QCD Evolution 2026
El Escorial
Since its beginning in 2011, QCD Evolution workshop series is a leading hadron physics meeting with a focus on hadron tomography and EIC and JLaB physics.
The main aim of the QCD Evolution Workshop is to provide a forum to discuss recent scientific accomplishments in areas such as generalized parton distributions, transverse momentum distributions,, and small-x physics, together with advances in perturbative and non-perturbative techniques within QCD, such as lattice QCD and effective field theory techniques.
This workshop also aims to support and guide the physics programs at facilities such as Jefferson Lab, the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Lab, Fermi National Accelerator Laboratory, and the Large Hadron Collider (LHC) complex at CERN. The workshop is also central to the building of the next-generation nuclear physics facilities.
Special guests: I. Balitsky (ODU), V. Bertone (CEA Saclay), D. Boer (Groeningen),V. Braun (Regensburg), Y. Mehtar-Tani (BNL), A. Mukherjee (Bombay), A. Prokudin (Penn State), J. Qiu (JLAB), I. Vitev (LANL)
Registration secretary: QCD2026@pacifico-meetings.com
Abstract submission closed
Welcome cocktail on SUNDAY MAY 10th, 8pm in Casa S. José
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Welcome
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First simultaneous analysis of transverse momentum dependent and collinear parton distributions in the proton
We present the first simultaneous global QCD analysis of unpolarized transverse momentum dependent (TMD) and collinear parton distribution functions (PDFs) in the proton. Our study incorporates data from deep-inelastic scattering, Drell-Yan, inclusive weak boson, W+ charm, and jet production involving PDFs, as well as TMD Drell-Yan and Z-boson production data from fixed target and collider experiments sensitive to both TMD and collinear distributions. The analysis is performed at next-to-next-to-leading logarithmic accuracy for QCD resummation in TMD observables and next-to-leading order for observables described in collinear factorization. The combined analysis improves knowledge of both TMD and collinear PDFs, particularly in the sea-quark sector, providing a consistent simultaneous description of the aforementioned observables.
Speaker: Alexei Prokudin (PSU Berks and Jefferson Lab) -
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NNNLO QCD corrections to Semi-Inclusive Deep-Inelastic Scattering
Driven by the high-precision demands of the upcoming Electron-Ion Collider (EIC), this talk presents the computation of the next-to-next-to-next-to-leading order QCD corrections to the semi-inclusive deep-inelastic scattering (SIDIS) cross section. To systematically handle the intricate infrared singularities at this order, we introduce a novel two-dimensional transverse-momentum subtraction formalism. I will outline this theoretical framework and discuss the phenomenological impact of the corrections on key kinematic observables.
Based on the works, arXiv:2602.06364 and arXiv:2603.29673
Speaker: Haitao Li (Shandong University) -
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An overview of parton and transverse distribution functions and the quark fragmentation function
I will present an overview of parton and transverse distribution functions and their relation to an elementary quark fragmentation function within a functional approach to QCD. Recent results on light and charm quark jet fragmentation functions will be presented.
Speaker: Bruno El-Bennich (Universidade Federal de São Paulo) -
Coffe break
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The $\gamma^* \to \eta\gamma$ and $\gamma^*\to \eta'\gamma$ form factors to NNLO accuracy
We use conformal symmetry to calculate the NNLO anomalous dimension matrix (three loops) for flavor-singlet axial-vector QCD operators for spin N ≤ 8 from a set of gauge-invariant two-point correlation functions. Combining this result with the recent calculation of the two-loop coefficient functions, we carry out the calculation of the $\gamma^* \to \eta\gamma$ and $\gamma^*\to \eta'\gamma$ form factors at large timelike momentum transfers to the NNLO accuracy in perturbative QCD.
Speaker: Prof. Vladimir Braun (University of Regensburg) -
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Effect of TMD evolution on the Sivers Asymmetry at EIC
In this talk, I'll discuss the effect of TMD evolution on the Sivers asymmetry in almost back-to-back production J/psi and jet and J/psi and photon at the upcoming EIC.
Speaker: Asmita Mukherjee -
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QCD Studies with the F2A structure function
Using charged lepton and neutrino scattering data in the deep-inelastic region, we have used the F2A structure function for a number of studies relevant to QCD. These data reside considerably in the regime of particular relevance to studies of the
EMC Effect. Recently, we have been looking at (anti)shadowing region for the envisioned 20-22 GeV kinematic region. This talk will cover our work including comparative studies between charged lepton and neutrino data, EMC ratios studies with F2n, as well as the recent study in the (anti) shadowing region.Speaker: Narbe Kalantarians (Virginia Union University) -
Lunch
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Session A1: TMD in multiple observables
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DUNE as a neutrino DIS experiment
Neutrinos constitute a powerful probe for determining Parton Distribution Functions (PDFs), owing to their flavor-dependent interactions with quarks. Historically, neutrino measurements have been limited, in part, by low statistics. However, recent experimental developments are opening a new era of high-statistics neutrino–nucleus interaction measurements with enhanced final-state reconstruction capabilities, as exemplified by the Deep Underground Neutrino Experiment (DUNE). These measurements could, for example, assess emerging tensions between neutrino–nucleon and charged lepton–nucleon deep inelastic scattering (DIS) data, that potentially point toward neutrino-specific nuclear effects. In this work, we assess the potential impact of future DUNE data on improving state-of-the-art PDF determinations. Preliminary results show improvements, specially in nuclear effects.
In addition, we find that if final-state events with a charm meson can be identified, DUNE would be particularly sensitive to the strange-quark PDF.Speaker: Ángel Felipe Ballesteros (University of the Basque Country, Spain (UPV-EHU)) -
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Quark transverse-momentum effects and the W boson mass
The mass of the W boson is a fundamental parameter of the Standard Model, providing a stringent test of its internal consistency. Its precise determination increasingly relies on measurements at hadron colliders, where effects related to nucleon structure and QCD corrections play a crucial role. Transverse Momentum Dependent (TMD) distributions offer a powerful framework to describe the three-dimensional structure of hadrons; however, their impact on the extraction of the W boson mass remains insufficiently explored. This talk will discuss ongoing efforts to investigate these effects using state-of-the-art TMD parametrizations and to quantify their impact on precision determinations of the W boson mass.
