][Green Version] - Lappi, T.; Mäntysaari, H. Next-to-leading order Balitsky-Kovchegov equation with resummation. Phys. Rev. D
**2016**, 93, 094004. [Google Scholar] [CrossRef][Green Version] - Korcyl, P. Numerical package for solving the JIMWLK evolution equation in C++. arXiv
**2020**, arXiv:2009.02045. [Google Scholar] - Cali, S.; Cichy, K.; Korcyl, P.; Kotko, P.; Kutak, K.; Marquet, C. On systematic effects in the numerical solutions of the JIMWLK equation. arXiv
**2021**, arXiv:2104.14254. [Google Scholar] - Hatta, Y.; Iancu, E. Collinearly improved JIMWLK evolution in Langevin form. J. High Energy Phys.
**2016**, 8, 083. [Google Scholar] [CrossRef] - Balitsky, I.; Chirilli, G.A. Photon impact factor and k
_{T}-factorization for DIS in the next-to-leading order. Phys. Rev. D**2013**, 87, 014013. [Google Scholar] [CrossRef][Green Version] - Beuf, G. NLO corrections for the dipole factorization of DIS structure functions at low x. Phys. Rev. D
**2012**, 85, 034039. [Google Scholar] [CrossRef][Green Version] - Beuf, G. Dipole factorization for DIS at NLO: Loop correction to the ${\gamma}_{T,L}^{\ast}\to $ light-front wave functions. Phys. Rev. D
**2016**, 94, 054016. [Google Scholar] [CrossRef][Green Version] - Beuf, G. Dipole factorization for DIS at NLO: Combining the $q\overline{q}$ and $q\overline{q}g$ contributions. Phys. Rev. D
**2017**, 96, 074033. [Google Scholar] [CrossRef][Green Version] - Lappi, T.; Paatelainen, R. The one loop gluon emission light cone wave function. Ann. Phys.
**2017**, 379, 34–66. [Google Scholar] [CrossRef][Green Version] - Hänninen, H.; Lappi, T.; Paatelainen, R. One-loop corrections to light cone wave functions: The dipole picture DIS cross section. Ann. Phys.
**2018**, 393, 358–412. [Google Scholar] [CrossRef][Green Version] - Ducloué, B.; Hänninen, H.; Lappi, T.; Zhu, Y. Deep inelastic scattering in the dipole picture at next-to-leading order. Phys. Rev. D
**2017**, 96, 094017. [Google Scholar] [CrossRef][Green Version] - Boussarie, R.; Grabovsky, A.V.; Ivanov, D.Y.; Szymanowski, L.; Wallon, S. Next-to-Leading Order Computation of Exclusive Diffractive Light Vector Meson Production in a Saturation Framework. Phys. Rev. Lett.
**2017**, 119, 072002. [Google Scholar] [CrossRef] [PubMed][Green Version] - Boussarie, R.; Grabovsky, A.V.; Szymanowski, L.; Wallon, S. On the one loop γ
^{(∗)}→$q\overline{q}$ impact factor and the exclusive diffractive cross sections for the production of two or three jets. J. High Energy Phys.**2016**, 11, 149. [Google Scholar] [CrossRef] - Boussarie, R.; Grabovsky, A.V.; Szymanowski, L.; Wallon, S. Towards a complete next-to-logarithmic description of forward exclusive diffractive dijet electroproduction at HERA: Real corrections. Phys. Rev. D
**2019**, 100, 074020. [Google Scholar] [CrossRef][Green Version] - Mäntysaari, H.; Penttala, J. Exclusive heavy vector meson production at next-to-leading order in the dipole picture. arXiv
**2021**, arXiv:2104.02349. [Google Scholar] - Roy, K.; Venugopalan, R. NLO impact factor for inclusive photon+dijet production in e+A DIS at small x. Phys. Rev. D
**2020**, 101, 034028. [Google Scholar] [CrossRef][Green Version] - Chirilli, G.A.; Xiao, B.W.; Yuan, F. One-loop Factorization for Inclusive Hadron Production in pA Collisions in the Saturation Formalism. Phys. Rev. Lett.
**2012**, 108, 122301. [Google Scholar] [CrossRef][Green Version] - Chirilli, G.A.; Xiao, B.W.; Yuan, F. Inclusive Hadron Productions in pA Collisions. Phys. Rev. D
**2012**, 86, 054005. [Google Scholar] [CrossRef][Green Version] - Altinoluk, T.; Armesto, N.; Beuf, G.; Kovner, A.; Lublinsky, M. Single-inclusive particle production in proton-nucleus collisions at next-to-leading order in the hybrid formalism. Phys. Rev. D
**2015**, 91, 094016. [Google Scholar] [CrossRef][Green Version] - Ducloué, B.; Lappi, T.; Zhu, Y. Single inclusive forward hadron production at next-to-leading order. Phys. Rev. D
**2016**, 93, 114016. [Google Scholar] [CrossRef][Green Version] - Iancu, E.; Mulian, Y. Forward dijets in proton-nucleus collisions at next-to-leading order: The real corrections. J. High Energy Phys.
