Resummation, Evolution, Factorization 2025

13 Oct 2025, 13:30 → 17 Oct 2025, 13:30 Europe/Rome

Sala Consiglio (Physics Department, Milan University)

Giancarlo Ferrera (Istituto Nazionale di Fisica Nucleare)

REF 2025 is the 12th edition in the series of workshops on Resummation, Evolution and Factorization. 

The workshop brings together specialists in different areas, from effective field theory to lattice to QCD factorization methods. The main focus will be on transverse momentum dependent distributions (TMDs) and their connection with Monte Carlo event generators, as well as on the experimental measurements aimed at extracting information on TMDs at present and future colliders. The interplay between the factorization theorems, resummation of large logarithms, and the corresponding evolution equations are crucial for higher precision calculations, necessary not only for understanding the data recorded by past and present facilities, such as the LHC, HERA and Belle, but especially for future experiments, such as HL-LHC, EIC, and FCC.

 

The 2025 edition of REF will be hosted at the Department of Physics, University of Milan and INFN, in Milan (Italy), from October 13th to 17th, 2025. To facilitate travel for those in Europe, the workshop will start on Monday at 14:00 and finish on Friday at the end of the morning session.

 

Organizing Committee:

Giancarlo Ferrera (Milan U. and INFN)

Stefano Forte (Milan U. and INFN)

Francesco Hautmann (Oxford U.)

Raoul Röntsch (Milan U. and INFN)

Lorenzo Rossi (Milan U. and INFN)

Alessandro Vicini (Milan U. and INFN)

Marco Zaro (Milan U. and INFN)

 

Advisory Board:

E. Aschenauer, A. Bacchetta, A. Bermudez Martinez, D. Boer, I. Cherednikov, M. Diehl, M.G. Echevarria, L. Favart, E. Gardi, F. Gelis, F. Hautmann, K. Kutak, N. Raicevic, G. Schnell, I. Scimemi, A. Signori, P. Van Mechelen

 

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This year's event is sponsored by:

Department. Physics "Aldo Pontremoli"   University of Milan

National Institute for Nuclear Physics (INFN)

 

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Previous meetings:

14-18 October 2024, Saclay (France)

23-27 October 2023, Madrid (Spain)

31-4 November 2022, U Montenegro Online

15-19 November 2021, Hamburg Online

7-11 December 2020, Edinburgh Online

25-29 November 2019, Pavia (Italy)

19-23 November 2018, Krakow (Poland)

13-16 November 2017, Madrid (Spain)

7-10 November 2016, Antwerp (Belgium)

2-5 November 2015, Hamburg (Germany)

8-11 December 2014, Antwerp (Belgium)

23-24 June 2014, Antwerp (Belgium)

Monday 13 October

Registration

Opening

Monday: Afternoon 1

1 Energy Correlators in High Energy Nuclear Physics

In recent years, energy-flow (light-ray) operators have emerged as a common language linking theory and experiment for mapping the dynamics of quantum field theories. In this talk, I will survey how multi-point energy correlators are used to characterize QCD matter in high-energy scattering, with emphasis on processes involving nuclear targets. I will review the theoretical status of light-ray correlation functions—including factorization, evolution, and medium-induced modifications—and summarize the corresponding experimental measurements. I will then argue that these observables provide controlled access to (non-vacuum) non-trivial quantum states, offering a bridge between collider phenomenology and formal developments in quantum field theory (including CFTs) where such states remain poorly understood.

Speaker: Joao Barata (CERN)

25_REF.pdf

2 Quantum Scaling in Energy Correlators: Perturbative and Non-perturbative Aspects

In this talk, I will first review the collinear factorization of energy correlators in perturbative QCD and introduce the light-ray operator product expansion formalism. We generalize this framework to describe both hadronization corrections in the pre-confinement (perturbative) regime as well as the post-confinement (free hadron) regime. Based on these results, we will propose a conjecture formula for the collinear EEC.

Speaker: Hao Chen

REF2025_Hao_Chen.pdf

3 TMDs: Twist-2 Matching, Observables, and High-Energy Evolution

We report on the N3LO twist-2 matching of polarized TMDs along with all N3LO polarized DGLAP kernels. Various qt-observables such as SIDIS qt, lepton-jet TEEC and dijet-TEEC are obtained at N3LL accuracy. Work towards precision small-x physics is also addressed based on Liptov Reggeon Field Theory and Glauber SCET.