Speaker: Sara Pontina (University of Turin) -
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First extraction of collinear unpolarised $\Lambda$ hyperon fragmentation functions at next-to-next-to-leading order in perturbative QCD
We present MAPFF1.0_Lambda, the first global analysis at next-to-next-to-leading order in perturbative QCD of the collinear unpolarised fragmentation functions for $\Lambda$ production. The fit is based on data from single-inclusive electron-positron annihilation and semi-inclusive deep-inelastic scattering, and both neutral and charged-current processes are included for the latter. We have adopted a statistical framework based on the Monte Carlo sampling method and parametrised the fragmentation functions in terms of a neural network for a total of 7 independent parton flavours and without imposing any constraint on the valence quarks. In particular, treating the strange quark as independent revealed its characteristic dominance over the up and down quarks. The analysed dataset together with the choice of independent flavours allowed us to extract for the first time a set of 7 fragmentation functions for $\Lambda$ and $\bar{\Lambda}$ separately, offering new insights into the hadronisation mechanism of strange baryons, and establishing a baseline for future phenomenological and experimental investigations.
Speaker: Alessia Bongallino (University of the Basque Country) -
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Next-to-leading Order QCD Factorization for Energy Flow in Electron-Ion Collisions at Twist 4
Energy-energy correlators (EECs) have recently emerged as powerful, rigorously proven infrared- and collinear-safe (IRC-safe) observables for probing QCD dynamics in the vacuum. However, their IRC safety and factorization properties in the presence of a nuclear medium have never been established. In this talk, I will present the first proof of QCD factorization at next-to-leading order (NLO), in the presence of nuclear medium, for an energy-flow observable in a real scattering process. Working within a high-twist framework, we calculate the twist-4 contributions to the angular width of the one-point energy correlator (OPEC) in semi-inclusive deep inelastic electron-ion scattering, explicitly demonstrating its IRC safety for medium-enhanced effects. We show that the OPEC angular spreading width is a highly sensitive, hadronization-free probe of transverse momentum broadening in cold nuclear matter. This NLO factorization framework establishes a critical theoretical foundation expected to be extended to a wide array of high-energy processes in nuclear environments, and paves the way for global analyses of nuclear property using OPEC.
Speaker: Omar Elgedawy (CPHT, Ecole Polytechnique) -
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In medium evolution of the energy-energy correlators
In this work we present a first-principles analysis of the scale evolution of the two-point energy-energy correlator (EEC) for quark and gluon jets propagating through QCD matter. The EEC is a jet substructure observable that encodes the angular distribution of energy flow within jets and has proven valuable for precision tests of QCD in elementary collisions. Extending this framework to reactions with nuclei, we derive a factorized description of the in-medium EEC using Soft Collinear Effective Theory with Glauber gluon interactions, allowing systematic inclusion of medium-induced interactions. Working in the opacity expansion, we compute the medium-modified quark and gluon jet functions at one loop and perform leading logarithmic resummation of large-scale logarithms. We find an experimentally accessible kinematic regime where medium effects manifest directly through medium-induced corrections to the anomalous dimensions, providing a transparent probe of in-medium dynamics. We test the theoretical framework by comparing our analytic predictions with EEC measurements in p–Pb collisions and discuss its implications for small collision systems and the EIC.
Speaker: Bianka Mecaj (Los Alamos National Lab) -
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Parton distribution and fragmentation functions with massive gluons
In this work, we compute the pion parton distribution function (PDF) and its elementary and full fragmentation functions (FFs) using the Curci-Ferrari (CF) model. This model enables the exploration of nonperturbative Quantum Chromodynamics (QCD) effects by introducing a gluon-mass scale within the Landau gauge QCD Lagrangian. The resulting pion PDF and FFs computed with the CF quark propagator and pion Bethe-Salpeter amplitude are in good qualitative and quantitative agreement with those obtained using the Qin-Chang model, a benchmark approach to nonperturbative QCD. These findings support the broader applicability of the CF model in hadron phenomenology.
Speaker: Gustavo Barbosa Bopsin (Universidade Estadual Paulista / Ecole Polytechnique)
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Coffe break
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T: Walk to the Silla de Felipe II
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Transverse momentum measurements in SIDIS with jets at next-to-leading power
We present a factorization formula for the e + h → e + jet + X cross section at small transverse momenta up to next-to-leading power (NLP), derived using the background field method (BFM) with explicit inclusion of soft modes. We discuss the relation between soft modes and overlap subtractions at NLP, showing that the inclusion of soft modes enables a definition of twist-3 operators with properly subtracted rapidity and endpoint divergences. We also derive the effective current operator at NLP and identify additional structures compared to previous approaches based on soft-collinear effective theory and the BFM without soft modes. Nevertheless, for the hadronic tensor, we find agreement at the perturbative order that we are working at, and identify a condition that needs to be satisfied for this agreement to extend to higher orders. Furthermore, we construct the most general form factors for this process, taking into account the polarization of the initial states. These involve perturbatively-calculable jet functions, opening a path to precise determinations of twist-3 hadronic distributions. Finally, our formalism is illustrated with phenomenological results for a specific azimuthal asymmetry, whose leading-logarithmic contribution depends solely on a twist-3 hadronic distribution and a twist-2 jet function.
Speaker: Max Jaarsma (JGU Mainz) -
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Collins effect in pion-in-jet production in hadron-hadron and lepton-hadron collisions
We present a phenomenological analysis of the Collins azimuthal asymmetries for pion-in-jet production in polarized $pp$ and $ep$ collisions within a TMD approach, adopting a collinear configuration for the initial state. To this aim, we employ the transversity and the Collins fragmentation functions as extracted from semi-inclusive DIS and $e^+ e^-$ annihilation processes.
