We present a detailed numerical investigation of semi-inclusive forward di-hadron production in proton–nucleus collisions employing the Color Glass Condensate effective theory. We focus on the regime where di-hadrons are produced nearly back-to-back in the transverse plane, thereby justifying a transverse-momentum-dependent factorization approach in terms of small- <italic>x</italic> gluon distributions. Our computation integrates several key elements: i) non-linear rapidity evolution via the Balitsky&#8211;Kovchegov equation with running coupling, ii) both perturbative and non-perturbative Sudakov resummation, and iii) a phenomenologically constrained model for the initial conditions for small- <italic>x</italic> gluon distributions. We compare this phenomenological framework to experimental data from the STAR Collaboration on azimuthal correlations in forward di-pion production in both proton&#8211;proton and proton&#8211;gold collisions. We analyze the systematic theoretical uncertainties associated with the saturation scales of nuclei at the initial scale for rapidity evolution and with those associated with the hadronization process. Finally, we make predictions for the kinematics anticipated to be covered by the ALICE Forward Calorimeter (FoCal) upgrade at the Large Hadron Collider.

France

Paul Caucal

United States

Zhong-Bo Kang

Poland

Piotr Korcyl

Farid Salazar

Björn Schenke

Tomasz Stebel

United Kingdom

Raju Venugopalan

China

Wenbin Zhao

Probing gluon saturation with forward di-hadron correlations in proton-nucleus collisions

<p>We perform a global Bayesian analysis of diffractive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">J</mi><mo>/</mo><mi>ψ</mi></math> production in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mo>+</mo><mi>p</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mo>+</mo><mi>Pb</mi></math> collisions using a color glass condensate (CGC) based calculation framework. As past calculations have shown that CGC-based models typically overpredict the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">J</mi><mo>/</mo><mi>ψ</mi></math> production in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mo>+</mo><mi>Pb</mi></math> collisions at high center of mass energy, we address the question of whether it is possible to describe coherent and incoherent diffractive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">J</mi><mo>/</mo><mi>ψ</mi></math> data from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mo>+</mo><mi>p</mi></math> collisions at Hadron–Electron Ring Accelerator (HERA) and the LHC, and from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mo>+</mo><mi>Pb</mi></math> collisions at the LHC simultaneously. Our results indicate that a simultaneous description of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mo>+</mo><mi>p</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mo>+</mo><mi>Pb</mi></math> data is challenging, with results improving when an overall <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math>-factor—scaling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mo>+</mo><mi>p</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mo>+</mo><mi>Pb</mi></math> cross sections to absorb model uncertainties—is introduced.</p>

Finland

Heikki Mäntysaari

Hendrik Roch

Chun Shen

Global Bayesian analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">J</mi><mo>/</mo><mi>ψ</mi></mrow></math> photoproduction on proton and lead targets

<p>Within the color glass condensate effective field theory, we assess the importance of including a finite size for the target on observables sensitive to small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> evolution. To this end, we study the Balitsky-Kovchegov (BK) equation with impact-parameter dependence in the initial condition. We demonstrate that neglecting the dependence on the impact parameter can result in overestimated saturation effects for protons, while it has little effect for heavy nuclei at the energies available at current experiments. When fixing the nonperturbative parameters to the energy dependence of the exclusive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">J</mi><mo>/</mo><mi>ψ</mi></math> photoproduction cross section with proton targets, predictions for lead targets are not sensitive to the applied running-coupling prescription, the scheme chosen to resum large transverse logarithms in the BK equation, or the infrared regulator in the evolution.</p>

Jani Penttala

Finite-size effects on small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> evolution and saturation in proton and nuclear targets

We study diffractive vector meson production at small-x in the collision of electrons and polarized deuterons <math><mi>e</mi><mo>+</mo><msup><mrow><mi>d</mi></mrow><mrow><mo>↑</mo></mrow></msup></math>. We consider the polarization dependence of the nuclear wave function of the deuteron, which results in an azimuthal angular dependence of the produced vector meson when the deuteron is transversely polarized. The Fourier coefficients extracted from the azimuthal angular dependence of the vector meson differential cross-section exhibit notable differences between longitudinally and transversely polarized deuterons. The angular dependence of the extracted effective deuteron radius provides direct insight into the structure of the polarized deuteron wave function. Furthermore, we observe slightly increased gluon saturation effects when the deuteron is longitudinally polarized compared to the transversely polarized case. The small-x observables studied in this work will be accessible at the future Electron-Ion Collider.

Spatial imaging of polarized deuterons at the Electron-Ion Collider

We calculate exclusive <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> photoproduction at high energies in the color glass condensate approach. The results are compared to the center-of-mass energy dependent <math><mi>γ</mi><mo>+</mo><mi>A</mi><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>+</mo><mi>A</mi></math> cross sections extracted from measurements in ultraperipheral heavy ion collisions at RHIC and LHC. We predict strong saturation-driven nuclear suppression at high energies, while LHC data prefer even stronger suppression. We explore effects of nucleon shaped fluctuations and show that the most recent measurement of the <math><mo>|</mo><mi>t</mi><mo>|</mo></math>-differential incoherent <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> cross section prefers large event-by-event fluctuations of the nucleon substructure in heavy nuclei, comparable to that found for a free proton.

