Towards a Global Search for Gluon Saturation in Collider Experiments 


Maddox Spinelli


Farid Salazar, Inspirehep (email:, and Yukari Yamauchi, Inspirehep (email:


Familiarity with particle physics (collider physics and scattering amplitudes), and basic programming skills would be helpful but not mandatory.

What Students Will Do:

In the first part of the project, the student will learn the basic theoretical building blocks for the computation of high-energy scattering amplitudes and cross sections within the CGC effective theory. The student will learn to compute simple scattering amplitudes (at lowest order in perturbation theory) following Feynman rules in the CGC background field [6, 7]. We will derive the equations describing the energy evolution of the background field, and test simple non-perturbative models for its initial condition. In the second part of the project, we will focus on the theory-to-data comparison of structure functions at HERA, and develop an efficient fitting Bayesian framework that can constrain the non-perturbative initial conditions of the dipole distribution [8]. We will also develop an efficient code to evaluate the energy-evolution equations. Next, we will test the universality of the CGC effective theory by incorporating the evolution equations into our fitting framework the single inclusive hadron production data. Depending on our progress, we could potentially promote this framework to implement one-loop corrections to theory calculations for both experimental observables [9, 10].

Expected Length:

One year




Figure for INTURN 24-5

Image Credits:

Project Description:

Quarks and gluons are the fundamental constituents of all hadronic and nuclear matter. Gluons are the force carriers that bind matter together and have been dubbed “the glue that binds us all” [1]. Previous experimental results from the Hadron–Electron Ring Accelerator (HERA) have revealed that gluon densities grow as the energy of the collision increases. This rapid proliferation of gluons at high energies will be tamed by gluon recombination, leading to gluon saturation. A crucial pillar of the scientific program of the future Electron Ion Collider (EIC) and upcoming upgrades of the Large Hadron Collider (LHC) is the discovery of a new regime of nuclear matter, known as color glass condensate (CGC), dominated by a highly dense and saturated system of gluons. As a universal form of matter that describes the properties of all high-energy strongly interacting particles, the unambiguous identification of the CGC is of utmost importance to fundamental science. While compelling signatures of gluon saturation have been observed in existing experimental data in collider experiments, definitive evidence is still missing [2]. A crucial step towards unambiguously uncovering the existence of gluon saturation is to develop a CGC-based global analysis framework that can be confronted with data across different experiments. The goal of this project is to perform Bayesian analysis of the structure functions in electron-proton collisions from HERA [3], and the single inclusive hadron production in proton-proton and proton-nucleus collision at RHIC [4] and the LHC [5]. Both of these processes can be described by the same universal object, the so-called CGC dipole distribution.


[1] A. Accardi et al., Eur. Phys. J. A 52, 268 (2016), arXiv:1212.1701 [nucl-ex].
[2] A. Morreale and F. Salazar, Universe 7, 312 (2021), arXiv:2108.08254 [hep-ph].
[3] F. D. Aaron et al. (H1, ZEUS), JHEP 01, 109, arXiv:0911.0884 [hep-ex].
[4] J. Adams et al. (STAR), Phys. Rev. Lett. 97, 152302 (2006), arXiv:nucl-ex/0602011.2
[5] B. Abelev et al. (ALICE), Phys. Rev. Lett. 110, 082302 (2013), arXiv:1210.4520 [nucl-ex].
[6] Y. V. Kovchegov and E. Levin, Quantum Chromodynamics at High Energy, Vol. 33 (Oxford University Press, 2013).
[7] F. Salazar, Private notes.
[8] T. Lappi and H. Mäntysaari, Phys. Rev. D 88, 114020 (2013), arXiv:1309.6963 [hep-ph].
[9] G. Beuf, H. Hänninen, T. Lappi, and H. M¨antysaari, Phys. Rev. D 102, 074028 (2020), arXiv:2007.01645 [hep-ph].
[10] Y. Shi, L. Wang, S.-Y. Wei, and B.-W. Xiao, Phys. Rev. Lett. 128, 202302 (2022), arXiv:2112.06975 [hep-ph]