After comparing our estimates for $pp$ collisions with recent STAR data, we give predictions for lepton-proton collisions for the future Electron-Ion Collider, taking into account the contribution of quasireal photon exchange.
We then show how this study could represent a further step in testing the hypothesis of the universality of the Collins function as well as of the TMD factorization for such processes.Speaker: Umberto D'Alesio (University and INFN Cagliari) -
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A neural-network extraction of TMD distributionsSpeaker: Valerio Bertone (CEA Saclay)
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Coffe break
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Interpolation between Sudakov and BFKL rapidity evolutions for TMD factorization at small x
Within the framework of rapidity-only small-$x$ TMD factorization, the evolution with respect to the rapidity cutoff is governed initially by Sudakov double-logarithmic evolution, followed by single-logarithmic BFKL/BK evolution. The evolution equation proposed in this paper correctly reproduces both the Sudakov and BFKL limits and provides a consistent interpolation between these two regimes.
Speaker: Ian Balitsky (JLab/ODU) -
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The Longitudinal Unpolarized Structure function in SIDIS: from small to large P_T
A unified description of the transverse-momentum spectrum in semi-inclusive deep-inelastic scattering (SIDIS) requires consistent matching between the low-$P_{hT}$ TMD regime and the high-$P_{hT}$ collinear regime. While this is well established at leading power for unpolarized structure functions, discrepancies arise at subleading power, where contributions may be phenomenologically significant and impact the extraction of universal TMDs.
We present a systematic study of longitudinal photon contributions within a unified framework connecting these regimes. Analyzing their behavior across the matching region, where resummed TMD dynamics transitions to fixed-order collinear factorization, we quantify their impact on unpolarized cross sections. We further investigate the longitudinal structure function $F_{UU,L}$ and the ratio $R_{\mathrm{SIDIS}}=F_{UU,L}/F_{UU,T}$ as probes of subleading dynamics. Our results clarify subleading-power effects in matching and provide constraints for global TMD analyses.
Speaker: Leonard Gamberg (Penn State University Berks) -
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Transverse momentum dependence in antiproton production from cosmic rays
We present predictions for antiproton production cross sections in proton–proton collisions, which describe the interaction of cosmic rays with the interstellar medium. The aim of the project is to test a claimed excess in the production of secondary vs primary antiprotons in pp collisions against the QCD factorization framework. We quantify the uncertainties of the involved cross sections in terms of PDFs, FFs, and missing higher orders and highlight the importance of understanding the low transverse momentum region for these specific observables.
Speaker: Andrea Signori (University of Turin and INFN) -
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Factorizing quarkonium production matrix elements using effective field theory
We use effective field theory to factorize production matrix elements that appear in the NRQCD framework for quarkonium cross sections. By applying a Hubbard–Stratonovich transformation and appropriate field redefinitions, we show that the soft and ultrasoft sectors of NRQCD can be decoupled from the heavy quark and antiquark fields in a hybrid vNRQCD/pNRQCD Lagrangian at leading order in the velocity power-counting. This enables us to re-factorize quarkonium production matrix elements in terms of matrix elements of color-singlet composite fields, which we can write as the wave-function at the origin, and state independent vacuum correlators of chromo-electric and chromo-magnetic gluon fields. This approach verifies powerful relationships between the LDMEs of different S-wave quarkonia originally derived using pNRQCD. Additionally, it allows us to derive new relationships for the production matrix elements used in the transverse momentum dependent factorization (TMD) framework, known as TMD soft transition functions, providing a much stronger set of constraints on these nonperturbative operators. This work significantly advances our understanding of quarkonium production, particularly at small transverse momentum, and should pave the way to address longstanding tensions between theory and experiment on quarkonium production cross sections at small pT
Speaker: Ivan` Vitev (LANL) -
Lunch
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Session B1: SIDIS: jets, mesons, quarkonia and data
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On the reconstruction of SIDIS observables in the Breit frame
We discuss the semi-inclusive deep inelastic scattering (SIDIS) process from a phenomenological perspective, focusing especially on the unpolarized Breit frame transverse momentum spectrum and its associated azimuthal modulations. We find that experimental measurements of the large-$P_{h\perp}$ cross section and azimuthal asymmetries may constrain the theoretical uncertainties associated with the collinear parton distributions, particularly the fragmentation functions. Additionally, we perform a case study on the reconstruction of the unpolarized cross section and azimuthal asymmetries at Jefferson Lab's Hall C, simulating its high momentum and super high momentum spectrometer acceptances. We find significant, non-trivial distortions in the reconstructed cross sections and significant systematic biases from the measured angular coverage. This result underscores the need to reframe the treatment of experimental data in global analyses through simulation-based inference.
Speaker: Richard Whitehill (Old Dominion University) -
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Hadroproduction of Pseudoscalar Heavy-Quarkonium Mesons via NRFF1.0
We investigate the inclusive hadroproduction of the pseudoscalar heavy-quarkonium mesons at high transverse momentum, focusing on the 13 TeV LHC energy scale. Our theoretical approach relies on the single-parton collinear factorization framework, where the formation of the heavy-quark bound state is described through Non-Relativistic QCD (NRQCD) at the initial scale at NLO. Central to this study is the first release of public fragmentation function sets for heavy-quarkonium species, NRFF1.0, which evolve via the DGLAP equations and account for all partonic thresholds. We present an analysis by implementing this setup within the symJETHAD multimodular interface, utilizing the NLL/NLO+ hybrid factorization framework and, within the fragmentation approximation, we use Heavy-Flavor Non-Relativistic Evolution (HF-NRevo) scheme to study the quarkonium formation. This work establishes a solid baseline for future phenomenological extensions, including the investigation of heavy-flavor fragmentation function evolution in dense media, such as the hot Quark-Gluon Plasma.