Energy dependent nuclear suppression from gluon saturation in exclusive vector meson production

We compute the back-to-back dijet cross section in deep inelastic scattering at small <math><mi>x</mi></math> to next-to-leading order (NLO) in the color glass condensate effective field theory. Our result can be factorized into a convolution of the Weizsäcker-Williams gluon transverse-momentum-dependent distribution function (WW gluon TMD) with a universal soft factor and an NLO coefficient function. The soft factor includes both double and single logarithms in the ratio of the relative transverse momentum <math><mrow><msub><mrow><mi>P</mi></mrow><mrow><mo>⊥</mo></mrow></msub></mrow></math> of the dijet pair to the dijet momentum imbalance <math><msub><mi>q</mi><mo>⊥</mo></msub></math>; its renormalization group (RG) evolution is resummed into the Sudakov factor. Likewise, the WW TMD obeys a nonlinear RG equation in <math><mi>x</mi></math> that is kinematically constrained to satisfy both the lifetime and rapidity ordering of the projectile. Exact analytical expressions are obtained for the NLO coefficient function of transversely and longitudinally polarized photons. Our results allow for the first quantitative separation of the dynamics of Sudakov suppression from that of gluon saturation. They can be extended to other final states and provide a framework for precision tests of novel QCD many-body dynamics at the Electron-Ion Collider.

Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small <math><mi>x</mi></math>: Complete NLO Results and Predictions

In [1], we performed the first complete computation of the back-to-back inclusive dijet cross-section in Deeply Inelastic Scattering (DIS) at small x Bj to next-to-leading order (NLO) in the Color Glass Condensate effective field theory (CGC EFT). We demonstrate here that for dijets with relative transverse momentum P ⊥ and transverse momentum imbalance q ⊥, to leading power in q ⊥/P ⊥, the cross-section for longitudinally polarized photons can be fully factorized into the product of a perturbative impact factor and the non-perturbative Weizsäcker-Williams (WW) transverse momentum dependent (TMD) gluon distribution to NLO accuracy. The impact factor can further be expressed as the product of a universal soft factor which resums Sudakov double and single logs in P ⊥/q ⊥ and a coefficient function given by a remarkably compact analytic expression. We show that in the CGC EFT the WW TMD satisfies a kinematically constrained JIMWLK renormalization group evolution in rapidity. This factorization formula is valid to all orders in Q  s /q ⊥ for q ⊥, Q  s  ≪ P ⊥, where Q  s  is the semi-hard saturation scale that grows with rapidity.

Back-to-back inclusive dijets in DIS at small x: gluon Weizsäcker-Williams distribution at NLO

Back-to-back dijet cross-sections in deeply inelastic scattering (DIS) at small x Bj are suppressed by many-body multiple scattering and screening effects arising from gluon saturation at high parton densities. They are similarly sensitive in these kinematics to large Sudakov logarithms from soft gluon radiation. Uncovering novel physics in this DIS channel therefore requires understanding the interplay of the two phenomena. In this work, we compute the small x Bj inclusive dijet DIS cross-section in back-to-back kinematics at next-to-leading order (NLO) in the Color Glass Condensate effective field theory (CGC EFT). Our result includes, for the first time, all real and virtual NLO contributions to the impact factor. These include all Sudakov double and single logarithm contributions, as well as all other finite   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (α  s ) terms that contribute at this order. We demonstrate explicitly that resummations of small x and Sudakov logarithms can be performed simultaneously in the CGC EFT. This requires that the JIMWLK kernel for small x evolution of the Weizsäcker-Williams (WW) gluon distribution satisfies a kinematic constraint imposed by lifetime ordering of successive gluon emissions; the corresponding modifications to the kernel, corresponding to resummations of large double transverse logarithms, are precisely of the type required to stabilize JIMWLK evolution beyond leading logarithmicaccuracy. We compute the azimuthal harmonics of the NLO back-to-back distributions and show their sensitivity to both the unpolarized and linearly polarized WW gluon distributions. Finally, we discuss how TMD factorization is broken by an emergent saturation scale at small x.

Back-to-back inclusive dijets in DIS at small x: Sudakov suppression and gluon saturation at NLO

We show that when saturation effects are included one obtains a good description of the exclusive <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> production spectra in ultraperipheral lead-lead collisions as recently measured by the ALICE Collaboration at the LHC. As exclusive spectra are sensitive to the spatial distribution of nuclear matter at small Bjorken-<math><mi>x</mi></math>, this implies that gluon saturation effects modify the impact parameter profile of the target as we move towards small <math><mi>x</mi></math>. In addition to saturation effects, we find a preference for larger nuclear strong-interaction radii compared to the typical charge radius. We demonstrate the role of finite photon transverse momentum and the interference between the cases for which the role of photon emitter and target are switched between the nuclei. We show that these effects are comparable to the experimental precision for <math><msub><mi>p</mi><mi>T</mi></msub></math>-differential cross sections and as such need to be included when comparing to LHC data. Finally, the integrated <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> production cross sections from the LHC and preliminary transverse momentum spectra from RHIC are shown to prefer calculations with fluctuating nucleon substructure, although these datasets would require even stronger saturation effects than predicted from our framework.

Nuclear geometry at high energy from exclusive vector meson production

Using Bayesian inference, we determine probabilistic constraints on the parameters describing the fluctuating structure of protons at high energy. We employ the color glass condensate framework supplemented with a model for the spatial structure of the proton, along with experimental data from the ZEUS and H1 Collaborations on coherent and incoherent diffractive <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production in e+p collisions at HERA. This data is found to constrain most model parameters well. This work sets the stage for future global analyses, including experimental data from e+p, p+p, and p+A collisions, to constrain the fluctuating structure of nucleons along with properties of the final state.