arXiv subjects

Paul Caucal

Publications and source records attributed to Paul Caucal.

At least 19 recordsLinked to original sources

arXiv2026

Jet Quenching Meets Gluon Saturation

We present a theoretical framework for jet fragmentation in heavy-ion collisions based on the resummation of large energy logarithms. Exploiting the hierarchy of scales characteristic of jet quenching, we show that the jet function obeys the Banfi-Marchesini-Smye evolution equation, with medium-induced energy loss and color decoherence encoded in the initial condition. This structure reveals a close correspondence with saturation physics. In particular, the coherence angle emerges as the analog of the saturation scale and exhibits the same asymptotic scaling behavior under nonlinear evolution. As a proof of principle, we compute the jet nuclear modification factor to quantify the interplay between vacuum radiation and medium-induced color decoherence. Our framework provides a unified perturbative description of vacuum-like parton showers, medium-induced radiation, and color-coherence effects, paving the way for precision studies of jet quenching at RHIC and the LHC.

hep-ph↗

arXiv2026

Color Coherence and the Soft Structure of QCD Jets in Vacuum and the QGP

We formulate a theoretical framework for the evolution of QCD jets in vacuum and in the quark--gluon plasma through the resummation of large energy logarithms. Exploiting the strong hierarchy between the hard scale of the jet and the energy scale associated with jet energy loss, we show that jet observables near threshold can be formulated in terms of Wilson-line correlators obeying Banfi-Marchesini-Smye (BMS) evolution. In this description, soft radiation resolves the internal color structure of the jet, leading to a hierarchy of non-linear evolution equations that govern the evolution of color coherence and the emergence of decoherent energy loss. For jets propagating through a QCD medium, we demonstrate that medium-induced interactions modify the boundary conditions of the evolution while leaving its ultraviolet structure unchanged. This separation of scales provides a unified description of vacuum-like radiation, medium-induced energy loss, and color coherence. In the large-$N_c$ limit, the resulting evolution is closely related to the Balitsky-Kovchegov equation of high-energy QCD, allowing concepts from saturation physics to be applied to jet quenching. In particular, the medium coherence angle plays a role analogous to the saturation scale and acquires the same asymptotic scaling behavior under evolution. Our framework establishes a perturbative foundation for the study of color coherence effects in jet quenching and provides a unified picture of soft jet evolution in vacuum and in dense QCD matter.

hep-ph↗

arXiv2026

Rotating the Color Glass Condensate

High-energy QCD evolution beyond leading order suffers from instabilities driven by large collinear logarithms. We present a framework, consistent with the standard high-energy operator product expansion (OPE), that restores perturbative stability order by order. The method involves a change of basis in the space of high-energy operators, which modifies both the evolution kernel and the coefficient functions while leaving physical observables invariant. Within this factorization scheme, we derive a next-to-leading-order renormalization-group equation whose numerical solution exhibits stable evolution up to large rapidities, paving the way for a systematic framework for precision studies of gluon saturation at current and future colliders.

hep-ph↗

arXiv2026

Forward trijet production in proton-nucleus collisions: gluon initiated channel

In this paper, we present results for the forward three-parton production differential cross section in the gluon-initiated channel in proton-nucleus collisions. This result is the leading-order contribution to forward trijet production and provides the real-emission building block required for the NLO dijet/dihadron cross section. The calculations are carried out within the Color Glass Condensate (CGC) effective theory, and in the dilute-dense approximation, using effective vertices for the quark and gluon propagators interacting with the small-$x$ background gluon field. We employ the covariant perturbation theory approach and disentangle the amplitudes into regular and instantaneous contributions. Our results are expressed as convolutions of multiparton color correlators of light-like Wilson lines and perturbative impact factors, organized in compact expressions in terms of the ``bare" topologies of the contributing diagrams. The gluon-initiated channel receives contributions from a $q\bar{q}g$ and a $ggg$ final state. Interestingly, when considering the $ggg$ final state, we observe, for the first time, that the four-gluon vertex topology follows a structure similar to the instantaneous contributions. This observation suggests a simplification in the organization of multigluon CGC amplitudes and may prove useful for future one-loop calculations. Furthermore, when integrating (one of) the real gluon(s) in the final state, we identify that the rapidity divergence is absorbed into the real part of the JIMWLK evolution of the leading-order Wilson-line correlator. In addition, we isolate the divergences arising when the unobserved parton becomes collinear to one of the observed hadrons in the final state. These divergences are absorbed by renormalizing the initial-state parton distribution functions and final-state fragmentation functions, which are shown to obey DGLAP evolution.