Speaker: Francesca Lonigro (UAH Madrid) -
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Matching relations for gluon TMDs up to one-loop accuracy
A fundamental ingredient for phenomenological studies of the three-dimensional (3D) momentum structure of the nucleon is provided by matching relations. These relations constrain the functional form of 3D parton distributions by connecting them to their collinear counterparts. For quark transverse-momentum–dependent distributions (TMDs), matching relations are known at one-loop accuracy, including contributions up to twist-3. In contrast, for gluon distributions such relations have so far been established only at leading twist. In this talk, I will present new results for gluon TMDs at tree level and one loop, including twist-3 contributions. At tree level, I will discuss the matching relations for both T-even and T-odd distributions, incorporating the complete series of mass corrections. At one-loop accuracy, the main result is the derivation of a Wandzura–Wilczek–type relation for the gluon worm-gear T distribution.
Speaker: Alessio Carmelo Alvaro (University of Pavia and INFN Pavia) -
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TMD from dijet production in SIDISSpeaker: Patricia Andrea Gutiérrez García (Universidad Complutense de Madrid)
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Tomography of nucleon through dimeson photoproduction
In this talk, we consider the exclusive photoproduction of a di-meson pair with large invariant mass, $\gamma N \rightarrow N' M_1M_2$, in the framework of collinear factorisation. The mesons considered $M_1$ and $M_2$ are either pions or rho mesons, charged or neutral. We consider the kinematic regime characterised by a large invariant mass of the two-meson system, and a small deflection of the nucleon in the centre-of-mass frame. In this kinematic domain, the amplitude factorises into a perturbative hard part and non-perturbative parts described by Generalised Parton Distributions (GPDs) and Distribution Amplitudes (DAs). We automate the calculation of the fully differential cross section at leading twist and leading order, and we present some numerical results at JLab 12 GeV kinematics. This class of processes provides yet more exclusive $2 \to 3$ channels that can be used to extract GPDs
Speaker: David PEREZ (IJCLab, Orsay) -
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Resummed azimuthal decorrelation and transverse momentum imbalance of dijets at the LHC
We present a theoretical study of the azimuthal decorrelation $\delta\phi$ and transverse momentum imbalance $q_T$ in dijet production at the LHC, offering intriguing insights into the dynamics of quantum chromodynamics. We define the jet axes using the recoil-free winner-take-all (WTA) recombination scheme. For the azimuthal decorrelation $\delta\phi$, this axis choice eliminates non-global logarithms (NGLs) entirely. For the transverse momentum imbalance $q_T$, NGLs emerge specifically in the small jet radius limit ($R \ll 1$). In this regime, the WTA scheme simplifies the theoretical framework by restricting jet radius logarithms to the soft sector. We derive factorization formulae for both observables within soft-collinear effective theory. To address the small-$R$ NGLs in the $q_T$ distribution, we refactorize the soft function into global soft, collinear-soft, and ultra-collinear-soft modes. We perform the resummation of global large logarithms $\ln(\delta\phi)$ and $\ln(q_T/Q)$ up to next-to-next-to-leading logarithmic accuracy. For the $q_T$ distribution, this is combined with a leading-logarithmic resummation of the non-global $\ln R$ terms. We match our predictions to leading fixed-order $\mathcal{O}(\alpha_s^3)$ calculations. We also numerically investigate the structure of the first subleading power corrections. Comparisons with \texttt{PYTHIA}~8 simulations demonstrate that the observables we consider are robust against non-perturbative multi-parton interactions and hadronization effects.
Speaker: Rong-Jun Fu (Fudan University)
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21
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Coffe break
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Session A2: Higher perturbative orders, SIDIS
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The DIS dipole picture cross section in exact kinematics
Predictions for the inclusive DIS total cross section at small $x$ are commonly obtained using the forward elastic scattering amplitude in the dipole picture. However, the usual dipole picture assumes an asymptotically large photon-proton center-of-mass energy $W$, such that the phase space of the produced partonic system at the unitarity cut remains unconstrained. In this work, we move away from the infinite-energy limit by implementing a finite-energy constraint that restricts the invariant mass of the produced partonic system by $W$. By explicitly integrating over the final-state phase space - which is possible when the optical theorem is not used - we derive the leading-order DIS cross section with a finite-energy constraint. We then quantify its phenomenological impact and find that, for $Q^2 = 1$ GeV$^2$, the constraint can modify the cross section by up to $\sim 35$% for charm quarks and $\sim 7$% for light quarks at $x = 0.01$, while the effect rapidly decreases at smaller $x$ or larger $Q^24. Our results are relevant for precision descriptions of HERA data and for future measurements at the EIC.
Speaker: Magnus Bertilsson (University of Jyväskylä) -
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Rapidity Dependent Beam Functions at NNLO
Jet vetoes are important tools that can be used to separate hard processes. A commonly used variable in which jets are identified and vetoed is the transverse-momentum of a jet. Experimentally, reconstructing small transverse momentum jets at forward rapidities is challenging, which motivates introducing a cut on a jets rapidity to reduce sensitivity to this region. Existing SCET leading-jet transverse-momentum beam functions have been used to produce partial N3LL resummed predictions for many processes but they do not include any rapidity cut.
Motivated in part by tension in the theory and experimental 0-jet WZ cross section, where the theoretical prediction does not include the rapidity cut in the jet definition used in the experimental result; we computed an addition to the SCET NNLO leading jet transverse momentum beam functions to include the effects of such a cut. Here we present this calculation and the effect of a rapidity cut on phenomenological results.Speaker: Thomas Clark (University of Manchester) -
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NNLO QCD corrections to hadron production in DIS at finite transverse momentum
We present the first complete calculation of hadron production in deep-inelastic scattering (DIS) at finite transverse momentum to next-to-next-to-leading order (NNLO) in perturbative QCD.
To overcome the long-standing challenge of infrared divergences in semi-inclusive processes with identified final state hadrons at finite transverse momentum, we implement the recently developed $q_T$-subtraction framework based on the recoil-free jet definition.
By utilizing the winner-take-all recombination scheme, we achieve a consistent factorization for hadron-jet associated production, enabling the inclusion of $\mathcal{O}(\alpha_s^3)$ corrections.
Our results demonstrate a significantly improved stabilization of the perturbative expansion and a reduction in scale uncertainties compared to previous next-to-leading order predictions.