Speaker: Yu Jiao Zhu (Max-Planck Institute for Physics)

REF_Zhu.pdf

15:30 Coffee Break

Monday: Afternoon 2

4 On the N3LO contributions to the PDF scale evolution

The four-loop DGLAP splitting functions are a key ingredient to control the scale evolution of the PDFs to N3LO accuracy in QCD. I present results for the first 10 moments of the four-loop splitting functions. I discuss the approximate N3LO PDF evolution, based on the computed moments and on the known information on the asymptotic limits of the splitting functions, and its relevance for LHC physics.

Speaker: Giulio Falcioni (University of Torino and University of Zürich)

falcioni.pdf

5 Perturbative RGE systematics in precision observables

QCD calculations for collider physics make use of perturbative solutions of renormalisation group equations (RGEs). Ambiguities related to these solutions can contribute significantly to systematic uncertainties of theoretical predictions for physical observables.
We propose a general method to estimate these systematic effects using techniques inspired by soft-gluon and transverse-momentum resummation approaches.
We first discuss the cases of the evolution of strong coupling αs, collinear parton-distribution functions (PDFs), and transverse-momentum-dependent distributions (TMDs).
We then study the implications for precision observables in hadron-collider processes, such as the deep-inelastic scattering structure functions and the transverse-momentum distribution of the lepton pair in Drell-Yan production.

Speaker: Giuseppe Bozzi (University of Cagliari and INFN, Cagliari)

Bozzi.pdf

6 N$^{3}$LO fits to DIS HERA data using the xFitter framework

We investigate the impact of recently computed N$^{3}$LO corrections to QCD splitting and DIS coefficient functions on global fits of Parton Distribution Functions (PDF) using the xFitter framework. By comparing fits performed at different perturbative orders, we analyze the modifications introduced to PDFs and their associated uncertainties, incorporating correlated experimental errors. Additionally, the effects of various approximations for splitting functions are assessed, providing a basis for estimating theoretical uncertainties. The results show the importance of the N$^{3}$LO corrections and the need for further theoretical refinement in the low-$x$ regime.

Speaker: Dr Francesco Giuli (Istituto Nazionale di Fisica Nucleare)

FGiuli_REF2025.pdf

Welcome Cocktail

Tuesday 14 October

Tuesday: Morning 1

7 Implementation of TMD non-perturbative effects in RadISH

In this work, we incorporate transverse momentum dependent (TMD) non-perturbative (NP) effects into the RadISH framework.
By accounting for these effects, we achieve an improvement in the theoretical description of the Drell-Yan cross section at low $p_{T, \ell \ell}$ (the transverse momentum of the final-state lepton pair).
A similar effect is observed in the $\phi_{\eta}^*$ differential cross section, where $\phi_{\eta}^*$ is a variable sensitive to the angular separation between the two outgoing leptons.
The inclusion of NP effects in RadISH is expected to play a significant role in the analysis of high-energy particle collisions.

Speaker: Yiyu Zhou (University of Turin)

RadISH-with-NP-2025-REF.pdf

8 On the PB Sudakov: NNLL coefficient, CS kernel and intrinsic-kt

The TMD Parton Branching (PB) method was developed to include elements of the TMD physics in MC generators. Its relation to stringent CSS formalism remained initially unclear. In this talk, we shed light on the relation of the PB Sudakov form factor to that of CSS. We discuss both perturbative and non-perturbative components. We present recent developments to include NNLL coefficient in the PB Sudakov. We discuss the CS kernel extractions for different evolution scenarios. We discuss the recent studies on intrinsic-kt vs center-of-mass (in)dependence in different approaches and their relation to the non-perturbative Sudakov.

Speaker: Aleksandra Lelek (University of Antwerp)

REF-FINAL.pdf

9 TMD evolution and intrinsic k_T in MC generators

The parton branching (PB) method allows using TMD evolution with standard
Monte Carlo event generators, replacing the current approximate treatment of initial state radiation with a rigorous prediction from first principles. A key parameter of PB is the intrinsic $k_\mathrm T$, which governs the low-scale behaviour of the TMD. In its first extraction from collider data, tensions appeared between experiments. We discuss their origin and consequences on the extraction of TMD parameters from high-energy collider data.

Speaker: Louis Moureaux (Universität Hamburg)

Moureaux_PB_TMD.pdf

10:00 Coffee Break

Tuesday: Morning 2

10 First Neural-Network Extraction of Unpolarized Transverse-Momentum-Dependent Distributions

We present the first extraction of transverse-momentum-dependent distributions of unpolarized quarks from experimental Drell-Yan data using neural networks to parametrize their nonperturbative part. We show that neural networks outperform traditional parametrizations providing a more accurate description of data. This work establishes the feasibility of using neural networks to explore the multi-dimensional partonic structure of hadrons and paves the way for more accurate determinations based on machine-learning techniques.