hep-ph↗

arXiv2026

Open quantum system approach to the transverse momentum broadening of a colour dipole

Using the open quantum systems formalism, we study the propagation of a quark-antiquark pair propagating through a dense QCD plasma of size $L$ and transverse momentum broadening transport coefficient $\hat q$, and we derive the Lindblad evolution equation for the density matrix of the system. We focus on the boosted regime where the opening angle $θ_{q\bar q}$ of this effective colour dipole satisfies $θ_{q\bar q}\ll 1$. In the correlation limit where the quark-antiquark relative transverse momentum $p_\perp$ is much larger than the imbalance $q_\perp$ as well as the medium typical transverse momentum scale $Q_s=\sqrt{\hat q L}$, we demonstrate that the resulting Wigner distribution displays quasi factorisation between a hard factor describing the hard splitting producing the $q\bar q$ pair and the transverse momentum imbalance $q_\perp$-distribution encoding the broadening induced by the medium. The factorisation is violated by a "colour decoherence" factor that controls the $θ_{q\bar q}$ dependence of the $q_\perp$-distribution through the ratio $θ_{q\bar q}/θ_c$, with $θ_c \sim (\hat q L^3)^{-1/2}$. The open quantum systems approach enables us to clarify the role of this critical angle $θ_c$ and its associated critical time $t_c$ in the genuine quantum decoherence of the density matrix in colour and kinematic space: in particular, $t_c$ controls both the suppression of the off-diagonal elements of the density matrix in colour space and the transition between singlet and octet states. We find, however, that colour decoherence sets in earlier than the full decoherence of the density matrix, thereby marking the onset of classical behaviour in the system. Finally, we investigate the corrections beyond the quasi-factorised picture due to the quantum diffusion term in $p_\perp$ of the Lindblad equation and we find that these corrections are mild.

hep-ph↗

arXiv2026

TMD factorization in diffractive heavy-quark production in photon-nucleus collisions

Using the Colour Glass Condensate effective theory, we study the diffractive production of a massive quark-antiquark pair accompanied by a gluon in coherent photon-nucleus collisions at high energy. This partonic configuration provides the leading twist contribution to the cross section in the correlation limit where two of the partons are hard and nearly back to back in the transverse plane, while the third one is semi-hard, with a transverse momentum of the order of the nuclear saturation momentum. We consider two scenarios: (i) a hard quark-antiquark pair together with a semi-hard gluon; in this case we demonstrate transverse momentum dependent (TMD) factorization with a mass-dependent ''hard'' factor and the standard expression for the gluon diffractive TMD, and (ii) a hard antiquark-gluon pair and a semi-hard quark; in this case we find TMD factorization with a mass-independent ''hard'' factor and a mass-dependent quark diffractive TMD, which represents a new result. We show that increasing the quark mass reduces (or even washes out) the effects of gluon saturation on the quark diffractive TMD. In particular, it leads to the suppression of the Cronin peak that we observe in the massless limit. Our results are the basis for future phenomenological studies of quarkonium and open charm production in the saturation regime in ultraperipheral collisions at the Large Hadron Collider, and in deep inelastic scattering at the Electron-Ion Collider.

hep-ph↗

arXiv2026

Unveiling the sea: universality of the transverse momentum dependent quark distributions at small $x$

Within the Colour Glass Condensate effective theory, we demonstrate that back-to-back dijet correlations in dilute-dense collisions involving a small-$x$ quark from the nuclear target can be factorised in terms of universal transverse momentum dependent distributions (TMDs) for the sea quarks. Two building blocks are needed to construct all these TMDs at the operator level: the sea quark TMD operator which appears in semi-inclusive Deep-Inelastic Scattering (SIDIS) or in the Drell-Yan process and the elastic $S$-matrix for a quark-antiquark dipole. Compared to SIDIS, the saturation effects are stronger for dijet production in forward proton-nucleus collisions, due to additional scattering in the initial and final state, effectively resulting in a larger value for the nuclear saturation momentum.

hep-ph↗

arXiv2026

Small-$x$ factorisation in the target fragmentation region

We consider the differential cross-section for single-inclusive jet production with transverse momentum $P_\perp$ in Deep Inelastic Scattering (DIS) at small Bjorken $x_{\rm Bj}$, mediated by a virtual photon with virtuality $Q^2$. Unlike most studies at small $x$, which focus on particle production in the current fragmentation region, we investigate the kinematic regime where the jet is produced in the target fragmentation hemisphere of the Breit frame, and with $P_\perp \ll Q$. For a longitudinally polarised photon, we demonstrate that this cross-section is not power suppressed in $P_\perp/Q$ and we derive a factorised expression in terms of extended quark and gluon jet fracture functions. Our formula, valid at next-to-leading order in $α_s$ at small $x$, is akin to the Altarelli-Martinelli identity for the longitudinal DIS structure function. Numerical estimates show that the extended quark jet fracture function is the most sensitive to saturation effects in large nuclei.

