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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Sensitivity of transverse momentum correlations to early-stage and thermal fluctuations

Transverse momentum correlations were recently measured by the ALICE collaboration at the LHC [Acharya et al (2020 Phys. Lett. B 804 135375)]. A long-range structure in terms of relative pseudorapidity of particle pairs is observed. This may imply some signal of the initial state owing to the sheer spread of the correlation. However, the fluctuations inside a thermally equilibrated medium have to be taken into account, serving as motivation for this paper. Using lattice Quantum Chromodynamics constraints, we predicted the development and spread of balancing correlations caused by energy-momentum conservation. At the same time, we propagated the Gaussian-shaped initial correlation using hydrodynamics to estimate its effects. Our findings suggest that the resulting correlation, known as ‘the ridge,’ is sensitive both to flucutations seeded in the pre-equilibrium stage and to those seeded in the equilibrated medium. This can provide important insight into the early stages of the collision.

ALICE↗
DOE OSTI2025

Measurements of differential two-particle number and transverse momentum correlation functions in pp collisions at $\sqrt{\textit{s}}$ = 13 TeV

Differential two-particle normalized cumulants (R 2 ) and transverse momentum correlations (P 2 ) are measured as a function of the relative pseudorapidity and azimuthal angle difference (Δη, Δφ) of charged particle pairs in minimum bias pp collisions at $\sqrt{s}$ = 13 TeV. The measurements use charged hadrons in the pseudorapidity region of |η| < 0.8 and the transverse momentum range 0.2 < p T < 2.0 in order to focus on soft multiparticle interactions and to complement prior measurements of these correlation functions in p–Pb and Pb–Pb collisions. The correlation functions are reported for both unlike-sign and like-sign pairs and their charge-independent and charge-dependent combinations. Both the R 2 and P 2 measured in pp collisions exhibit features qualitatively similar to those observed in p–Pb and Pb–Pb collisions. The Δη and Δφ root mean square widths of the near-side peak of the correlation functions are evaluated and compared with those observed in p–Pb and Pb–Pb collisions and show smooth evolution with the multiplicity of charged particles produced in the collision. The comparison of the measured correlation functions with predictions from PYTHIA8 shows that this model qualitatively captures their basic structure and characteristics but feature important differences. In addition, the R$^{CD}_{2}$ is used to determine the charge balance function of hadrons produced within the detector acceptance of the measurements. The integral of the balance function is found to be compatible with those reported by a previous measurement in Pb–Pb collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Long-Range Transverse-Momentum Correlations and Radial Flow in Pb-Pb Collisions at the LHC

This Letter presents measurements of long-range transverse-momentum correlations using a new observable, 𝑣 0⁡ (𝑝 T ), serving as a probe of event-by-event radial-flow fluctuations, the underlying radial expansion, and the medium’s properties in heavy-ion collisions. Results are reported for inclusive charged particles, pions, kaons, and protons across various centrality intervals in Pb-Pb collisions at $\sqrt{𝑠_{\textrm{NN}}}$ = 5.02 TeV, recorded by the ALICE detector. A pseudorapidity-gap technique, similar to that used in anisotropic-flow studies, is employed to suppress short-range correlations. At low 𝑝 T , a characteristic mass ordering consistent with hydrodynamic collective flow is observed. At higher 𝑝 T (>3 GeV/𝑐), protons exhibit larger 𝑣 0 ⁡(𝑝 T ) than pions and kaons, in agreement with expectations from quark-recombination models. Comparisons to viscous hydrodynamic calculations with varying bulk viscosity and equation of state demonstrate the sensitivity of the 𝑣 0 ⁡(𝑝 T ) observable to these key medium properties. The findings establish 𝑣 0 ⁡(𝑝 T ) as a valuable addition to the set of observables used in Bayesian analyses for extracting the transport properties and constraining the equation of state of strongly interacting matter, while also helping to systematically explore its sensitivity and impact within such global studies.

Acharya, S. [INFN] (ORCID:0000000292135329)↗
DOE OSTI2026

Beam-energy dependence of correlations between mean transverse momentum and anisotropic flow of charged particles in Au+Au collisions at RHIC

The correlation between the mean transverse momentum, [ p T ], and the squared anisotropic flow, $v^2_n$, on an event-by-event basis has been suggested to be influenced by the initial conditions in heavy-ion collisions. We present measurements of the variances and covariance of [ p T ] and $v^2_n$, along with their dimensionless ratio, for Au+Au collisions at various beam energies: $\sqrt{s_{NN}}$ = 14.6, 19.6, 27, 54.4, and 200 GeV. Our measurements reveal a distinct energy-dependent behavior in the variances and covariances. In addition, the dimensionless ratio displays a similar behavior across different beam energies. We compare our measurements with hydrodynamic models and similar measurements from Pb+Pb collisions at the Large Hadron Collider (LHC). These findings provide valuable insights into the beam energy dependence of the specific shear viscosity ( η/s ) and initial-state effects, allowing for differentiating between different initial-state models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1985