Speaker: Dr Matteo Cerutti (CEA Paris-Saclay)

Cerutti_REF.pdf

11 On the sensitivity of energy-energy correlation to TMD dynamics

The transverse momentum dependent factorization framework provides for energy-energy correlation in the back-to-back limit the highest order result ever achieved in perturbation theory: N$^4$LL+N$^3$LO.

We implemented this setup, using the $\zeta$-prescription within ARTEMIDE's code, to study the possibilities of obtaining information on the Collins-Soper kernel and the strong coupling constant through a global fit to all available experimental data .

Speaker: Alejandro Bris (Universidad Complutense Madrid - IPARCOS)

AlejandroBris-REF_2025.pdf

12 Kinematic Power Corrections in TMD factorization

In this talk, I present a study of Drell-Yan (DY) and semi-inclusive deep inelastic scattering (SIDIS) structure functions within the framework of the transverse momentum dependent (TMD) factorization theorem, including kinematic power corrections (KPCs). This formalism enables us to describe parts of the cross-section that were previously inaccessible to theory in a Lorentz-invariant manner using only twist-two TMD distributions. Applications include Drell-Yan (DY) angular distributions, the Lam-Tung relation, and the subleading structure functions $F_{UU,T}$ and $F_{UU,L}$. I also discuss the potential impact of these corrections on current and future SIDIS measurements.

Speaker: Sara Piloñeta (Complutense University of Madrid)

Piloñeta_REF_2025.pdf

13 New insights on partonic Sivers distribution

We present an extraction of Sivers TMDs from an updated set of DY and SIDIS asymmetries using the MAP framework

Speaker: Filippo Delcarro (Istituto Nazionale di Fisica Nucleare)

Delcarro REF 2025.pdf

12:10 Lunch Break

Colloquium

14 Factorization (or not)?

Factorization is one of the central organizing principles in Quantum Chromodynamics (QCD) and, more broadly, in all of physics. It allows us to separate dynamics occurring at different energy, length, or time scales — turning complex problems into manageable ones and enabling precise predictions at collider experiments such as the LHC.

At the core of this framework lies the factorization of collinear singularities, which leads to the universality of parton distribution functions (PDFs). This universality is what allows us to describe a wide range of high-energy processes with the same non-perturbative input,
providing the essential bridge between theory and experiment in QCD.

In this talk, I will focus on how and why factorization can break down when two partons become collinear, particularly in space-like configurations relevant to hadron–hadron collisions. Using explicit one- and two-loop results, I will show how color correlations among
non-collinear partons lead to subtle violations of collinear factorization, and how these effects challenge the strict universality on which modern QCD predictions are built.

The discussion will also address the physical implications of these violations — such as the appearance of “super-leading” logarithms in hadronic cross sections — and the delicate mechanisms through which QCD may restore factorization at the observable level.

Speaker: Daniel de Florian (UNSAM)

deflorian.pdf

15:15 Coffee Break

Tuesday: Afternoon 2

15 Generalization of collinear factorization in perturbative QCD

We consider the most general factorization properties of scattering amplitudes in perturbative QCD in both collinear and collinear-soft limits. While scattering amplitudes obey strict collinear factorization (SCF) in the time-like collinear region to all perturbative orders, SCF is known to break in the so-called space-like collinear region. We generalize previously known results of SCF breaking to more than one collinear direction. We also extend our analysis to the simultaneous collinear-soft factorization.

Speaker: Prasanna Kumar Dhani (University of Zurich)

Dhani@REF25.pdf

16 Low-energy theory of jet processes and PDF factorization

Factorization theorems for non-global observables at hadron colliders can be used to resum super-leading logarithms (SLLs). These SLLs are closely related to collinear factorization breaking and are driven by a double-logarithmic evolution equation in an effective field theory. The compatibility of this double-logarithmic evolution with single-logarithmic PDF evolution at low scales implies stringent consistency conditions on the low-energy matrix element of this effective theory. By analyzing these contributions at the three-loop order, I will show consistency with PDF factorization. The crucial element for factorization is a genuine Glauber contribution which first arises at this order.