**2021**, 3, 005. [Google Scholar] [CrossRef] - Caucal, P.; Salazar, F.; Venugopalan, R. Dijet impact factor in DIS at next-to-leading order in the Color Glass Condensate. arXiv
**2021**, arXiv:2108.06347. [Google Scholar] - Stasto, A.M.; Xiao, B.W.; Zaslavsky, D. Towards the Test of Saturation Physics Beyond Leading Logarithm. Phys. Rev. Lett.
**2014**, 112, 012302. [Google Scholar] [CrossRef] [PubMed] - Ducloué, B.; Lappi, T.; Zhu, Y. Implementation of NLO high energy factorization in single inclusive forward hadron production. Phys. Rev. D
**2017**, 95, 114007. [Google Scholar] [CrossRef][Green Version] - Ducloué, B.; Iancu, E.; Lappi, T.; Mueller, A.H.; Soyez, G.; Triantafyllopoulos, D.N.; Zhu, Y. Use of a running coupling in the NLO calculation of forward hadron production. Phys. Rev. D
**2018**, 97, 054020. [Google Scholar] [CrossRef][Green Version] - Liu, H.Y.; Kang, Z.B.; Liu, X. Threshold resummation for hadron production in the small-x region. Phys. Rev. D
**2020**, 102, 051502. [Google Scholar] [CrossRef] - Dumitru, A.; Jalilian-Marian, J.; Lappi, T.; Schenke, B.; Venugopalan, R. Renormalization group evolution of multi-gluon correlators in high energy QCD. Phys. Lett. B
**2011**, 706, 219–224. [Google Scholar] [CrossRef][Green Version] - Iancu, E.; Triantafyllopoulos, D.N. JIMWLK evolution in the Gaussian approximation. J. High Energy Phys.
**2012**, 4, 025. [Google Scholar] [CrossRef][Green Version] - Dumitru, A.; Petreska, E. Initial conditions for dipole evolution beyond the McLerran-Venugopalan model. Nucl. Phys. A
**2012**, 879, 59–76. [Google Scholar] [CrossRef][Green Version] - Dumitru, A.; Jalilian-Marian, J.; Petreska, E. Two-gluon correlations and initial conditions for small-x evolution. Phys. Rev. D
**2011**, 84, 014018. [Google Scholar] [CrossRef][Green Version] - Giannini, A.V.; Nara, Y. Non-perturbative renormalization of the average color charge and multi-point correlators of color charge from a non-Gaussian small-x action. Nucl. Phys. A
**2021**, 1010, 122178. [Google Scholar] [CrossRef] - Dumitru, A.; Miller, G.A.; Venugopalan, R. Extracting many-body color charge correlators in the proton from exclusive DIS at large Bjorken x. Phys. Rev. D
**2018**, 98, 094004. [Google Scholar] [CrossRef][Green Version] - Dumitru, A.; Skokov, V.; Stebel, T. Subfemtometer scale color charge correlations in the proton. Phys. Rev. D
**2020**, 101, 054004. [Google Scholar] [CrossRef][Green Version] - Dumitru, A.; Paatelainen, R. Sub-femtometer scale color charge fluctuations in a proton made of three quarks and a gluon. Phys. Rev. D
**2021**, 103, 034026. [Google Scholar] [CrossRef] - Dumitru, A.; Mäntysaari, H.; Paatelainen, R. Color charge correlations in the proton at NLO: Beyond geometry based intuition. arXiv
**2021**, arXiv:2103.11682. [Google Scholar] - Altinoluk, T.; Boussarie, R. Low x physics as an infinite twist (G)TMD framework: Unravelling the origins of saturation. J. High Energy Phys.
**2019**, 10, 208. [Google Scholar] [CrossRef][Green Version] - Boussarie, R.; Mehtar-Tani, Y. Gauge invariance of transverse momentum dependent distributions at small x. Phys. Rev. D
**2021**, 103, 094012. [Google Scholar] [CrossRef] - Fujii, H.; Marquet, C.; Watanabe, K. Comparison of improved TMD and CGC frameworks in forward quark dijet production. J. High Energy Phys.
**2020**, 12, 181. [Google Scholar] [CrossRef] - Kovchegov, Y.V.; Pitonyak, D.; Sievert, M.D. Helicity Evolution at Small-x. J. High Energy Phys.
**2016**, 1, 072, Erratum in**2016**, 10, 148. [Google Scholar] [CrossRef][Green Version] - Kovchegov, Y.V.; Pitonyak, D.; Sievert, M.D. Small-x asymptotics of the quark helicity distribution. Phys. Rev. Lett.
**2017**, 118, 052001. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kovchegov, Y.V.; Pitonyak, D.; Sievert, M.D. Helicity Evolution at Small x: Flavor Singlet and Non-Singlet Observables. Phys. Rev. D
**2017**, 95, 014033. [Google Scholar] [CrossRef][Green Version] - Kovchegov, Y.V.; Pitonyak, D.; Sievert, M.D. Small-x Asymptotics of the Quark Helicity Distribution: Analytic Results. Phys. Lett. B
**2017**, 772, 136–140. [Google Scholar] [CrossRef] - Kovchegov, Y.V.; Pitonyak, D.; Sievert, M.D. Small-x Asymptotics of the Gluon Helicity Distribution. J. High Energy Phys.