hep-ph↗

arXiv2025

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

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-$x$ gluon distributions. Our computation integrates several key elements: i) non-linear rapidity evolution via the Balitsky-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-$x$ 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-proton and proton-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.

hep-ph↗

arXiv2025

Gluon splitting at small $x$: a unified derivation for the JIMWLK, DGLAP and CSS equations

We revisit the calculation of the next-to-leading order (NLO) corrections to dijet production in electron-ion collisions at small $x$. We focus on the back-to-back configuration where the relative transverse momentum $P_\perp$ of the measured jets is much larger than both their momentum imbalance $K_\perp$ and the target saturation momentum $Q_s(x,A)$. In this regime, we present for the first time a complete calculation of the real NLO corrections at leading power in $1/P_\perp$. Our result exhibits TMD factorisation, with the same hard factor as at tree-level and a NLO correction to the Weiszäcker-Williams (WW) gluon transverse momentum dependent (TMD) distribution which involves four Wilson-line operators. By studying different kinematical regimes for $K_\perp$ and for the radiated gluon, we recover all the quantum evolutions that were previously identified for this process at NLO: the B-JIMWLK high-energy evolution and the CSS evolution of the gluon WW TMD, and the DGLAP evolution of the gluon PDF. When both $K_\perp$ and the transverse momentum transferred by the target are large compared to $Q_s$, all the Wilson-line operators boil down to the unintegrated gluon distribution and our NLO result for the gluon TMD can be used to isolate the transverse-momentum dependent gluon splitting function.

hep-ph↗

arXiv2025

Collinear Structure of Nonlinear Small-$x$ Evolution

We introduce a novel approach to high-energy QCD factorization of cross-sections for processes involving a dilute projectile and a dense target. Our method preserves the factorization between "fast" and "slow" modes in the longitudinal momentum $k^+$ for a projectile moving along the positive light-cone direction, making it compatible with higher-order loop computations done within the standard formulation of the Color Glass Condensate (CGC) effective field theory. Moreover, it eliminates the anomalous double collinear logarithms that typically hinder the convergence of perturbation theory at small-$x$. Our scheme amounts to a change of basis in the space of CGC operators, introducing an arbitrary transverse scale dependence while leaving physical cross-sections invariant. Implementing this scheme requires a modification of the high-energy renormalization group equation for the CGC operators, which we explicitly derive at next-to-leading order (NLO) and in the non-linear regime for the case of the dipole operator and the DIS impact factor. This general framework provides a consistent and systematic prescription for computing observables in the small-$x$ regime of QCD, free from collinear instabilities.

hep-ph↗

arXiv2025

Evolution of the transverse-momentum dependent gluon distribution at small $x$

Using the colour dipole picture for photon-nucleus interactions at small $x$ together with the Color Glass Condensate (CGC) effective theory, we demonstrate that the next-to-leading (NLO) order corrections to the cross-section for the inclusive production of a pair of hard jets encode not only the JIMWLK evolution with decreasing $x$, but also the DGLAP evolution of the gluon distribution function and the CSS evolution of the gluon transverse momentum dependent (TMD) distribution. The emergent CSS equation takes the form of a rate equation describing the evolution of the dijet distribution in the transverse momentum imbalance $K_\perp$ when increasing the dijet relative momentum $P_\perp$. All three types of evolution become important when both $P_\perp$ and $K_\perp$ are much larger than the nuclear saturation momentum $Q_s(x)$ and we propose a framework which encompasses all of them. The solution to the JIMWLK equation provides the source term for the DGLAP evolution with increasing $K_\perp$, which in turn generates the initial condition for the CSS evolution with increasing $P_\perp$.

hep-ph↗

arXiv2025

Prospective report of the French QCD community to the ESPPU 2025 with respect to the program of the LHC Run 5 and beyond and future colliders at CERN

This document summarizes the prospective physics plans of the French QCD and Heavy-Ion community, including the experimental programs at the LHC Run 5 and beyond and future colliders at CERN, within the context of the French contribution to the update of the European Strategy in Particle Physics (ESPPU 2025), as discussed in the workshop on European Strategy for Particle Physics Update 2025 organised by the QCD GdR in Oct. 2024.