Speaker: Dominik Schwienbacher (University of Bern)

REF_Schwienbacher.pdf

Discussion on Future Measurements

ERF_LHCb.pdf

FGiuli_futureDY_141025.pdf

moureaux.pdf

Documentary

17 Touschek with AdA in Orsay

Projection of the documentary with the introduction of Giulia Pancheri

Pancheri-Touschek.pdf

Wednesday 15 October

Wednesday: Morning 1

18 Top-antitop production and decay near threshold

Speaker: Paolo Nason (Istituto Nazionale di Fisica Nucleare)

nason.pdf

19 Towards Next-to-Leading-Log corrections in High Energy Jets

The High Energy Jets (HEJ) framework maintains constraints of a full QCD amplitude - such as crossing symmetry, gauge and Lorentz invariance - and adds a leading high energy logarithmic resummation. We recently showed that this leads to an excellent description of measurements at large invariant mass, where approaches without high energy logarithmic considerations fail to obtain a reasonable description. In this talk, I will describe how to include Next-to-Leading-Log corrections to the jet impact current, while maintaining the analytic properties mentioned before. This approach requires the preservation of the full two-jet NLO infrared structure. This ultimately allows for the direct application of standard regularization methods. For HEJ the plan is to utilise the FKS subtraction scheme.

Speaker: Malina Rosca

REF 2025 - MRosca.pdf

20 A parton shower consistent with parton densities at LO and NLO: PDF2ISR

We present a method for obtaining an initial-state parton shower model where the (backward) evolution fully consistent with the (forward) evolution of the collinear parton density used. As a proof-of-concept we use parton densities obtained with the Parton Branching (PB) approach, and modify the default initial-state shower in PYTHIA8 with this method to be consistent with them. PB is ideally suited for checking the validity of our method since, in addition to producing collinear parton densities, it also produces the corresponding transverse-dependent (TMD) ones, and these can then be directly compared to the transverse momentum distribution obtained from the parton shower. We show that TMD distributions which we in this way obtain from our modified PYTHIA8 shower using leading order (LO) parton densities and splitting functions are fully consistent with the corresponding leading order TMD densities. At next-to-leading order (NLO) it is not possible to achieve the same consistency using the built-in LO splitting functions in the shower, but we show that by introducing NLO splitting functions using a reweighting procedure, we can achieve consistency also at NLO. The method presented here, which we have named PDF2ISR, can be easily extended to any collinear parton densities, as long as the exact conditions for the evolution are known. With the PDF2ISR method we obtain an initial-state parton shower which in principle has no free parameters, and is fully consistent with collinear parton densities at LO and NLO.

Speaker: Mikel Mendizabal (DEST)

REF2025_Mikel.pdf

10:00 Coffee Break

Wednesday: Morning 2

21 Phenomenology of heavy flavour jet angularities at hadron colliders

I will present resummed and matched predictions for jet angularities in hadronic $Z+$jet events, where the jet is initiated by a $b$ quark. The analysis is performed both with and without grooming the candidate jets using the Soft drop algorithm. Mass effects are consistently included at both fixed-order and resummed levels and our theoretical predictions also incorporate non-perturbative corrections from the underlying event and hadronisation.
We compare our results with previous implementations in the Sherpa resummer plugin and show the impact of mass effects.

Speaker: Lorenzo Mai (University of Genova & INFN)

LM_REF_2025_Milan.pdf

22 Heavy-hadron production based on $k_t$-factorization with scale-dependent fragmentation functions

We present a comprehensive study of heavy-hadron production, including $D$ and $B$ mesons, heavy baryons, and the $B_c$ meson. Our calculations are based on the $k_t$-factorization and scale-dependent fragmentation functions, completing the program of implementing this formalism within a variable-flavor-number scheme, as initiated in Phys. Rev.D 104 (2021) 9 094038. Special emphasis is placed on the gluon-to-heavy-hadron contribution, which improves the description of data at small transverse momenta.

Speaker: Benjamin Guiot (Universidad federico santa maria)

REF25.pdf

23 Double quarkonium production in hadronic collisions: quark polarization and TMD effects

We present new results for double quarkonium production in (un)polarized hadronic collisions at fixed-target experiments. Our approach combines the transverse momentum dependent (TMD) factorization with the Color-Singlet Model. We present new analytical expressions for the angular structure of the cross section for the $q \bar q$-induced channel, and provide predictions for the unpolarized cross section and transverse single-spin asymmetries for present and future fixed-target experiments at CERN and the LHC.