**2017**, 10, 198. [Google Scholar] [CrossRef][Green Version] - Kovchegov, Y.V.; Sievert, M.D. Small-x Helicity Evolution: An Operator Treatment. Phys. Rev. D
**2019**, 99, 054032. [Google Scholar] [CrossRef][Green Version] - Kovchegov, Y.V.; Tawabutr, Y. Helicity at Small x: Oscillations Generated by Bringing Back the Quarks. J. High Energy Phys.
**2020**, 8, 014. [Google Scholar] [CrossRef] - Adamiak, D.; Kovchegov, Y.V.; Melnitchouk, W.; Pitonyak, D.; Sato, N.; Sievert, M.D. First analysis of world polarized DIS data with small-x helicity evolution. arXiv
**2021**, arXiv:2102.06159. [Google Scholar] - Cougoulic, F.; Kovchegov, Y.V. Helicity-dependent generalization of the JIMWLK evolution. Phys. Rev. D
**2019**, 100, 114020. [Google Scholar] [CrossRef][Green Version] - Cougoulic, F.; Kovchegov, Y.V. Helicity-dependent extension of the McLerran Venugopalan model. Nucl. Phys. A
**2020**, 1004, 122051. [Google Scholar] [CrossRef] - Altinoluk, T.; Armesto, N.; Beuf, G.; Martinez, M.; Salgado, C.A. Next-to-eikonal corrections in the CGC: Gluon production and spin asymmetries in pA collisions. J. High Energy Phys.
**2014**, 7, 068. [Google Scholar] [CrossRef][Green Version] - Altinoluk, T.; Armesto, N.; Beuf, G.; Moscoso, A. Next-to-next-to-eikonal corrections in the CGC. J. High Energy Phys.
**2016**, 1, 114. [Google Scholar] [CrossRef] - Altinoluk, T.; Dumitru, A. Particle production in high-energy collisions beyond the shockwave limit. Phys. Rev. D
**2016**, 94, 074032. [Google Scholar] [CrossRef][Green Version] - Agostini, P.; Altinoluk, T.; Armesto, N. Non-eikonal corrections to multi-particle production in the Color Glass Condensate. Eur. Phys. J. C
**2019**, 79, 600. [Google Scholar] [CrossRef] - Agostini, P.; Altinoluk, T.; Armesto, N. Effect of non-eikonal corrections on azimuthal asymmetries in the Color Glass Condensate. Eur. Phys. J. C
**2019**, 79, 790. [Google Scholar] [CrossRef][Green Version] - Altinoluk, T.; Beuf, G.; Czajka, A.; Tymowska, A. Quarks at next-to-eikonal accuracy in the CGC I: Forward quark-nucleus scattering. arXiv
**2020**, arXiv:2012.03886. [Google Scholar] - Armesto, N.; McLerran, L.; Pajares, C. Long Range Forward-Backward Correlations and the Color Glass Condensate. Nucl. Phys. A
**2007**, 781, 201–208. [Google Scholar] [CrossRef][Green Version] - Dumitru, A.; Gelis, F.; McLerran, L.; Venugopalan, R. Glasma flux tubes and the near side ridge phenomenon at RHIC. Nucl. Phys. A
**2008**, 810, 91–108. [Google Scholar] [CrossRef][Green Version] - Dumitru, A.; Dusling, K.; Gelis, F.; Jalilian-Marian, J.; Lappi, T.; Venugopalan, R. The Ridge in proton-proton collisions at the LHC. Phys. Lett. B
**2011**, 697, 21–25. [Google Scholar] [CrossRef][Green Version] - Kovchegov, Y.V.; Wertepny, D.E. Long-Range Rapidity Correlations in Heavy-Light Ion Collisions. Nucl. Phys. A
**2013**, 906, 50–83. [Google Scholar] [CrossRef][Green Version] - Kovchegov, Y.V.; Wertepny, D.E. Two-Gluon Correlations in Heavy-Light Ion Collisions: Energy and Geometry Dependence, IR Divergences, and k
_{T}-Factorization. Nucl. Phys. A**2014**, 925, 254–295. [Google Scholar] [CrossRef][Green Version] - Altinoluk, T.; Armesto, N.; Beuf, G.; Kovner, A.; Lublinsky, M. Bose enhancement and the ridge. Phys. Lett. B
**2015**, 751, 448–452. [Google Scholar] [CrossRef][Green Version] - Altinoluk, T.; Armesto, N.; Wertepny, D.E. Correlations and the ridge in the Color Glass Condensate beyond the glasma graph approximation. J. High Energy Phys.
