Due to confinement, much of the richness as well as the challenge of quantum chromodynamics lies in relating the partonic degrees of freedom in the fundamental field theory to the hadronic degrees of freedom that we can observe. Within the context of high-energy QCD, the ability to factorize short-distance, perturbatively calculable partonic scattering cross sections from long-distance...

In this talk, I will give an overview of General-Purpose Event Generators for High-Energy physics, and attempt to highlight their HL-LHC and EIC-relevant aspects, such as their hard physics modelling, QCD and electroweak resummation properties (and recent developments), as well as non-perturbative modelling relevant for TMD physics.

The QCD evolution of transverse momentum dependent (TMD) distribution functions has recently been formulated in a parton branching (PB) formalism. In this approach, soft-gluon coherence effects are taken into account by introducing the soft-gluon resolution scale and exploiting the relation between transverse-momentum recoils and branching scales. In this talk we investigate the implications...

Transverse Momentum Dependent parton distributions obtained from the Parton Branching method are combined with leading-order calculations of Drell-Yan production with up to three partons in the final state. A modified version of the MLM merging algorithm is applied in order to remove double counting from the different jet multiplicities. The merging is tested using the differential jet rate...

We present NLO predictions from Powheg (POWHEG_BOX_V2) and MC@NLO merged with Parton Branching TMD's for inclusive Z and bbar production. We compare predictions for range of mass 60 < Mz < 120 and 60 < Mbbbar < 120 (around Z mass) in order to study soft gluon radiation and resummation from quarks and gluons.

We present a parton shower based on Transverse Momentum Dependent (TMD)

parton distributions obtained with the Parton Branching method. We investigate

how well the TMD parton shower reproduces the TMD parton distributions.

Applications of the TMD parton shower to LHC processes will be presented.

We present an overview of the calculation of transverse momentum dependent (TMD) real emission contributions to splitting functions within kT-factorization. We discuss their properties, such as the limits in which they reduce to well known kernels.

We present an implementation of the splitting functions in a Monte Carlo simulation, based on the Parton Branching method. Results of TMD...

An overview will be given of recent experimental results on quarkonium production at the LHC, both inclusive and in association with other particles, such as W, Z bosons or another quarkonium. The challenges of making such measurements will be highlighted, and possible applications for extracting gluon TMDs will be discussed.

Quarkonium production has been advertised as a tool to probe the gluon TMDs. Among the eight gluon TMDs, gluon Sivers function has been receiving paramount of interest both theoretically and experimentally. We study the single-spin asymmetry (SSA) in proton-proton collision process in $J/\psi$ production by employing the generalized parton model (GPM), and compare SSA with PHENIX data. We...

We discuss resummation of large logarithms in heavy quarkonium production cross sections. Due to the nonrelativistic nature of heavy quarkonium states, nonperturbative matrix elements of heavy quarkonia can involve singular distributions. In such cases, standard methods of solving evolution equations can lead to nonconverging integrals or series. We discuss methods to overcome these...

We present our recent calculations on the production of pseudoscalar charmonia eta_c(1S) and eta_c(2S) in the k_T factorization approach. We discuss the regions of longitudinal and transverse momenta of gluons probed in the kinematics of the LHCb or ATLAS experiments.

The crucial ingredient is the off-shell matrix element, which in this case is

related to a g^*g^*eta_c form factor. Its...

We present Parton Reggeization Approach --the gauge-invariant scheme of kT factorization based on Lipatov's gauge-invariant EFT for Multi-Regge processes in QCD.

After review of LO formalism, our recent [1] calculation of inclusive differential distributions of pairs of prompt J/psi produced in pp-collisions at the LHC in the framework of LO PRA and NRQCD-factorization formalism will be...

A new method of consistent merging of jet calculations in $k_T$-factorization with higher-order matrix elements is proposed. We study azimuthal correlations between leading and subleading jets in large$-p_T$ multijet production with two, three and four jets in final state within the parton Reggeization approach (PRA). PRA is based on $k_T-$factorization of hard processes in the...