Speaker: Dr Carlo Flore (Università di Cagliari e INFN, Sezione di Cagliari)

di-onium-talk-REF-2025.pdf

11:45 Lunch Break

Wednesday: Afternoon 1

24 Resummation and zero momentum modes.

We rivisit Touschek’s resummation procedure for QED and highlight the
possibility of zero momentum modes, insofar neglected in the passage from
the discrete to the continuum, but possible under special boundary conditions.
We shows how to separate and extract the zero momentum mode in soft
photon emission both in the relativistic and non-relativist limit. An ansatz is presented to extend the procedure to QCD, and the possibility that this mode manifest itself in the forward peak in elastic pp scattering. A preliminary phenomenology is discussed.

Speaker: Giulia Pancheri (Istituto Nazionale di Fisica Nucleare)

pancheri2.pdf

25 Vacuum versus medium evolution effects in photon-jet productions

Within ultrarelativistic heavy ion collisions the hot and dense medium of a quark gluon plasma (QGP) can be recreated.
While the QGP medium cannot be directly measured, jets, i.e. highly energetic,
collimated, sprays of strongly interacting particles provide a suitable indirect means to access the QGP.
In the medium jets can evolve by the jet-medium interactions of scattering off medium particles as well as by medium induced radiations of jet particles.
In addition it is possible that the color degrees of freedom of jet particles
are not resolved by the medium and appear as color neutral combinations. In these cases emission
of bremsstrahlung as in vacuum, vacuum like emissions (VLEs), can still occur.
I will present a Monte-Carlo algorithm that combines jet evolution via VLEs and jet-medium interactions
considers production and evolution of jet particles via scattering off medium particles and medium
induced emissions. Numerical results were obtained for the productions of photon-jet pairs within heavy ion collisions.
Due to the consideration of VLEs the angular azimuthal correlations between photons and jets show a larger broadening
as compared to the effects from in-medium scattering and medium induced radiations alone.

Speaker: Martin Rohrmoser (Jan Kochanowski University of Kielce)

ref2025Rohrmoser.pdf

26 Multiplicity distributions in QCD jets and jet topics

In this talk, I will talk about our recent studies of the Koba–Nielsen–Olesen (KNO) scaling within QCD jets. Specificially, We evaluate the KNO scaling functions for quark- and gluon-initiated jets by incorporating energy conservation into the Double Logarithmic Approximation (DLA). The resulting modified DLA (MDLA) expressions differ substantially from the DLA predictions and qualitatively align with the recently proposed QCD-inspired expressions, albeit with some quantitative differences. By fixing the two parameters in the MDLA expressions, we show that the inclusive charged-particle multiplicity distributions of the two leading jets in $pp$ collisions at $\sqrt{s} = 13$ TeV, measured by ATLAS over a wide jet $p_T$ range of $0.1$–$2.5$ TeV, are well described within experimental uncertainties and consistent with PYTHIA simulations. This conclusion is further supported by direct comparisons with quark- and gluon-initiated jet distributions extracted via jet topics, though the propagated uncertainties from experimental data remain sizable.

Speaker: Bin Wu (IGFAE, Universidade de Santiago de Compostela)

REF2025_Bin_Wu.pdf

15:15 Coffee break

Wednesday: Afternoon 2

27 Beyond Leading Power in SIDIS Jet Production via Soft Background Fields

In this talk, I present a new approach to studying next-to-leading power (NLP) contributions in inelastic processes, based on the background field method with the explicit inclusion of soft modes. I first detail the different structures contributing to the effective current operator at NLP in this framework and discuss how they differ from previous results. The method is then applied to semi-inclusive deep inelastic scattering (SIDIS) to derive the NLP factorization formula for the hadronic tensor at small transverse momentum. I explain how this formulation enables the definition of twist-3 distributions with properly subtracted rapidity and endpoint divergences. Finally, I present the most general form factors contributing to the $e + h \rightarrow e + \text{jet} + X$ cross section at this power accuracy and illustrate the formalism with phenomenological results for a specific azimuthal asymmetry. This work represents a step toward extending TMD factorization theorems beyond leading power, which is an essential ingredient for high-precision QCD predictions and future extractions of twist-3 distributions at facilities like the EIC.

Speaker: Oscar del Rio Garcia (Complutense University of Madrid)

REF2025_Oscar.pdf

28 The TQ4Q1.1 fragmentation functions: A case study for $T_{4Q}$ tetraquark production

We investigate the core dynamics behind exotic matter formation via the TQ4Q1.1 set of collinear, variable-flavor-number-scheme fragmentation functions for fully charmed or bottomed tetraquarks in three quantum configurations: scalar ($0^{++}$), axial vector ($1^{+-}$), and tensor ($2^{++}$). We adopt single-parton fragmentation at leading power and implement a nonrelativistic QCD factorization scheme tailored to tetraquark Fock-state configurations. Short-distance inputs at the initial scale are modeled using updated calculations for both gluon- and heavy-quark-initiated channels. A threshold-consistent DGLAP evolution is then applied via HF-NRevo. We provide the first systematic treatment of uncertainties propagated from the color-composite long-distance matrix elements that govern the nonperturbative hadronization of tetraquarks. Our analysis represents a further step toward bridging the domains of hadronic structure, precision QCD, and exotic matter.