We find that the NNLO corrections are essential for a robust description of high precision multiplicity data from the ZEUS collaborations.
This work provides a high precision theoretical foundation for the upcoming Electron-Ion Collider era and establishes a new benchmark for the exploration of the nucleon's three-dimensional structure.Speaker: Shen Fang (Fudan University)
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Excursion
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Lunch
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Session C1: Lattice and tools
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Fragmentation functions on quantum computers
The real-time phenomenology of interacting quarks and gluons remains largely beyond the reach of computational techniques based on stochastic methods due to the fermionic sign problem. As a consequence, simulations of parton dynamics—particularly their transformation into final-state hadrons through fragmentation and hadronisation—are currently not feasible with these approaches.
In this work, we present an algorithm to compute fragmentation functions on quantum computers and provide proof-of-concept simulations performed on classical hardware. Along the way, we introduce several strategies to address the challenges of the problem, all based on a codification paradigm in which particles and their internal degrees of freedom are treated as the fundamental objects.
Speaker: Juan José Gálvez Viruet (Univ. Complutense de Madrid) -
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Pionic gluons from global QCD analysis of experimental and lattice data
We perform the first global QCD analysis of parton distribution functions (PDFs) in the pion, with lattice-QCD data on gluonic pseudo--Ioffe-time distributions fitted simultaneously with experimental Drell-Yan and leading neutron electroproduction data. Inclusion of the lattice results with parametrized systematic corrections significantly reduces the uncertainties on the gluon PDF at parton momentum fractions x≳0.2, revealing a higher gluon density in the pion at large x than in the proton. The similar gluon momentum fractions in the pion and proton further suggests a relative suppression of the pion gluon density at small x.
Speaker: William Good (Michigan State University) -
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Connecting Baryon Light-Front Wave Functions to Quasi-Transverse-Momentum-Dependent Correlators in Lattice QCD
Within light-front quantization, hadrons can be represented on a Fock-space basis of configurations of elementary partons. The coefficients of the expansion are called light-front wave functions (LFWFs), and encode all the dynamical degrees of freedom. We show how to extract the LFWFs of baryons, such as the proton, from equal-time correlators suitable for Lattice QCD simulations. Using an operator product expansion, we prove the factorization of the relevant correlator in the three-quark color-singlet LFWF, a residual lattice factor, and a soft factor that systematically subtracts the additional divergences arising from the factorization. We verify up to next-to-leading order the independent renormalizability of the LFWF, and we derive the evolution equations that govern its scale dependence.
Speaker: Andrea Schiavi -
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Score-based diffusion models for lattice gauge theory and prospects for TMD/FF reconstruction
Score-based diffusion models are applied to two-dimensional SU(2) lattice pure gauge theory with the Wilson action, using a quaternion parameterization of the group manifold. Trained at a single coupling on an 8×8 lattice, the model generates configurations at different couplings via physics-conditioned sampling and generalizes to larger lattice sizes through a fully convolutional U-Net with periodic boundary conditions, reproducing exact analytical predictions with biases |Δ| ≤ 0.001 near the training point. The extension to four-dimensional non-Abelian gauge theories and the prospects for applying the diffusion model framework to the reconstruction of transverse-momentum-dependent parton distribution functions (TMD PDFs) and fragmentation functions (FFs) are discussed.
Speaker: Bao-Dong Sun (Ruhr University Bochum) -
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Quasi Parton Distribution Functions in Covariant Quark Models
Quasi-parton distribution functions (qPDFs) are defined through QCD fields at spacelike separations evaluated in matrix elements of hadrons moving with finite velocity $v$. In the limit $v \to 1$, qPDFs converge to standard parton distribution functions (PDFs). It is therefore instructive to study their properties and convergence in effective models. We present a general analysis of unpolarized quark and antiquark qPDFs in general quark models. For this class of models, we provide general proofs of the convergence of qPDFs to PDFs and of the corresponding sum rules, for both Dirac structures $\gamma^0$ and $\gamma^3$. We then use the Covariant Parton Model as an explicit example to illustrate these general results and to derive analytic expressions for the small-$x$ behavior of qPDFs and for the quark energy-momentum tensor form factor $\bar c^{\,q}(t)$ at zero momentum transfer. These results correspond to a Wandzura-Wilczek-type approximation.
Speaker: Asli Tandogan (University of Connecticut) -
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qT/Q corrections for unpolarized Drell-Yan in TMD factorizationSpeaker: Arturo Arroyo Castro (Universidad Complutense de Madrid)
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30
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Coffe break
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Session A2: Higher perturbative orders, resummations
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36
NNLO extraction of Unpolarized Di-hadron fragmentation Functions
Di-hadron Fragmentation Functions (DiFFs) provide a unique tool to probe the chiral-odd transversity parton distribution in a collinear framework. Current determinations of transversity using this approach are performed at leading-order (LO) accuracy, so achieving higher precision requires extending the extraction of DiFFs beyond LO. In this presentation, I will report a new extraction of the unpolarized DiFF up to NNLO accuracy, employing both a physics-informed parametrization and a neural network approach. If available, I will also discuss preliminary results from the ongoing work on the NLO extraction of the polarized chiral-odd DiFF that partners the chiral-odd transversity.
Speaker: LUCA POLANO (University of Pavia, Istituto Nazionale di Fisica Nucleare) -
37
From Collinear to TMD Distributions in the Large-x Regime
This talk addresses the large-x behavior of Transverse Momentum Dependent distributions (TMDs) through the resummation of leading logarithmic corrections to their collinear matching coefficients. Rather than working at the process level, resummation is carried out directly within the TMD framework, thereby maintaining process-independence. A notable feature of this approach is its extension to distributions that match onto twist-three collinear Parton Distribution Functions (PDFs), a class not previously treated in this context. General resummation formulas are derived for all leading power TMDs, encompassing both TMDPDFs and TMDFFs, with the sole exception of the pretzelosity distribution, whose connection to a twist-four operator places it beyond the scope of the current framework. A key outcome is that the resummation accuracy achieved here reaches N3^3LL, exceeding existing fixed-order results for several distributions. Beyond formal developments, these results have direct phenomenological impact: they accelerate perturbative convergence, provide systematic estimates of higher-order corrections, and help constrain non-perturbative inputs, offering a well-founded basis for the analysis of TMD-sensitive processes.
