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At least 37 records · Page 2
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DOE OSTI2025

TMD Handbook

This handbook provides a comprehensive review of transverse-momentum-dependent parton distribution functions and fragmentation functions, commonly referred to as transverse momentum distributions (TMDs). TMDs describe the distribution of partons inside the proton and other hadrons with respect to both their longitudinal and transverse momenta. They provide unique insight into the internal momentum and spin structure of hadrons, and are a key ingredient in the description of many collider physics cross sections. Understanding TMDs requires a combination of theoretical techniques from quantum field theory, nonperturbative calculations using lattice QCD, and phenomenological analysis of experimental data. The handbook covers a wide range of topics, from theoretical foundations to experimental analyses, as well as recent developments and future directions. It is intended to provide an essential reference for researchers and graduate students interested in understanding the structure of hadrons and the dynamics of partons in high energy collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

TMD fragmentation functions at N 3 LO

We compute the unpolarized quark and gluon transverse-momentum dependent fragmentation functions (TMDFFs) at next-to-next-to-next-to-leading order (N 3 LO) in perturbative QCD. The calculation is based on a relation between the TMDFF and the limit of the semi-inclusive deep inelastic scattering cross section where all final-state radiation becomes collinear to the detected hadron. The required cross section is obtained by analytically continuing our recent computation of the Drell-Yan and Higgs boson production cross section at N 3 LO expanded around the limit of all final-state radiation becoming collinear to one of the initial states. Our results agree with a recent independent calculation by Luo et al.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Bayesian Inferring Nucleon Gravitational Form Factors via Near-Threshold 𝐽/𝜓 Photoproduction

With Bayesian inference, we investigate the impact of recent near-threshold 𝐽/𝜓 production measurements by the 𝐽/𝜓⁢007 experiment and GlueX Collaboration on the extraction of proton gravitational form factors. We apply the generalized parton distribution framework at the next to leading order and demonstrate a stable expansion for the near-threshold kinematics. We find that the experimental constraints are in good agreement with the state-of-the-art lattice simulations, where negative 𝐶 𝑞 ⁡(𝑡) and 𝐶 𝑔 ⁡(𝑡) are strongly preferred. This highlights a great potential to extract them from future high-precision experiments.

QCD phenomenology↗
DOE OSTI2026

The role of charm and unflavored mesons in prompt atmospheric lepton fluxes

The all-sky very-high-energy (10 4 − 10 6 GeV) atmospheric muon flux measured by IceCube shows a spectral hardening at the highest energies, indicating the presence of a prompt component. IceCube has also measured the atmospheric muon neutrino flux at high energy. However, since this flux is dominated by astrophysical neutrinos, only an upper bound can be placed on the prompt atmospheric ν μ + $\overline{ν}$ μ contribution. In this work, we provide a new evaluation of the prompt atmospheric muon flux including an intrinsic charm component in the cosmic ray-air interactions. The latter enhances the forward production of $\overline{D}$ 0 , D – and Λc, which subsequently decay into final states containing muons and muon neutrinos. We show how the increase in the prompt muon flux due to intrinsic charm is accompanied by a corresponding enhancement in the prompt muon neutrino flux. We implement different intrinsic charm production models in MCEq to calculate the resulting lepton fluxes. We discuss the challenges of achieving predictions that are simultaneously consistent with both IceCube’s high-energy atmospheric muon flux measurements and IceCube upper bounds on the prompt muon neutrino flux, and we quantify the resulting discrepancies. As possible solutions, we explore scaling of the unflavored meson contributions to the prompt atmospheric muon flux to assess how such adjustments can reconcile these differences. The tensions emphasized in our work call for a refinement of the hadronic interaction models, especially the production of unflavored mesons, and for new experimental data sensitive to unflavored meson and heavy flavor production with reliable estimates of the associated uncertainties. We suggest that the energy and zenith angle dependence of muon and neutrino flux ratios from future neutrino telescope measurements may help to disentangle different scenarios.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Proton’s gluon GPDs at large skewness and gravitational form factors from near threshold heavy quarkonium photoproduction