hep-ph↗

arXiv2025

Jet Definition and Transverse-Momentum-Dependent Factorization in Semi-Inclusive Deep-Inelastic Scattering

Using the colour dipole picture of Deep Inelastic Scattering (DIS) and the Colour Glass Condensate effective theory, we study semi-inclusive jet production in DIS at small $x$ in the limit where the photon virtuality $Q^2$ is much larger than the transverse momentum squared $P_\perp^2$ of the produced jet. In this limit, the cross-section is dominated by aligned jet configurations, that is, quark-antiquark pairs in which one of the fermions -- the would-be struck quark in the Breit frame -- carries most of the longitudinal momentum of the virtual photon. We show that physically meaningful jet definitions in DIS are such that the effective axis of the jet sourced by the struck quark is controlled by its virtuality rather than by its transverse momentum. For such jet definitions, we show that the next-to-leading order (NLO) cross-section admits factorisation in terms of the (sea) quark transverse momentum dependent (TMD) distribution, which in turn satisfies a universal Dokshitzer-Gribov-Lipatov-Altarelli-Parisi and Sudakov evolution.

hep-ph↗

arXiv2024

Dihadron correlations in small-$x$ DIS at NLO: transverse momentum dependent fragmentation

We compute inclusive dihadron cross-section in Deep Inelastic Scattering at next-to-leading order (NLO) and small $x$ in the Color Glass Condensate. We focus on the kinematic limit where the hadrons are produced at forward rapidities (in the direction of the virtual photon) and back-to-back in the transverse plane. Our calculation demonstrates that the coefficient of the Sudakov double logarithm for this process is $-\frac{α_s}{2π}\left[C_F+\frac{N_c}{2}\right]$ instead of $-\frac{α_s N_c}{4π}$ when back-to-back jets are measured in the final state. To preserve the universality of the Sudakov soft factor associated with the Weizsäcker-Williams transverse momentum dependent (TMD) gluon distribution, we promote the collinear fragmentation functions into TMD fragmentation functions. We then perform the resummation of the Sudakov logarithms through Collins-Soper-Sterman evolution of the TMD fragmentation functions and the Weizsäcker-Williams TMD gluon distribution. Finally, analytic expressions are obtained for the NLO coefficient functions in the $\overline{\rm MS}$-scheme. These results pave the way towards numerically calculating dihadron correlations at small $x$ at the future Electron-Ion Collider with full NLO accuracy.

hep-ph↗

arXiv2024

Back-to-back inclusive dijets in DIS at small $x$: Complete NLO results and predictions

We compute the back-to-back dijet cross-section in deep inelastic scattering (DIS) at small $x$ 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 $P_\perp$ of the dijet pair to the dijet momentum imbalance $q_\perp$; its renormalization group (RG) evolution is resummed into the Sudakov factor. Likewise, the WW TMD obeys a nonlinear RG equation in $x$ that is kinematically constrained to satisfy both 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.

hep-ph↗

arXiv2024

Predictions for the sPHENIX physics program

sPHENIX is a next-generation detector experiment at the Relativistic Heavy Ion Collider, designed for a broad set of jet and heavy-flavor probes of the Quark-Gluon Plasma created in heavy ion collisions. In anticipation of the commissioning and first data-taking of the detector in 2023, a RIKEN-BNL Research Center (RBRC) workshop was organized to collect theoretical input and identify compelling aspects of the physics program. This paper compiles theoretical predictions from the workshop participants for jet quenching, heavy flavor and quarkonia, cold QCD, and bulk physics measurements at sPHENIX.

nucl-ex↗

arXiv2024

Semi-inclusive single-jet production in DIS at next-to-leading order in the Color Glass Condensate

Within the Color Glass Condensate (CGC) effective field theory, we derive the next-to-leading order (NLO) cross-section for the single-jet semi-inclusive cross-section in deep inelastic scattering (DIS) at small $x$, for both longitudinally and transversely polarized virtual photons. We provide analytic expressions, valid at finite $N_c$ and suitable for numerical evaluation, for both the cross-section differential in rapidity and transverse momentum and the cross-section differential in rapidity only. Our NLO formulae demonstrate that the very forward rapidity regime is plagued by large double logarithmic corrections coming from phase space constraints on soft gluons close to the kinematic threshold for jet production. A joint resummation of small-$x$ and threshold logarithms at single logarithmic accuracy is proposed to remedy the instability of the cross-section in this regime. By integrating over the single-jet phase space, we recover known results for the NLO DIS structure functions at small $x$, previously obtained using the optical theorem.

hep-ph↗