**2018**, 5, 207. [Google Scholar] [CrossRef] - Altinoluk, T.; Armesto, N.; Kovner, A.; Lublinsky, M. Double and triple inclusive gluon production at mid rapidity: Quantum interference in p-A scattering. Eur. Phys. J. C
**2018**, 78, 702. [Google Scholar] [CrossRef] [PubMed][Green Version] - Altinoluk, T.; Armesto, N. Particle correlations from the initial state. Eur. Phys. J. A
**2020**, 56, 215. [Google Scholar] [CrossRef] - Krasnitz, A.; Nara, Y.; Venugopalan, R. Classical gluodynamics of high-energy nuclear collisions: An Erratumn and an update. Nucl. Phys. A
**2003**, 727, 427–436. [Google Scholar] [CrossRef][Green Version] - Lappi, T. Production of gluons in the classical field model for heavy ion collisions. Phys. Rev. C
**2003**, 67, 054903. [Google Scholar] [CrossRef][Green Version] - Blaizot, J.P.; Lappi, T.; Mehtar-Tani, Y. On the gluon spectrum in the glasma. Nucl. Phys. A
**2010**, 846, 63–82. [Google Scholar] [CrossRef][Green Version] - Schenke, B.; Schlichting, S.; Venugopalan, R. Azimuthal anisotropies in p+Pb collisions from classical Yang–Mills dynamics. Phys. Lett. B
**2015**, 747, 76–82. [Google Scholar] [CrossRef][Green Version] - Schlichting, S.; Skokov, V. Saturation corrections to dilute-dense particle production and azimuthal correlations in the Color Glass Condensate. Phys. Lett. B
**2020**, 806, 135511. [Google Scholar] [CrossRef] - Chirilli, G.A.; Kovchegov, Y.V.; Wertepny, D.E. Classical Gluon Production Amplitude for Nucleus-Nucleus Collisions: First Saturation Correction in the Projectile. J. High Energy Phys.
**2015**, 3, 015. [Google Scholar] [CrossRef][Green Version] - Kovchegov, Y.V.; Skokov, V.V. How classical gluon fields generate odd azimuthal harmonics for the two-gluon correlation function in high-energy collisions. Phys. Rev. D
**2018**, 97, 094021. [Google Scholar] [CrossRef][Green Version] - Li, M.; Skokov, V.V. First Saturation Correction in High Energy Proton-Nucleus Collisions: II. Single Inclusive Semi-Hard Gluon Production. arXiv
**2021**, arXiv:2104.01879. [Google Scholar] - Li, M.; Skokov, V.V. First Saturation Correction in High Energy Proton-Nucleus Collisions: I. Time evolution of classical Yang-Mills fields beyond leading order. arXiv
**2021**, arXiv:2102.01594. [Google Scholar] - Hoffmann, A. The Physics of Synchrotron Radiation; Cambridge Monographs on Particle Physics; Cambridge University Press: Cambridge, UK, 2004. [Google Scholar]
- Seidel, M.; Hoffmann, M. Vacuum induced backgrounds in the new HERA interaction regions. In Proceedings of the 9th European Particle Accelerator Conference (EPAC 2004), Lucerne, Switzerland, 5–9 July 2004. [Google Scholar]
- Tanigawa, H. et al. [Belle-II SVD Collaboration] Beam background study for the Belle II Silicon Vertex Detector. Nucl. Instrum. Methods A
**2020**, 982, 164580. [Google Scholar] [CrossRef] - Bartel, W.; Foster, B.; Kotz, U.; Kose, R.; Lohrmann, E.; Schroder, V.; Trines, D. Synchrotron Radiation Background at the Hera Interaction Regions. Report of a Working Group. Available online: https://inspirehep.net/literature/220472 (accessed on 20 August 2021).
- Department of Energy (USA). Artificial Intelligence and Technology Office. Available online: https://www.energy.gov/articles/us-department-energy-provide-16-million-machine-learning-and-artificial-intelligence (accessed on 22 April 2020).
- Feickert, M.; Nachman, B. A Living Review of Machine Learning for Particle Physics. arXiv
**2021**, arXiv:2102.02770. [Google Scholar] - Kasieczka, G.; Nachman, B.; Shih, D.; Amram, O.; Andreassen, A.; Benkendorfer, K.; Bortolato, B.; Brooijmans, G.; Canelli, F.; Collins, J.K.; et al. The LHC Olympics 2020: A Community Challenge for Anomaly Detection in High Energy Physics. arXiv
**2021**, arXiv:2101.08320. [Google Scholar] - Amoroso, S.; Azzurri, P.; Bendavid, J.; Bothmann, E.; Britzger, D.; Brooks, H.; Buckley, A.; Calvetti, M.; Chen, X.; Chiesa, M.; et al. Les Houches 2019: Physics at TeV Colliders: Standard Model Working Group Report. In Proceedings of the 11th Les Houches Workshop on Physics at TeV Colliders, Les Houches, France, 10–28 June 2019. [Google Scholar]
- Guest, D.; Cranmer, K.; Whiteson, D. Deep Learning and its Application to LHC Physics. Ann. Rev. Nucl. Part. Sci.
**2018**, 68, 161–181. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**In the CGC, EFT partons are organized as color sources or fields according to their longitudinal momentum fraction x relative to the characteristic momentum fraction of the probe ${x}_{0}$. Sources are stochastic and their distribution is characterized by a gauge invariant weight functional ${W}_{{x}_{0}}\left[\rho \right]$ (represented in blue). The gauge field is a solution to Yang–Mills equations in the presence of the sources (represented in red).