The unintegrated gluon distribution (UGD) provides the description of the gluon content in the proton in the high-energy regime and it is formulated in $\kappa_T$-factorization approach. In this theoretical framework, the helicity amplitude is a convolution of the UGD in the proton with the impact factor, which depends on the considered process and where the structure of the meson is encoded...

Heavy-quark production is of first importance at the LHC, allowing to test factorization formulas, and to probe cold and hot nuclear matter. In the first part of the presentation, I will quickly review heavy-quark production in the case of the collinear factorization, making some useful remarks for the second part of the talk. Then, I will switch to heavy-quark production with...

Drell-Yan pair production using transverse momentum dependent parton distributions evolved

with the Catani-Ciafaloni-Fiorani-Marchesini-Kwieci\'nski (CCFM-K) equations in the single loop approximation will be discussed. Such equations are obtained assuming angular ordering of emitted partons (coherence) for $x\sim 1$ and transverse momentum ordering for $x \ll 1$. This evolution scheme also...

The valence double parton distribution of the pion is analyzed in the framework of chiral quark models, where in the chiral limit factorization between the longitudinal and transverse degrees of freedom occurs. This feature leads, at the quark-model scale, to a particularly simple distribution of the form $D(x_1,x_2, \vect{y}) = \delta(1-x_1-x_2) F(\vect{y})$, where x1,2 are the longitudinal...

We present prospects for the direct measurement of ratios of differential cross sections for the production of Z and Higgs bosons in proton-proton collisions, using data taken by CMS during the LHC Run II. The aim of the measurement is to study soft and hard gluon emission in the initial statefor Higgs and Z production mechanisms. Hence, we focus on variables known to be sensitive to the...

In this talk we will show the necessary ingredients of a N3LO perturbative QCD calculation using the qT-subtraction prescription. We will show which are the partially known (or missing) coefficients at the third order in the strong coupling and how we can circumvent this problem using the total cross section at the same perturbative order. We will apply this formalism to the particular case of...

I present the ARES method for the resummation of final-state observables at NNLL accuracy. I discuss the main feature of the method, and the most important results obtained with it. I will then present its most recent developments.

I present recent developments in the direct-space resummation of transverse observables in colour-singlet production in the RadISH framework, with particular focus on the NNLL joint resummation for the transverse momentum of the Higgs boson and of the leading jet in gluon fusion at the LHC.

Soft gluon resummation for associated t-tbar pair and a H, Z or W boson is performed up to the NNLL accuracy in QCD. The results are matched to the NLO QCD and calculations. The total hadroproduction cross sections at the LHC are obtained as well as selected kinematical distributions. It is shown that the resummation leads to higher theoretical precision. Results are compared to data from the LHC.

We present a new determination of Transverse Momentum Dependent (TMD) parton distributions applying the Parton Branching method. The PB TMDs are obtained from fits to precision DIS data using DGLAP splitting functions at leading and higher order. In addition the CCFM splitting function will be applied to include small x effects.

Applications of these new TMD distributions will be discussed.

The PB TMDs were successfully used for obtaining predictions for LHC measurements. However, these measurements turned out to not be sensitive to some of the non-perturbative parameters existing in the PB approach. In this talk we show preliminary results for the application of PB TMDs to low energy DY data. We illustrate the role of non-perturbative dynamics, including intrinsic transverse...

We present an extraction of unpolarized transverse-momentum dependent (TMD) parton distribution functions (PDFs) based on a fit on data from Drell-Yan processes in different experiments and kinematic ranges, including in particular LHC experiments. The analysis is performed in the TMD factorization framework with perturbative accuracy up to next-to-next-to-next-to-leading-log ($N^3LL$),...

I present the analysis of the unpolarized SIDIS and Drell-Yan data within the TMD factorization approach and the extraction of unpolarized TMD distributions and non-perturbative TMD evolution kernel. The joined fit of SIDIS and DY leads to an accurate determination of the TMD evolution kernel. I also discuss the influence of collinear distributions on TMD physics and the interpretation of the...

While the investigation of TMDs is a major objective of the EIC, Double Parton Ditributions (DPDs) are crucial for a first principle QCD description of double parton interactions at LHC, which contribute to the standard model background for various BSM searches. Both groups of functions are genuinely non-collinear and non-perturbative. The non-collinearity required the development of new...