Speaker: Dr Francesco Giovanni Celiberto (UAH Madrid)

talk_LHC_REF_2025_Celiberto_TQ4Q11.pdf

29 Heavy-quark mass effects in Energy-Energy Correlation

Energy-Energy Correlation (EEC) in electron-positron
annihilation into hadrons at high energy, gives the distribution
of the angular distance between hadronic jets in the final state.
The measure is usually inclusive over quark flavors,
implying that also beauty (charm) quark Correlations
are included. Given the great accuracy reached in both
experimental and present theoretical (perturbative) calculations,
the inclusion of beauty mass effects is highly recommended.
We present a simple formalism to consistently include
heavy-quark mass effects in the Energy-Energy Correlation
in the two-jet region, dominated by large Sudakov logarithms
which need to be resummed to all orders of perturbation theory.

Speaker: Ugo Aglietti (Rome University & INFN)

aglietti.pdf

20:00 Workshop dinner

Thursday 16 October

Thursday: Morning 1

30 The CGC/TMD correspondence: TMD factorisation and evolution at small x

We discuss TMD factorisation at high energy (or small $x$), as emerging from the Color Glass Condensate (CGC) effective theory. We first present exemples of high-energy processes for which TMD factorisation was shown to hold at leading order in CGC perturbation theory. This includes back-to-back di-jet production in electron-nucleus ($eA$) and proton-nucleus ($pA$) collisions, single inclusive jet production in $eA$ deep inelastic scattering, and di-lepton production in $pA$ collisions. The relevant TMD PDFs describe small-$x$ partons in the nuclear target and include saturation effects associated with the high gluon occupancy. We then focus on the next-to-leading order corrections to selected processes. We show that these corrections preserve TMD factorisation and, moreover, they generate three types of evolution equations, as needed for the resummation of the large kinematical logarithms: the BK/JIMWLK equation for the rapidity logarithms, the DGLAP equation for the collinear ones, and the CSS equation for the Sudakov logarithms. We argue that TMD factorisation endowed with these three evolutions is well suited for studies of gluon saturation in hard processes at the Large Hadron Collider and the future Electron-Ion Collider.

Speaker: Edmond Iancu (Institut de Physique Théorique de Saclay)

Milano-REF2025.pdf

31 Diffractive jets and evolution of DTMDs in coordinate and momentum space

We consider diffractive production of two or three jets in high energy photon-nucleus collisions. We show that the leading twist contribution for two hard jets is sensitive to gluon saturation and is determined by large three-parton configurations with size $R \sim 1/Q_s$, with $Q_s$ the nuclear saturation momentum. The corresponding cross section can be written in a factorized form and in terms of diffractive TMDs. The dijet imbalance is much smaller than the hard jets momentum and consequently such TMDs follow CSS evolution. This can be done in momentum or in coordinate space and we perform a direct comparison between the two formulations.

Speaker: DIONYSIS TRIANTAFYLLOPOULOS (ECT*, Trento)

Dionisi.pdf

32 Transverse momentum dependent factorisation in the target fragmentation region at small x

In this talk, based on [1], I will discuss the differential cross-section for single-inclusive jet/hadron 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, this study emphasises 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, I will demonstrate that this cross-section is not power suppressed in $P_\perp/Q$ and can be factorised in terms of extended quark and gluon jet fracture functions. I will finally comment on the phenomenological implications for saturation physics at the future Electron-Ion Collider. In particular, preliminary numerical estimates show that the extended quark jet fracture function is the most sensitive to saturation effects in large nuclei. .

[1] P. Caucal, F. Salazar, arXiv:2502.02634

Speaker: Paul Caucal (SUBATECH, Nantes Université, IN2P3/CNRS)

caucal_REF-2025.pdf

10:00 Coffee Break

Thursday: Morning 2

33 From JIMWLK to CSS

We demonstrate how the low x evolution (JIMWLK Hamiltonian) can be adapted to derive an evolution equation for TMDs. The latter are traditionally described using the CSS equation.Our work establishes
a connection between the two formalisms.