Nucleus-nucleus interaction above several hundred GeV/n

The Japanese-American Cooperative Emulsion Experiment (JACEE) have been investigating high energy nuclear interactions of cosmic ray nuclei by means of balloon-borne emulsion chamber. Current exposure parameters are listed. Analysis of the last two experiments (JACEE4 and JACEE5) are still in progress. A result of semi-inclusive analysis of a sample set of central collision events is presented here, concerning multiplicity, rapidity fluctuation for extremely high multiplicity events and correlation between transverse momentum and estimated energy density.

Burnett, T. H.↗
DOE OSTI2025

Joint Factorization of QCD and QED Radiation in Lepton-Hadron Scattering

The factorization theorem plays an important role in the analysis of high energy quantum chromodynamic (QCD) processes, separating the nonperturbative hadronic interaction into the universal parton distribution functions (PDFs) and fragmentation functions (FFs) and the process-dependent interactions into short distance perturbative calculations, with any interference power suppressed. With a virtual photon exchange, lepton-hadron deep inelastic scattering (DIS) provides an electromagnetic hard probe for the partonic structure of colliding hadrons and has played an important role in the development of QCD factorization. However, the collision induced QED radiation can change the momentum of the exchanged but unobserved virtual photon, making the photon-hadron frame, where the factorization formalism for DIS and semi-inclusive DIS (SIDIS) was derived, ill defined. A new analogous factorization approach has been introduced to separate the leading power process-independent QED radiative contributions to the single photon exchange by introducing lepton distribution functions (LDFs) and lepton fragmentation functions (LFFs), while process-dependent effects are perturbatively calculated with large logarithms removed [J. High Energ. Phys. 2021, 157 (2021)]. These LDFs and LFFs are considered global, as they appear in many different interactions, such as e+e-, DIS and SIDIS, so data from experiments can be used to fit and describe these functions across a wide range of lepton scattering. In this work, I will apply this new hybrid factorization approach to lepton-hadron DIS and SIDIS. For DIS, I derive the NLO short distance perturbative contribution to the cross section and demonstrate the effects the QED radiation has on the cross section using this approach using the CTEQ parameterization for the QCD functions. As part of the SIDIS analysis, I study the cross-section in two different kinematic regions: (1) the scattered lepton and observed hadron are not near back-to-back, and (2) they are close to back-to-back, where collinear QCD factorization works for (1) and TMD QCD factorization for (2) while collinear QED factorization works for both. As part of this work, I show the effects on the SIDIS cross section using fixed order calculations for the unpolarized structure function by first showing the effect of the radiative corrections on the main kinematic variables, especially how the internal transverse momentum is significantly correlated to the external angular dependence, and then the unpolarized structure function (or cross section) with matching between the descriptions for low and high transverse momentum. This work will impact the calculations for predictions for data from COMPASS and various Jefferson Lab experiments.

Cammarota, Justin [Univ. of Kentucky, Lexington, K↗
NASA NTRS1998

Transverse momentum dependent two-pion Bose-Einstein correlations in Au + Au collisions at 11.6 A (center-dot) GeV/c

Bose-Einstein correlations of (pi)(sup +)(pi)(sup +) and (pi)(sup -) (pi)(sup -) pairs collected by the BNL-E866 Forward Spectrometer in 11.6 A(center-dot)GeV/c Au + Au collisions have been measured. The data were analyzed using three-dimensional correlation functions parameterized by the Yano-Koonin-Potgoretskii and Bertsch-Pratt formalism to study transverse momentum dependent source parameters. Rapid decreases of longitudinal source radii and slower decreases in the transverse parameters with increasing transverse momentum were observed, which suggests a strong longitudinal and some transverse expansion. A freeze-out time (tau)(sub 0) was derived as 4.5--5 fm/c, under the assumption of the freeze-out temperature T = 130 MeV, and the duration of emission was found to be (delta)(tau) (approx) 2--4 fm/c.

