<p>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 Letter establishes the feasibility of using neural networks to explore the multidimensional partonic structure of hadrons and paves the way for more accurate determinations based on machine-learning techniques.</p>

Italy

Alessandro Bacchetta

France

Valerio Bertone

United States

Chiara Bissolotti

Matteo Cerutti

Marco Radici

Germany

Simone Rodini

Lorenzo Rossi

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

We present the one-loop matching coefficients necessary to match all of the leading-twist generalised transverse-momentum-dependent distributions (GTMDs) onto generalised parton distributions (GPDs). Matching functions are extracted by computing the first radiative corrections to partonic bilocal correlators with staple-like Wilson lines, as appropriate for high-energy collisions. These correlators are characterised by a transverse displacement and skewed kinematics of external states. Using the proton helicity basis, they are parametrised in terms of GTMDs, which are subsequently related to leading-twist GPDs. Our results provide new insights into the complex dynamics of GTMDs generated by radiative corrections. In particular, we show that time-reversal even and odd contributions to GTMDs in the so-called ERBL region mix both under matching and evolution. Finally, we present a selection of numerical results and comment on the quantitative behaviour of GTMDs.

Spain

Miguel Echevarria

Oscar Rio

One-loop matching for leading-twist generalised transverse-momentum-dependent distributions

We present <small-caps>MAPPDFpol1.0</small-caps>, a new determination of the helicity-dependent parton distribution functions (PDFs) of the proton from a set of longitudinally polarised inclusive and semi-inclusive deep-inelastic scattering data. The determination includes next-to-next-to-leading order QCD corrections to both processes, and is carried out in a framework that combines a neural-network parametrisation of PDFs with a Monte Carlo representation of their uncertainties. We discuss the quality of the determination, in particular its dependence on higher-order corrections, on the choice of data set, and on theoretical constraints.

United Kingdom

Amedeo Chiefa

Emanuele R. Nocera

Helicity-dependent parton distribution functions at next-to-next-to-leading order accuracy from inclusive and semi-inclusive deep-inelastic scattering data

We present an extraction of the unpolarized transverse-momentum-dependent parton distribution and fragmentation functions that takes into account possible differences between quark flavors and final-state hadrons. The extraction is based on experimental measurements from Drell-Yan processes and semi-inclusive deep-inelastic scattering, whose combination is essential to distinguish flavor differences. The analysis is carried out at N3LL accuracy. The extracted flavor-dependent distributions give a very good description of the data (χ 2/N dat = 1.08). The resulting error bands take fully into account also the uncertainties in the determination of the corresponding collinear distributions.

Giuseppe Bozzi

Filippo Delcarro

Andrea Signori

Flavor dependence of unpolarized quark transverse momentum distributions from a global fit

We present a benchmark comparison of the massless inclusive deep-inelastic-scattering (DIS) structure functions up to  $$\mathcal {O}(\alpha _s ^3)$$  <math> <mrow> <mi>O</mi> <mo>(</mo> <msubsup> <mi>α</mi> <mi>s</mi> <mn>3</mn> </msubsup> <mo>)</mo> </mrow> </math>   in perturbative QCD. The comparison is performed using the codes apfel++ and hoppet within the framework of the variable-flavour-number scheme and over a broad kinematic range relevant to the extraction of parton distribution functions. We provide results for both the single structure functions and the reduced cross sections in both neutral- and charged-current DIS. Look-up tables for future reference are included, and we also release the code used for the benchmark.

CERN

Alexander Karlberg

Benchmark of deep-inelastic-scattering structure functions at  $$\mathcal {O}\left( \alpha _s ^3\right) $$  <math> <mrow> <mi>O</mi> <mfenced> <msubsup> <mi>α</mi> <mi>s</mi> <mn>3</mn> </msubsup> </mfenced> </mrow> </math>

We present a new determination of unpolarised charged pion and kaon fragmentation functions from a set of single-inclusive electron-positron annihilation and lepton-nucleon semi-inclusive deep-inelastic scattering data. The determination includes next-to-next-to-leading order QCD corrections to both processes, and is carried out in a framework that combines a neural-network parametrisation of fragmentation functions with a Monte Carlo representation of their uncertainties. We discuss the quality of the determination, in particular its dependence on higher order corrections.

Rabah Abdul Khalek

Alice Khoudli

Pion and kaon fragmentation functions at next-to-next-to-leading order

We revisit the evolution of generalized parton distributions at the leading order in the strong coupling constant <math><mrow><msub><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math> for all of the twist-2 quark and gluon operators. We rederive the relevant one-loop evolution kernels, expressing them in a form suitable for implementation, and check analytically that some basic properties, such as Dokshitzer-Gribov-Lipatov-Altarelli-Parisi/Efremov-Radyushkin-Brodsky-Lepage limits and polynomiality conservation, are fulfilled. We also present a number of numerical results obtained with a public implementation of the evolution in the library apfel++ and available within the partons framework.

Rafael F. del Castillo

Miguel G. Echevarria

Óscar del Río

One-loop evolution of twist-2 generalized parton distributions

Exclusive heavy-vector meson photoproduction is a prominent signal in collider experiments with hadron beams. At the highest photon-hadron collision energies, this process is considered as a candidate to constrain the gluon parton distribution function (PDF) at small longitudinal momentum fractions. However, in the framework of collinear factorization, exclusive particle production is described in terms of generalized parton distributions (GPDs). In this contribution, we investigate the connection between GPDs and PDFs at the leading order in <math><msub><mi>α</mi><mi>s</mi></msub></math>. Our main result is a proposal to quantify the systematic uncertainty inherent to this connection. We put our approach into context with respect to the Shuvaev transform. Our uncertainty estimate can be straightforwardly adapted to higher fixed orders and small-<math><mi>x</mi></math> resummation. The question of extrapolating GPDs to vanishing skewness is paramount for the program of the Electron Ion Collider, notably for the extraction of the radial distributions of partons.

Hervé Dutrieux

Michael Winn

Exclusive meets inclusive particle production at small Bjorken <math><msub><mi>x</mi><mi>B</mi></msub></math>: How to relate exclusive measurements to PDFs based on evolution equations

We map the distribution of unpolarized quarks inside a unpolarized pion as a function of the quark’s transverse momentum, encoded in unpolarized transverse momentum distributions (TMDs). We extract the pion TMDs from available data of unpolarized pion-nucleus Drell–Yan processes, where the cross section is differential in the lepton-pair transverse momentum. In the cross section, pion TMDs are convoluted with nucleon TMDs that we consistently take from our previous studies. We obtain a fairly good agreement with data. We present also predictions for pion-nucleus scattering that is being measured by the COMPASS Collaboration.

Simone Venturini

Extraction of pion transverse momentum distributions from Drell-Yan data

The operator definition of generalised transverse momentum-dependent (GTMD) distributions is exploited to compute for the first time the full set of one-loop corrections to the off-forward matching functions. These functions allow one to obtain GTMDs in the perturbative regime in terms of generalised parton distributions (GPDs). In the unpolarised case, non-perturbative corrections can be incorporated using recent determinations of transverse-momentum-dependent (TMD) distributions. Evolution effects for GTMDs closely follow those for TMDs and can thus be easily accounted for up to next-to-next-to-leading logarithmic accuracy. As a by-product, the relevant one-loop anomalous dimensions are derived, confirming previous results. As a practical application, numerical results for a specific kind of GTMD are presented, highlighting some salient features.

Matching generalised transverse-momentum-dependent distributions onto generalised parton distributions at one loop