Speaker: Michael Lublinsky (BGU)

talk_REF2025.pdf

34 Reggeon exchange off the lightcone

The relationship between Regge theory and the formalism of Collins-Soper-Sterman is explored by considering the off lightcone effects induced in color octet exchange in $2\to2$ forward scattering. An attempt to unify the language of rapidity divergences and high-energy asymptotic behavior is presented, with insights on the extensions of $k_T$-factorization beyond leading-log accuracy and the role of Collins-Soper kernel in characterizing the Regge trajectory.

Speaker: Andrea Simonelli (Istituto Nazionale di Fisica Nucleare)

REF2025.pdf

35 Higher-twist corrections to exclusive vector meson production at high energies

We present a framework that combines the higher-twist formalism for exclusive processes in the $s$-channel with the semi-classical effective theory describing small-$x$ dynamics in the $t$-channel. This framework is applied to the exclusive production of a transversely polarized light vector meson—a process that starts at next-to-leading power and for which standard collinear factorization breaks down. Within this approach, we perform a comprehensive analysis of the full spin density matrix of the exclusive $\rho$-meson leptoproduction, focusing on the kinematic regime relevant for the Electron-Ion Collider (EIC).

Speaker: Michael Fucilla

REF2025.pdf

36 Conformal Small-$x$ Evolution at the QCD Wilson–Fisher Point

We develop a conformal formulation of small-$x$ QCD at the Wilson--Fisher point $d=4-2\epsilon_\ast$. In $d=4$ the LO BK kernel is M\"obius invariant, and at the critical coupling the BK/BFKL evolution \emph{remains} conformal through NLO (with the appropriate composite/conformal dipole), yielding power-law eigenfunctions, an explicitly organized $b_0$ dependence, and a shifted Pomeron intercept. Matching a four-point correlator in the Regge/light-cone double limit recovers the standard BFKL--DGLAP consistency relation that ties the intercept to twist-2 anomalous dimensions of gluon light-ray operators—showing, in particular, that in $\overline{\mathrm{MS}}$ the anomalous dimensions at $d=4-2\epsilon_\ast$ coincide with those at $d=4$, even though the intercept differs. The framework unifies resummation (BFKL/NLL), evolution (BK/DGLAP), and factorization (high-energy OPE) with an explicit treatment of the rapidity regulator, and it suggests a route to NNLO information via $O(\epsilon)$ pieces of NLO BK $\to O(\alpha_s^2 b_0)$ terms.

Speaker: Giovanni Antonio Chirilli (University of Salento)

REF-Milan16oct25_chirilli.pdf

12:10 Lunch Break

Thursday: Afternoon 1

37 Small-x resummation of photon impact factors and virtual photon scattering at high energies

I present the renormalization group improved collinear resummation of the
photon-gluon impact factors. We construct the resummed cross section for
virtual photon-photon (𝛾∗𝛾∗) scattering
which incorporates the impact factors and BFKL gluon Green’s function up
to the next-to-leading logarithmic accuracy in energy. The impact factors
include important kinematical effects which
are responsible for the most singular poles in Mellin space at
next-to-leading order. Further conditions on the resummed cross section
are obtained by requiring the consistency with the
collinear limits. Our analysis is consistent with previous impact factor
calculations at NLO, apart from a new term proportional to C_F that we
find for the longitudinal polarization. Finally, we
use the resummed cross section to compare with the LEP data on the
𝛾∗𝛾∗ cross section and with previous calculations. The resummed result
is lower than the leading logarithmic approximation
but higher than the pure next-to-leading one, and is consistent with the
experimental data.

Speaker: Dimitri Colferai (Istituto Nazionale di Fisica Nucleare)

colferai.pdf

38 On the interplay between the BFKL resummation and high-energy factorization in Mueller-Navelet dijet production

We study the interplay between the high-energy resummation based on the BFKL equation [1] and initial state radiation effects, taken into account within the framework of the high-energy factorization [2-4] in the production of Mueller-Navelet dijets [5] at hadron colliders. We use the solution of the NLO BFKL equation built out of eigenfunctions perturbatively constructed up to NLO [6] to avoid the need for a special renormalization scale setting. We demonstrate that the various data sets from the FNAL Tevatron and CERN LHC can be described in this way and the both, initial state radiation effects of the high-energy factorization and NLL BFKL resummation, are crucial for the uniform description of the data across all values of rapidity difference between the jets.
[1] L.N. Lipatov, 1976; E.A. Kuraev, L.N. Lipatov, V.S. Fadin 1976-77; I.I. Balitsky, L.N. Lipatov 1986; V.S. Fadin, L.N. Lipatov, 1998.
[2] L.V. Gribov, E.M. Levin, M.G. Ryskin, 1983.
[3] J.C. Collins, R.K. Ellis, 1991.
[4] S. Catani, M. Ciafaloni, F. Hautmann, 1991.
[5] A.H. Mueller, H. Navelet, 1987.
[6] G.A. Chirilli, Y.V. Kovchegov, 2013-14.