**Figure 2.**The interaction of a quark with the background field of the nucleus is encoded in a light-like Wilson line which re-sums multiple eikonal scatterings.

**Figure 4.**Feynman diagram for the forward scattering amplitude ${\mathcal{M}}^{{\gamma}^{\ast}A\to {\gamma}^{\ast}A}$ of virtual photon–nucleus collision. The amplitude contains two light-like Wilson lines, which appear from the interaction of the quark anti-quark pair with the nucleus. This amplitude is related to the total DIS cross section by virtue of the optical theorem ${\sigma}^{{\gamma}^{\ast}A}=2\mathrm{Im}\left({\mathcal{M}}^{{\gamma}^{\ast}A\to {\gamma}^{\ast}A}\right)$. In the high-energy limit, the forward amplitude is purely imaginary.

**Figure 5.**Feynman diagram for the amplitude ${\mathcal{M}}^{pA\to q+X}$ for quark production in proton-nucleus collisions. A light-like Wilson line appears in the amplitude; thus, the cross section will feature a dipole correlator.

**Figure 6.**Fourier transform of the dipole correlator as a function of ${k}_{\perp}$ for two different values of the saturation scale. A transition between saturation and perturbative regime is observed near ${k}_{\perp}\sim {Q}_{s}$. The x dependence of the distribution is effectively accounted by the saturation scale. In a more careful treatment, the functional shape of the distribution also depends on x.