We study the exclusive near threshold photoproduction of heavy quarkonium in the framework of the generalized parton distribution (GPD) factorization, taking the 𝐽/𝜓 production as an example. Because of the threshold kinematics, the Compton-like amplitudes are related to gluon GPDs at large skewness 𝜉, distinct from the common kinematics in asymptotic high energy where the skewness is typically small. We discuss the nature of large-𝜉 expansion of these amplitudes in terms of the moments of gluon GPDs in the large-𝜉 limit. Based on that, we propose several ways to extract the first few moments of the gluon GPDs from these amplitudes, with the leading ones corresponding to the gluonic gravitational or energy-momentum tensor form factors (GFFs). We apply these methods to analyze the recent near threshold 𝐽/𝜓 production measurements by the 𝐽/𝜓 007 experiment and GlueX Collaboration and find that the 𝜉 scaling of the measured differential cross sections is consistent with the asymptotic behavior. However, the current data are not accurate enough yet for a complete determination of the gluonic GFFs, and therefore we consider some prospects for better extractions in the future.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Transverse Momentum Distributions from Lattice QCD without Wilson Lines

The transverse-momentum-dependent distributions (TMDs), which are defined by gauge-invariant 3D parton correlators with staple-shaped lightlike Wilson lines, can be calculated from quark and gluon correlators fixed in the Coulomb gauge on a Euclidean lattice. These quantities can be expressed gauge invariantly as the correlators of Coulomb-gauge-dressed fields, which reduce to the standard TMD correlators under principal-value prescription in the infinite boost limit. In the framework of large-momentum effective theory, a quasi-TMD defined from such correlators in a large-momentum hadron state can be matched to the TMD via a factorization formula, whose exact form is derived using soft collinear effective theory and verified at one-loop order. Compared to the currently used gauge-invariant correlators, this new method can substantially improve statistical precision and simplify renormalization for the time-reversal-even TMDs, which will greatly enhance the predicative power of lattice QCD in the nonperturbative region.

Effective field theory↗
DOE OSTI2024

Extracting transition generalized parton distributions from hard exclusive pion-nucleon scattering

We study the extraction of transition generalized parton distributions (GPDs) from production of two back-to-back high transverse momentum photons ( γ γ ) and a massive pair of leptons ( ℓ + ℓ − ) in hard exclusive pion-nucleon scattering. We argue that the exclusive scattering amplitude of both processes could be factorized into nonperturbative pion distribution amplitude and nucleon transition GPDs that are convoluted with perturbatively calculable short-distance matching coefficients. We demonstrate that the exclusive diphoton production not only is complementary to the Drell-Yan-type dilepton production for extracting the GPDs but also provides enhanced sensitivities for extracting the parton momentum fraction x dependence of the GPDs. We show that both exclusive observables are physically measurable at the J-PARC and AMBER experiment energies. If the target nucleon can be polarized, corresponding spin asymmetries can offer additional sensitivities for extracting transition GPDs. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Field-theoretic analysis of hadronization using soft drop jet mass

One of the greatest challenges in quantum chromodynamics is understanding the hadronization mechanism, which is also crucial for carrying out precision physics with jet substructure. In this paper, we bring together recent advancements in our understanding of nonperturbative structure of the soft drop jet mass based on field theory, with precise perturbative calculations at next-to-next-to-leading logarithmic accuracy of its multidifferential variants. This allows for a model-independent analysis of power corrections associated with hadronization in a systematic manner. We test and calibrate hadronization models and their interplay with parton showers by comparing our universality predictions with various event generators for quark and gluon initiated jets in both lepton-lepton and hadron-hadron collisions. Our findings reveal that hadronization models perform better for quark jets relative to gluon jets. Our results provide a valuable toolbox for precision studies with the soft drop jet mass and pave the way for future analyses using real-world collider data. The stringent constraints derived in our framework are useful for improving the modeling of hadronization and its interplay with parton showers in next-generation event generators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Pion gravitational form factors in the QCD instanton vacuum. I