Speaker: Alexey Chernyshev (BLTP JINR)

REF’25.pdf

39 Small-x resummation for muon colliders

In the context of an ongoing project, I will motivate the interest for the inclusion of small-x resummation in the computation of the parton distributions in a muon, relevant for the description of scattering processes at a future muon collider. To achieve this task, some technical developments have been made, that I will briefly review.

Speaker: Marco Bonvini (Istituto Nazionale di Fisica Nucleare)

bonvini_REF2025.pdf

Discussion on Small-x Topical Issues

discussion.pdf

15:35 Coffee Break

Visit to Milan Cathedral (Duomo)

Friday 17 October

Friday: Morning 1

40 The Collins-Soper Kernel from Lattice QCD

I will present the first complete determination of the quark Collins-Soper kernel, which relates TMDs at different rapidity scales, using lattice QCD and including systematic control of quark mass, operator mixing, and discretization effects. Next-to-next-to-leading logarithmic matching is used to match lattice-calculable distributions to the corresponding TMDs. The continuum-extrapolated lattice QCD results are consistent with several recent phenomenological parametrizations of the Collins-Soper kernel and are precise enough to disfavor other parametrizations. I will also discuss a first exploration of the gluon Collins-Soper kernel.

Speaker: Michael Wagman (Fermilab)

Wagman_REF25.pdf

41 Towards the complete one-loop two-gluon central emission vertex in QCD

Recently there has been significant progress in understanding the
Regge limit in massless scattering amplitudes. In particular, all
the ingredients needed for the computation of the BFKL kernel at
NNLO have been determined in QCD, apart from the two-gluon
central emission vertex at one loop, which is known so far only
in maximally supersymmetric Yang-Mills theory. We present the
calculation of the next-to-multi-Regge-kinematic (NRMK) limit of
the six-gluon amplitude in QCD, from which this vertex can be
determined. Due to the complexity of the expressions for the
next-to-maximally-helicity-violating (NMHV) amplitude and the
high powers of spurious poles in the NMRK expansion parameter, we
use p-adic evaluation to obtain numerical samples for the leading
NMRK behaviour. We then employ analytic reconstruction techniques
to recover analytic results in a minimal set of independent
variables. In particular, allowed partial fraction depositions
are identified through nested p-adic limits near codimension-two
varieties.

Speaker: Giuseppe De Laurentis (University of Edinburgh)

REF_GDL.pdf

REF_GDL_html

09:50 Coffee Break

Friday: Morning 2

42 Subleading power factorisation of amplitudes

Calculations in perturbative QCD suffer from large logarithms that appear at all orders in perturbation theory, endangering the perturbative description. In pursuit of precise predictions for cross sections, factorisation theorems have been established with the benefit to resum these large logarithms to all orders in perturbation theory, improving the predictive power of the theory. This procedure is well understood at leading power (LP) in these large logarithms, but much work is still to be done at next-to-leading power (NLP). In order to better understand the NLP structure, a factorisation theorem has been developed at this accuracy within diagrammatic QCD. This introduces new jet functions that contribute to this subleading power behaviour. We verify the factorisation theorem by giving definitions to these new jet functions and calculate them up to two loops. We compare their contributions to a region calculation of the two-loop massive fermion form factor and find perfect agreement.

Speaker: Robin van Bijleveld (Nikhef)

REF_vanBijleveld.pdf

43 Factorization violation in gluon amplitudes

We study scattering amplitudes and form factors in planar N=4 Super Yang-Mills theory and planar QCD in the limit where two pairs of gluons become collinear. We find that, when the virtualities of both collinear pairs are spacelike, the collinear factorisation of the amplitude involves a generalised splitting amplitude that correlates the two collinear directions. In N=4, we find that our generalised splitting amplitude agrees with the Bern-Dixon-Smirnov (BDS) subtracted six-point amplitude in multi-Regge kinematics. The latter can be explicitly evaluated using integrability to all orders in the coupling. We also present compelling evidence for the universality of the generalised splitting amplitude.

Speaker: Aniruddha Venkata (Uni Bonn, BCTP)

generalized-splitting-REF.pdf

Open discussion

Closing

ref2026.pdf