**Figure 7.**Feynman diagram for the amplitude ${\mathcal{M}}^{{\gamma}^{\ast}A\to q\overline{q}+X}$ for the quark–anti-quark dijet production in virtual photon-nucleus collisions. The amplitude contains the production of two light-like Wilson lines; thus, the amplitude will feature a quadrupole (and dipole) correlator.

**Figure 8.**WW gluon TMD distribution as a function of ${k}_{\perp}$ for two different values of the saturation scale. A transition between saturation and perturbative regime is observed near ${k}_{\perp}\sim {Q}_{s}$. The x dependence of the distribution is effectively accounted by the saturation scale. In a more careful treatment, the functional shape of the distribution also depends on x.

**Figure 9.**A subset of Feynman diagrams for the quantum evolution of the dipole correlator. Upper diagrams correspond to real gluon emission, while lower diagrams correspond to virtual contributions.

**Figure 10.**Schematic representation of the quantum evolution of the weight-functional. Quantum fluctuations in the interval $[{x}_{1},{x}_{0}]$ (shown in yellow) are absorbed into stochastic fluctuations of the color sources by redefinition of the weight functional ${W}_{{x}_{0}}\left[\rho \right]\to {W}_{{x}_{1}}\left[\rho \right]$ (compare with Figure 1). The choice of the scale separating small-x and large-x partons is thus arbitrary and different choices are related by the JIMWLK renormalization group equations. The long right bracket represents how large-x partons and fluctuations are considered as sources after properly evolving of weight functional.

**Figure 11.**(

**Left**) Dipole amplitude ${D}_{x}\left({r}_{\perp}\right)$ small-x evolution drives a more rapid transition to the strong scattering regime. (

**Right**) Small-x evolution of the saturation scale ${Q}_{s}^{2}$ normalized by the saturation scale at ${x}_{0}$.

**Figure 12.**Predictions for shadowing compared to data from the New Muon Collaboration. Center: predictions for Right: Predictions for Q${}^{2}=5$ GeV${}^{2}$ as a function of x. Figure from the work in [50].

**Figure 13.**Comparison of the CGC at NLO compared to HERA data. (

**Left**) Reduced cross section at small-x. (

**Right**) ${F}_{L}$ structure function. Figure from the work in [61].

**Figure 14.**Contribution to the structure functions ${F}_{2}$ (

**left**) and ${F}_{L}$ (

**right**) from dipole sizes smaller than ${r}_{\mathrm{max}}$ at different photon virtualities. ${F}_{L}$ sensitivity to large dipoles is reduced compared to ${F}_{2}$ due to the different structure of light-cone wave functions between longitudinally and transversely polarized photons. Figure from the work in [63].