Speaker: Óscar del Río García (Universidad Complutense Madrid)
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36
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Session C2
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Gluon production at small-x
We discuss the new derivation of the linear but with complicated kernel and non-homogeneous evolution equations for the cross sections of productions of $n$-cut Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomerons in the final states of high energy DIS on a nucleus, resumming all multiple rescatterings and all leading logarithms of energy. These equations coincide with the equations that have been derived using the Abramovsky, Gribov and Kancheli (AGK) cutting rules but based on the dipole approach to QCD. In the second part of the talk we discuss approximate analytical solutions for the equations in the small-$n$ and large-$n$ approaches and compute the multiplicity distribution for the produced gluons, their probability to be found and the entropy content of the multiplicity distribution for the large-$n$ solution at high values of the geometric scaling variable $z=\ln(r^2 Q_s^2)$.
Speaker: José Garrido (Federico Santa María Technical University)
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All-Orders Evolution of Parton Distributions
Parton distribution functions (PDFs) are defining expressions of hadron structure. Exploiting the role of effective charges in quantum chromodynamics, an algebraic scheme is described which, given any hadron's valence parton PDFs at the hadron scale, delivers predictions for all its PDFs (unpolarized and polarized) at any higher scale. The scheme delivers results that are largely independent of both the value of the hadron scale and the pointwise form of the charge; and, inter alia, enables derivation of a model-independent identity that relates the strength of the hadron's gluon helicity PDF, to that of the analogous singlet polarized quark PDF and valence quark momentum fraction.
Speaker: José Rodríguez Quintero (Universidad de Huelva) -
40
The Fate of Ultra-Collinear Modes in On-Shell Massive Sudakov Form Factors
Individual multi-loop diagrams for the massive Sudakov form factor contain an infinite tower of ultra-collinear momentum regions. We show that, for the on-shell form factor in QCD, these contributions cancel to all orders as a consequence of gauge invariance, so the leading-power SCETII factorization formula is unchanged. Using the η rapidity regulator, we compute the soft function and the massive jet function of the quark and gluon Sudakov form factors through two loops and resum logarithms at NNLL accuracy, including hierarchies of fermion masses. We also show that with a gauge-boson mass regulator, the infinite tower of modes is truncated and ultra-collinear and ultra-soft modes become manifest and factorize explicitly, providing a direct EFT derivation of the regulated infrared dependence.
Speaker: Jacob Schönleber (Technical University Munich) -
41
Azimuthal asymmetries in lepton and heavy-quark pair production in UPCs
Azimuthal modulations in electron-positron pair production in ultraperipheral collisions (UPCs) of gold ions have been observed by the STAR collaboration at RHIC. The modulations arise from the collisions of unpolarized and polarized photons emanating from the highly charged ions. In this talk the theoretical description in terms of Generalized Transverse Momentum Dependent parton distributions (GTMDs) of photons inside ions will be discussed. From this description it can be understood that in principle harmonics of all (even) orders will arise. From a model that is able to describe the RHIC data, it furthermore follows that the results depend considerably on the mass of produced particles. The most promising channels to experimentally demonstrate this in UPCs at RHIC and LHC will be discussed. This talk is based on work done together with Cristian Pisano and Luca Maxia, published in JHEP01(2025)076.
Speaker: Daniel Boer (University of Groningen) -
Coffe break
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42
Probing TMDs through double quarkonium production in hadronic collisions
Transverse momentum dependent parton distribution functions (TMDs) encode essential information on the transverse motion of partons inside nucleons, as well as their spin-orbit correlations. In this talk I will show how, by looking at the azimuthal asymmetries in the inclusive production of pairs of vector quarkonia, one can probe different TMDs. In particular, quark and antiquark TMDs could be accessed in pion-proton scattering at the COMPASS and AMBER experiments at CERN, where the contributions of gluons is negligible. The impact of the present and future fixed-target experiments at the LHC (SMOG, LHCspin) on this kind of studies will be discussed as well. This work is mainly based on work done together with Carlo Flore, published in JHEP 02 (2026) 085.
Speaker: Cristian Pisano -
43
Evolution and Transversely Polarized processes: a Sivers function determinationSpeaker: Filippo Delcarro (INFN Torino)
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44
Nuclear corrections to Deeply Virtual Compton Scattering
We present a systematic study of nuclear-enhanced power corrections in deeply virtual Compton scattering (DVCS) on nuclear targets, extending techniques developed for inclusive deep inelastic scattering to exclusive processes. Using a light-cone operator product expansion and the method of regions, we identify coherent final-state interactions of the struck quark as the dominant source of higher-twist nuclear modifications. These contributions can be resummed to all orders, leading to compact expressions for the DVCS amplitude characterized by a single nonperturbative scale and enhanced by nuclear size effects. Our formalism provides a controlled framework for quantifying nuclear modifications to generalized parton distributions at small momentum transfer and moderate photon virtuality. The results establish a direct theoretical connection between inclusive DIS dynamics and exclusive nuclear observables, with important implications for three-dimensional imaging of nuclei at future facilities such as the Electron–Ion Collider.
Speaker: John Terry (LANL) -
Session A1
- 45
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Lunch
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46
From Sub-eikonal DIS to Quark Distributions and their High-Energy Evolution
I show that the first sub-eikonal correction reproduces the standard quark and helicity light-ray operator structure of DIS and, in the inclusive limit, recovers the corresponding distributions at nonzero Bjorken $x_B$. I then derive dipole-form expressions for the corrections to $F_L$, $F_T$, and $g_1$, and identify the relevant operator combinations in the singlet and non-singlet sectors.