The pion form factors of the QCD energy-momentum tensor (EMT) are studied in the instanton liquid model (ILM) of the QCD vacuum. In this approach, the breaking of conformal symmetry is encoded in the form of stronger-than-Poisson fluctuations in the number of instantons. For the trace of the EMT, it is shown that the gluonic trace anomaly term contributes half the pion mass, with the other half coming from the quark-mass-dependent σ term. The Q 2 dependence of the form factors is governed by glueball and scalar meson exchanges. For the EMT, the spin-0 (trace) and spin-2 (traceless rank-2 tensor) form factors are computed at next-to-leading order in the instanton density using effective quark operators. Relations between the gluon and quark contributions to the EMT form factors are derived. The form factors are also expressed in terms of the pion light-front wave functions in the ILM. The results at the low resolution scale of the inverse instanton size are evolved to higher scales using the renormalization group equation. The ILM results compare well with those of recent lattice QCD calculations. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Learning PDFs through interpretable latent representations in Mellin space

Representing the parton distribution functions (PDFs) of the proton and other hadrons through flexible, high-fidelity parametrizations has been a long-standing goal of particle physics phenomenology. This is particularly true since the chosen parametrization methodology can play an influential role in the ultimate PDF uncertainties as extracted in QCD global analyses; these, in turn, are often determinative of the reach of experiments at the LHC and other facilities to nonstandard physics, including at large 𝑥, where parametrization effects can be significant. In this study, we explore a series of encoder-decoder machine-learning (ML) models with various neural-network topologies as efficient means of reconstructing PDFs from meaningful information stored in an interpretable latent space. Given recent effort to pioneer synergies between QCD analyses and lattice-gauge calculations, we formulate a latent representation based on the behavior of PDFs in Mellin space, i.e., their integrated moments, and test the ability of various models to decode PDFs from this information faithfully. We introduce a numerical package, PDFdecoder, which implements several encoder-decoder models to reconstruct PDFs with high fidelity and use this end-to-end tool to explore how such neural-network-based models might connect PDF parametrizations to underlying properties like their Mellin moments. We additionally dissect patterns of learned correlations between encoded Mellin moments and reconstructed PDFs that suggest opportunities for further improvements to ML-based approaches to PDF parametrizations and uncertainty quantification.

Machine learning↗
DOE OSTI2024

Parametrization of Generalized Parton Distributions from 𝑡-Channel String Exchange in AdS Spaces

We introduce a string-based parametrization for nucleon quark and gluon generalized parton distributions (GPDs) that is valid for all skewness. Our approach leverages conformal moments, representing them as the sum of spin-𝑗 nucleon 𝐴-form factor and skewness-dependent spin-𝑗 nucleon 𝐷-form factor, derived from 𝑡-channel string exchange in AdS spaces consistent with Lorentz invariance and unitarity. This model-independent framework, satisfying the polynomiality condition due to Lorentz invariance, uses Mellin moments from empirical data to estimate these form factors. With just five Regge slope parameters, our method accurately produces various nucleon quark GPD types and symmetric nucleon gluon GPDs through pertinent Mellin-Barnes integrals. Our isovector nucleon quark GPD is in agreement with existing lattice data, promising to improve the empirical extraction and global analysis of nucleon GPDs in exclusive processes, by avoiding the deconvolution problem at any skewness, for the first time.

QCD phenomenology↗
DOE OSTI2020

Fully coherent energy loss effects on light hadron production in pA collisions

We single out the role of fully coherent induced gluon radiation on light hadron production in pA collisions. The effect has the same general features as for quarkonium production, however with a richer color structure as the induced radiation depends on the global color charge of the partonic subprocess final state. Baseline predictions for light hadron nuclear suppression in pPb collisions at the LHC are provided, taking into account only the effect of fully coherent energy loss, which proves to be of the same order of magnitude as gluon shadowing or saturation. This underlines the need to include fully coherent energy loss in phenomenological studies of hadron production in pA collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Full treatment of the thrust distribution in single inclusive e + e – → h X processes