**Figure 15.**IPsat and IPnonsat (linearized IPsat) independent fits to inclusive reduced cross section HERA data. Both fits result in almost indistinguishable results, hindering the extraction of a signal of gluon saturation at HERA. Figure from [63].

**Figure 16.**$J/\psi $ exclusive electroproduction data from HERA compared to saturation models (bCGC and IPsat). (

**Left**) energy dependence. (

**Right**) $\left|t\right|$ spectra. Figure from the work in [54].

**Figure 18.**(

**Left**) Color charge density for four different events. (

**Right**) Coherent and incoherent H1 data compared to predictions from CGC incorporating sub-nucleonic (and ${Q}_{s}$ saturation fluctuations).

**Figure 19.**BRAHMS data on the nuclear modification factor ${R}_{dAu}$ of charged particles at midrapidity and forward rapidity (data from [110]) compared with the saturation based results in [113]. The midrapidity ${p}_{\perp}$ distribution is characterized by a Cronin peak, while at forward rapidities this peak is washed away.

**Figure 20.**$J/\psi $ and $\psi \left(2S\right)$ at five center of mass energies from the ALICE experiment compared to summed CGC-NRQCD and FONLL calculations [139].

**Figure 21.**$J/\psi $ Production cross sections as a function of ${p}_{\perp}$ in pp collisions at $\sqrt{s}=$ 510 and 500 GeV measured through the ${\mu}^{+}{\mu}^{-}$ (blue stars) and ${e}^{+}{e}^{-}$ decay channels (red circles). From the STAR experiment [141]. The lower panels of the figure quantify the results to different predictions, including CGC via ratios.

**Figure 22.**The ${\psi}^{\prime}$ (top curve) and $J/\psi $ (other four curves) differential cross section as a function of p${}_{T}$. Figure from the work in [137].

**Figure 23.**Azimuthal correlation for ${\pi}^{0}$ production compared to PHENIX data [151]. (

**Top**) Proton–proton collision. (

**Bottom**) Central deuteron–gold collisions. Figures from the works in [148,152]. More modern version of this work both experimentally [150] and theoretically exist with forthcoming publications.

**Figure 27.**Comparison of the structure function ${F}_{2}$ obtained from the rcBK solutions to those from extrapolated nuclear PDFs. Figure from [191].

**Figure 29.**Ratio of diffractive to inclusive DIS cross section in eA normalized to pA (double ratio). Comparison between saturation predictions and the leading twist approach. Figure from the work in [185].

**Figure 30.**Transverse momentum spectra for the diffractive coherent production of vector mesons in electron-gold ion collisions. (

**Left**) $J/\psi $ production. (

**Right**) $\rho $ production. The figures show the comparison between models with and without saturation. Figure from the work in [185].

**Figure 31.**(

**Left**) Dihadron correlation function in electron collisions with different nuclei showing a depletion of the back-to-back peak. (

**Right**) Comparison of the correlation function with and without saturation. The gray band is a result of varying the saturation scale. Figure from the work in [185].

**Figure 32.**Nuclear modification factor for single semi-inclusive hadron production displaying a Cronin peak and its disappearance. (

**Left**) Dependence on the virtuality. (

**Right**) Dependence on rapidity of the produced particle. In this figures ${\overline{Q}}^{2}=z(1-z){Q}^{2}$, where z is the longitudinal momentum fraction of the hadron relative to the virtual photon, and is chosen to be close to unity. Figure from the work in [205].

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Morreale, A.; Salazar, F.
Mining for Gluon Saturation at Colliders. *Universe* **2021**, *7*, 312.
https://doi.org/10.3390/universe7080312

**AMA Style**

Morreale A, Salazar F.
Mining for Gluon Saturation at Colliders. *Universe*. 2021; 7(8):312.
https://doi.org/10.3390/universe7080312

**Chicago/Turabian Style**

Morreale, Astrid, and Farid Salazar.
2021. "Mining for Gluon Saturation at Colliders" *Universe* 7, no. 8: 312.
https://doi.org/10.3390/universe7080312