The operator basis thus obtained is naturally organized in terms of dipole operators that vanish in the zero-size limit, making unitarity and small-dipole behavior manifest. I further show that the logarithmic singularities of the sub-eikonal correction to the dipole structure functions are precisely the one-loop evolution of the quark and helicity light-ray operators. In the double-logarithmic approximation, I recover the Kirschner-Lipatov exponent and clarify its relation to previous small-$x_B$ helicity resummations.
Speaker: Giovanni Antonio Chirilli (National Centre for Nuclear Research (NCBJ), Warsaw) -
Session B2: GPD
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47
Computation of NLO evolution equations of GPDs in the lightcone gauge
We present our ongoing calculation of the next-to-leading order evolution equations for Generalized Parton Distributions (GPDs) in the flavour-non-singlet sector. We discuss the advantages and challenges associated with the use of the lightcone gauge. We show how the calculation can be automated using a set of analytically computable master integrals. The (spurious) rapidity divergences appear at the intermediate stage due to gluon propagators in the lightcone gauge. We explicitly prove their cancellation between different diagrams providing a strong consistency check.
Speaker: Oskar Grocholski (IRFU/CEA, France) -
48
Constraining QCD energy-momentum tensor via dispersion relations
Quantum Chromodynamics (QCD) is the theoretical framework to study hadrons by means of their fundamental degrees of freedom, i.e. quarks and gluons, collectively referred to as partons. QCD defines many types of distributions describing a given hadron in terms of partons and, for the purposes of this talk, we are interested in the so-called generalized parton distributions (GPDs). These ones are off-forward matrix elements of parton operators whose convolutions with kernels describing the interactions at the partonic level are named Compton form factors (CFFs). Real and imaginary parts of CFFs are related by dispersion relations (DRs). At the lowest order approximation, DRs relate the CFFs (accessible in experiments of exclusive scattering) to the pressure inside the hadron. In a recent publication, we showed that by including kinematic power corrections (twist effects), DRs also allow to extract distributions of angular and linear momentum. These results bypass the calculation of moments of GPDs for accessing these properties, which typically requires either their modelling or lattice simulations; and conect the mechanical properties of hadrons to experimentally measurable quantities (the CFFs). In this talk, I will present my latest work in the topic after review of the concepts of exclusive scattering and twist.
Speaker: Victor Martinez Fernandez (IRFU/CEA (France) and CFNS (USA))
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47
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Session B2
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49
Unpolarized twist-two GPDs and the role of different IR regulators
We present a one-loop perturbative study of unpolarized twist-two generalized parton distributions (GPDs) of quarks for external on-shell gluon states. A finite quark mass m is kept throughout the calculation and serves as an infrared regulator, allowing us to study the collinear limit of the GPDs. We also analyze this limit using dimensional regularization to regulate infrared divergences, and we discuss the implications of our results for the box diagram in deeply-virtual Compton scattering. Furthermore, by taking the second Mellin moment of the GPDs, we extract the associated form factors of the energy-momentum tensor (EMT) in both QED and QCD, with a special focus on the trace of the EMT. Particular attention is also given to potential anomaly-related pole contributions. This analysis complements our previous work on polarized twist-two GPDs and the axial anomaly.
Speaker: Ignacio Castelli (Temple University) -
50
A Finite Element Method Analysis of Shadow Ambiguities in Generalized Parton Distributions
Generalized Parton Distributions (GPDs) and the exclusive processes that probe them present an important insight into hadronic structure. However, extracting GPDs from experimental data constitutes a challenging inverse problem. In this work we revisit the Finite Elements Method (FEM) to study GPDs via their double distribution (DD) representation, focusing on the Radon transform that connects DDs to GPDs. We investigate the existence and structure of "shadow" double distributions, DD functions whose associated physical observables all vanish identically, yet when added to physical DDs, can modify the GPD in the entire kinematic domain. Using the FEM discretization of the DD support, we quantify how experimental constraints, particularly measurements at different x and ξ values, progressively reduce the shadow DD solution space. This analysis reveals the fundamental relationship between experimental precision and the theoretical resolution with which we can reconstruct GPDs, providing a framework for optimizing future experimental programs targeting hadronic structure.
Speaker: Marija Čuić (Irfu, CEA, Université Paris-Saclay/Aidas)
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49
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Coffe break
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Session C2
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51
Conformal moments of the two-loop coefficient functions in DVCS
I introduce a new technique to calculate the conformal (Gegenbauer) moments of two-loop coefficient functions in DVCS and present selected results. These are necessary for GPD extractions within a Mellin-Barnes approach.
Speaker: Patrick Gotzler -
52
Momentum-Space BK Evolution with RG-Improved Resummation and Kinematical Constraints
We perform an analysis of the BK evolution equation formulated in momentum space, supplemented by higher-order resummation corrections motivated by renormalization group improvements and the kinematical constraints. The equation is solved over a wide range of transverse momenta and longitudinal momentum fractions using GPU-optimized numerical computation. The solutions are fitted to HERA data, allowing us to extract the unintegrated gluon density over a broad momentum range. The pattern of the resulting saturation scale obtained from the gluon density shows behavior consistent with the expected QCD evolution map.
Speaker: Wanchen Li (Fudan University)
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51
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Session B3
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53
TMD factorization for massive quark production in photon-nucleus collisions
We study the diffractive production of a massive quark pair in coherent photon-nucleus collisions within the Color Glass Condensate framework. We work in the correlation limit, where we explicitly distinguish between hard and semi-hard scales. In a first study, we consider the emission of an unmeasured semi-hard gluon with transverse momentum of the order of the saturation scale by the massive quark pair. In this regime, the differential cross section factorizes into a mass-dependent hard factor, which describes the formation of the quark-antiquark, and the diffractive gluon transverse momentum dependent (TMD) distribution. In a second study, we consider the production of a semi-hard quark and a hard antiquark and gluon, which have transverse momenta much larger than the saturation scale. We then factorize the differential cross section into a mass-independent hard factor and a mass-dependent quark diffractive TMD distribution. Our results are the base for future phenomenology predictions for quarkonium and open charm production in the saturation regime in ultraperipheral collisions at the LHC.