Extending the transverse momentum dependent factorization to thrust dependent observables entails a series of difficulties, ultimately associated to the behavior of soft radiation. As a consequence, the definition of the transverse momentum dependent functions has to be revised, while preserving (and possibly extending) their universality properties. Moreover, the regularization of the rapidity divergences generates non trivial correlations between rapidity and thrust. In this paper, we show how to deal with these correlations in a consistent treatment of the thrust dependence of e + e – → h X cross section, where the hadron transverse momentum is measured with respect to the thrust axis. In this framework all results obtained in the past few years properly fit together, leading to a remarkable phenomenological description of the experimental measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Small-𝑥 gluon GPD constrained from deeply virtual 𝐽/𝜓 production and gluon PDF through universal-moment parametrization

We phenomenologically constrain the small-𝑥 and small-𝜉 gluon generalized parton distributions (GPDs) with the deeply virtual 𝐽/𝜓 production (DV⁢𝐽/𝜓⁢P) in the framework of GPDs through universal moment parameterization (GUMP). We use a hybrid cross-section formula combining collinear factorization to the next-to-leading order (NLO) accuracy of the strong coupling 𝛼 𝑠 , with corrections from nonrelativistic QCD to account for the power corrections due to the heavy 𝐽/𝜓 mass. We reach reasonable fit to the measured differential cross sections of DV⁢𝐽/𝜓⁢P by H1 at the Hadron-Electron Ring Accelerator as well as forward gluon parton distribution functions (PDFs) from JAM22 global analysis. We find that both NLO and nonrelativistic corrections are significant for heavy vector meson productions. Of course, the gluon GPD we obtain still contains considerable freedom in need of inputs from other constraints, particularly in the distribution-amplitude-like region.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Transverse Λ polarization in e + e – processes within a TMD factorization approach and the polarizing fragmentation function

We perform a re-analysis of Belle data for the transverse Λ and Λ¯ polarization in e + e – annihilation processes within a transverse momentum dependent (TMD) factorization approach. We consider two data sets, one referring to the associated production of Λ’s with a light unpolarized hadron in an almost back-to-back configuration, and one for the inclusive Λ production, with the reconstruction of the thrust axis. We adopt the Collins-Soper-Sterman framework and employ the recent formulation on the factorization of single-inclusive hadron production. This extends a previous phenomenological study carried out in a more simplified TMD approach, leading to a new extraction of the polarizing fragmentation function (FF). While confirming several features of the previous analysis, here we include the proper QCD scale dependence of this TMD FF and carefully exploit the role of its nonperturbative component. Here, the compatibility, within a unique TMD factorization scheme, of double and single-inclusive hadron production is discussed in detail. Moreover, we consider another data set for inclusive Λ production, at much larger energies, from the OPAL Collaboration, in order to test the consistency of the entire approach. Finally, we elaborate on some fundamental issues like the role of SU(2) isospin symmetry and the heavy quark contributions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Probing transverse momentum dependent structures with azimuthal dependence of energy correlators

We study the azimuthal angle dependence of the energy-energy correlators $\langle \mathcal{E}\left({\widehat{n}}_{1}\right)\mathcal{E}\left({\widehat{n}}_{2}\right)\rangle $ in the back-to-back region for e + e - annihilation and deep inelastic scattering (DIS) processes with general polarization of the proton beam. We demonstrate that the polarization information of the beam and the underlying partons from the hard scattering is propagated into the azimuthal angle dependence of the energy-energy correlators. In the process, we define the Collins-type EEC jet functions and introduce a new EEC observable using the lab-frame angles in the DIS process. Furthermore, we extend our formalism to explore the two-point energy correlation between hadrons with different quantum numbers ${\mathbb{S}}_{i}$ in the back-to-back limit $\langle {\mathcal{E}}_{{\mathbb{S}}_{1}}\left({\widehat{n}}_{1}\right){\mathcal{E}}_{{\mathbb{S}}_{2}}\left({\widehat{n}}_{2}\right)\rangle $. We find that in the Operator Product Expansion (OPE) region the nonperturbative information is entirely encapsulated by a single number. Using our formalism, we present several phenomenological studies that showcase how energy correlators can be used to probe transverse momentum dependent structures.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