In this talk I will discuss the concept of quasi-TMDPDFs, which are transverse momentum dependent parton distribution functions defined with operators on a spatial (equal-time) slice. These distributions must be defined so that they have the same infrared physics as the standard TMDPDF, but can be directly calculated with Lattice QCD. As a nice application, I discuss our proposal for using...

Abstract: The most known scheme to regulate the rapidity/UV divergences of the Transverse Momentum Distribution operators due to the infinite light-like gauge links is the Collis Soper Sterman formalism or the Soft Collinear Effective Theory formalism. An alternative choice is provided by the scheme used in the small-x physics. The corresponding evolution equations differ already at leading...

Recent BELLE measurements provide the cross section for single hadron production from e+e- annihilations, differential in the hadron transverse momentum with respect to the thrust axis.

Universality breaking effects due to process-dependent soft factors make it very difficult to relate this cross section to that corresponding to hadron-pair production in e+e- annihilations, where TMD...

Jet technics have been used and developed for a while at LHC. I will discuss the compatibility of jet definition with the TMD factorization theorem and how they can be used in TMD investigations.

I am going to present recent results on the broadening phenomenon in p-p, p-A and A-A collisions. In p-p and p-A the broadening is described in terms of the ITMD factorization, accounting for Sudakov effects and saturation. In A-A it is due to soft multiple collisions of the jet traversing the QGP.

In this work, we investigate the photoproduction of three jets at low-x. We calculate the cross section using the Color Glass Condensate (CGC) effective theory, allowing us to resum the multiple scattering of the hard partons off the dense semi-classical gluon fields in the highly boosted proton or nucleus. In the so-called correlation limit, in which the sum q_T of the transverse momenta of...

We consider the inclusive production in proton-proton collisions of two heavy quarks, separated by a large rapidity interval, that can be experimentally investigated at the Large Hadron Collider (LHC) to test QCD predictions in the semi-hard regime. The process is studied in the Regge kinematical region by the Balistky-Fadin-Kuraev-Lipatov (BFKL) approach. A full resummation of leading energy...

We perform a detailed analysis of the different forms of the kinematical constraint imposed on the low x evolution. We find that all of them generate the same leading anti-collinear poles in Mellin space which agree with BFKL up to NLL order and up to NNLL in N=4 sYM. The coefficients of subleading poles vanish up to NNLL order for all constraints and we prove that this property should be...

Recently, there has been significant progress in computing scattering amplitudes in the high-energy limit using rapidity evolution equations. I describe the state-of-the-art and demonstrate the interplay between exponentiation of high-energy logarithms and that of infrared singularities.

The focus in this talk is the imaginary part of 2 to 2 partonic amplitudes, which can be determined by...

I will discuss the continuity between small x physics and moderate x physics by showing how semiclassical descriptions of small x amplitudes can be fully rewritten in terms of TMD distributions.

With this equivalence in mind, I will reinterpret saturation models in terms of these distributions.

The PROSA PDF fit was the first in the literature showing the impact of the inclusion of open-heavy flavour production data on low-x gluons.

We present a new version of the fit, including a more extended set of experimental data than our previous fit, which allows to better constrain gluon and sea quark distributions and we show its performances in applications of interest for neutrino astronomy.

While significant steps toward the formal definition of quark TMDs and their extraction from experimental data through global fits has been made in the last years, the gluon-TMD field represents a largely unexplored territory. Pursuing the goal of extendending our knowledge of this sector, we present analytic expressions for all $T$-even gluon TMDs at twist-2, calculated in a spectator model...

We discuss the relation between the infrared singularities of on-shell partonic form factors and parton distribution functions (PDFs) near the elastic limit, through their factorisation in terms of Wilson-line correlators. Ultimately we identify the difference between the anomalous dimension controlling single poles of these two quantities to all loops in terms of the closed parallelogram...

The small-x evolution equations for the quark and gluon helicity distribution have recently been constructed by finding sub-eikonal corrections to the eikonal shock wave formalism. Those equations are written for correlators of infinite light-cone Wilson lines along with the so-called polarized Wilson lines. Those equations close in the large $N_c$-limit ($N_c$ is the number of quark colors),...