Speaker: Patricia Gimeno-Estivill (University of Jyväskylä) -
54
Extraction of quantum interference within the protonSpeaker: Guillermo Portela Maller (Universidad Complutense de Madrid)
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53
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55
Workshop Dinner: Restaurante La Rueda, Av. de la Constitución, 41, 28280 El Escorial
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39
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56
A Pixel-Based Bayesian Approach for Model-Independent TMD Reconstruction
The extraction of Transverse Momentum Dependent distributions (TMDs) from experimental data is a fundamental inverse problem in hadronic physics. Traditionally, this challenge is addressed by assuming specific analytical functional forms. However, these choices can introduce a parameterization bias and limit our ability to explore the full uncertainty of the results. In this talk, we present a novel "Pixel-Based" approach that treats TMD imaging as a discrete reconstruction task. By formulating the TMD convolutions through discrete tensor algebra, we treat each pixel in the impact parameter $b_T$-space as a stochastic variable. This framework allows for a non-parametric reconstruction of the TMDs within a robust Bayesian inference scheme. To efficiently sample the high-dimensional posterior distribution of the pixels, we employ modern Machine Learning techniques, specifically Normalizing Flows. We focus on a systematic study of the resolution limits and stability of this inversion process. By analyzing the resolution matrix in $b_T$-space, we quantify how different kinematic coverages and experimental precision constrain the underlying 3D structure. This work serves as a proof-of-concept for a low-bias imaging framework, establishing a solid foundation for model-independent extractions of nucleon structure.
Speaker: Marco Zaccheddu (Jefferson Lab) -
57
Fast next-to-leading order evolution of generalized parton distributionsSpeaker: Adam Freese (Center for Nuclear Femtography)
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58
Digging into the deep infrared with TMDs
Extracting information on the three-dimensional structure of hadrons from transverse-momentum data is a challenging task, as it requires disentangling well-controlled perturbative contributions from genuinely non-perturbative effects, which are unavoidably influenced by phenomenological assumptions. This subtle interplay often obscures the interpretation of phenomenological analyses, even when they provide an accurate description of experimental data. In this talk, I present a systematic procedure to analytically continue perturbative calculations into the deep infrared region, below the 1–2 GeV scale. I identify two primary sources of non-perturbative effects: the low-energy behavior of the strong coupling and that of the parton distribution functions. This framework turns transverse-momentum-dependent observables into a privileged probe of strong interactions in a poorly understood regime, offering novel insights into the strong coupling and PDFs where they are least constrained.
Speaker: Andrea Simonelli (Jefferson Lab and ODU) -
Coffe break
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59
The Cahn Effect and Equation of Motion Relations
I investigate proton structure through the subleading observable called the Cahn effect. Equation of motion relations constrain the TMDs in the observable and relate them to leading power TMDs. I calculate the relevant functions and verify the equation of motion relation at LO and NLO in the strong coupling. In the calculation I show the cancelation of rapidity divergences using a novel regulator associated with the lightcone propagator. These calculations are necessary to study the large qT matching, particularly in the context of the independence of the observable on rapidity divergent terms.
Speaker: Owen Page (Pennsylvania State University) -
Session C2
- 60
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61
Rapidity regulators for low x QCD
In recent years, numerous studies have aimed at improving the precision of the theoretical description of the nonlinear QCD regime of gluon saturation in high-energy collisions, in order to match the precision of the data coming from the LHC and the future EIC. In particular, NLO QCD corrections have been calculated for many high-energy processes sensitive to gluon saturation.
In most of such NLO calculations, the chosen regularization procedure is dimensional regularization for the transverse integrals complemented by a naive cut-off for the light-cone momentum k^+ integrals. Although convenient in that context, this regularization procedure has disadvantages. On the one hand, it does not allow us to disentangle soft and rapidity divergences, which are then both regulated by the cut-off. On the other hand, it complicates the comparison with results obtained in other formalisms for QCD valid in different kinematical regimes, for example collinear or TMD factorizations, which typically use other regularization schemes.
As an alternative, we discuss how to implement in these NLO gluon saturation calculations various rapidity regulators similar to the ones used by the TMD or SCET communities. As a first application and consistency check, we revisit the calculation of the NLO corrections to the DIS structure functions at low x in the dipole factorization approach, now with these rapidity regulators together with dimensional regularization. When combining the results from all diagrams, we find as expected that the UV divergences are canceling each other, as well as the soft divergences. The only surviving divergence is the rapidity divergence associated with the Balitsky-Kovchegov evolution of the dipole operator.
Among the finite NLO corrections to the structure functions, the ones which are found to depend on the rapidity regularization scheme are compatible with the expected scheme dependence concerning the choice of evolution variable for the BK equation. This suggests that choosing one of the three rapidity regulators we propose amounts to choosing the precise evolution variable in the definition of the low x evolution: light-cone momentum k^+ or k^- or rapidity.
Speaker: Guillaume Beuf (National Centre for Nuclear Research (NCBJ), Warsaw) -
62
QCD–QG Duality and Discrete BFKL Evolution in Multi-Regge Kinematics
QCD–QG Duality and Discrete BFKL Evolution in Multi-Regge Kinematics We present a novel approach to computing duality relations between Quantum Chromodynamics (QCD) and Quantum Gravity (QG) in the Multi-Regge Kinematics (MRK) limit. This framework leverages Mathematica-based tools—FeynArts, FeynCalc, and FeynGrav—with a new implementation that integrates FeynGrav into FeynArts, enabling significantly faster generation of QG diagrams. We outline the procedure through which duality relations naturally emerge, focusing on the conceptual structure rather than technical detail. Within the same MRK framework, we also present recent results on a discretized formulation of the BFKL equation. By constructing recursion relations, we describe the evolution of the gluon Green function and establish a connection with the Knizhnik–Zamolodchikov equation. This approach reveals the appearance of Harmonic Polylogarithms and leads to a direct link with anomalous dimension coefficients, which we successfully recover within our formalism.
Speaker: Josep Rubi Bort (IFT)
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Lunch
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56