Lee, J. H.↗
DOE OSTI2024

Dihadron correlations in small- x DIS at NLO: transverse momentum dependent fragmentation

We compute the inclusive dihadron cross-section in Deep Inelastic Scattering at next-to-leading order (NLO) and small x in the Color Glass Condensate. We focus on the kinematic limit where the hadrons are produced at forward rapidities (in the direction of the virtual photon) and back-to-back in the transverse plane. Our calculation demonstrates that the coefficient of the Sudakov double logarithm for this process is –$\frac{αs}{2π}$ [C F + $\frac{Nc}{2}$] instead of –$\frac{αsNc}{4π}$ when back-to-back jets are measured in the final state. To preserve the universality of the Sudakov soft factor associated with the Weizsäcker-Williams transverse momentum dependent (TMD) gluon distribution, we promote the collinear fragmentation functions into TMD fragmentation functions. We then perform the resummation of the Sudakov logarithms through Collins-Soper-Sterman evolution of the TMD fragmentation functions and the Weizsäcker-Williams TMD gluon distribution. Finally, analytic expressions are obtained for the NLO coefficient functions in the $\overline{MS}$-scheme. These results pave the way towards numerically calculating dihadron correlations at small x at the future Electron-Ion Collider with full NLO accuracy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Observation of nuclear modification of energy-energy correlators inside jets in heavy ion collisions

Energy-energy correlators are constructed by averaging the number of charged particle pairs within jets, weighted by the product of their transverse momenta, as a function of the angular separation of the particles within a pair. They are sensitive to a multitude of perturbative and nonperturbative quantum chromodynamics phenomena in high-energy particle collisions. Using lead-lead data recorded with the CMS detector, energy-energy correlators inside high transverse momentum jets are measured in heavy ion collisions for the first time. The data are obtained at a nucleon-nucleon center-of-mass energy of 5.02 TeV and correspond to an integrated luminosity of 1.70 nb −1 . A similar analysis is done for proton-proton collisions at the same center-of-mass energy to establish a reference. The ratio of lead-lead to proton-proton energy-energy correlators reveals significant jet substructure modifications in the quark-gluon plasma. The results are compared to different models that incorporate either color coherence or medium response effects, where the two effects predict similar substructure modifications.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Dynamics of heavy quarks in strongly coupled $\mathcal{N}$ = 4 SYM plasma

We calculate the probability distribution P(k) for a heavy quark with velocity v propagating through strongly coupled N = 4 SYM plasma in the ’t Hooft limit (N c → ∞, λ = g 2 N c → ∞) at a temperature T to acquire a momentum k due to interactions with the plasma. This distribution encodes the well-known drag coefficient η D and the transverse and longitudinal momentum diffusion coefficients κ T and κ L . The jet quenching parameter $\hat{q}$ can be extracted from P(k) for v = 1. Going beyond these known Gaussian characteristics of P(k), our calculation determines all of the higher order and mixed moments to leading order in 1/$\sqrt{λ}$ for the first time. These non-Gaussian features of P(k) include qualitatively novel correlations between longitudinal energy loss and transverse momentum broadening at nonzero v. We show that all higher moments scale characteristically with an effective temperature of the boosted plasma in the heavy quark rest frame, and we demonstrate that these non-Gaussian characteristics can be sizable in magnitude and even dominant in physically relevant situations. We use these results to derive a Kolmogorov equation for the evolution of the probability distribution for the total momentum of a heavy quark that propagates through strongly coupled plasma. This evolution equation accounts for all higher order correlations between transverse momentum broadening and longitudinal energy loss, which we have calculated from first principles. It reduces to a Fokker-Planck equation when truncated to only include the effects of η D , κ T and κ L . Remarkably, while heavy quarks do not reach kinetic equilibrium with the plasma if evolved with this Fokker-Planck equation, by showing that the Boltzmann distribution is a static solution of the all-order Kolmogorov equation that we have derived we demonstrate that heavy quarks do reach kinetic equilibrium if evolved with this equation. Our results thus provide a dynamically complete framework for understanding the thermalization of a heavy quark that may be initially far from equilibrium in the strongly coupled N = 4 SYM plasma — as well as new insight into heavy quark transport and equilibration in quark-gluon plasma.

Holography and Hydrodynamics↗
DOE OSTI2026

Impact of QCD energy evolution on observables in heavy-ion collisions

Here, we study how the inclusion of energy dependence as dictated by quantum chromodynamic (QCD) small-x evolution equations affects key observables in ultra-relativistic heavy-ion collisions. Specifically, we incorporate JIMWLK evolution into the IP-Glasma framework, which serves as the initial condition for a simulation pipeline that includes viscous relativistic hydrodynamics and a hadronic afterburner. This approach enables a consistent modeling of highly energetic nuclei across varying Bjorken-x values, which are relevant for different collision energies and rapidity regions. In comparison to the standard IP-Glasma setup without small-x evolution, we observe pronounced changes in particle multiplicities and spectral distributions, especially in smaller systems and at the highest available energies. We further explore effects on anisotropic flow observables and correlations between mean transverse momentum and elliptic flow. Our findings underscore the critical role of nonlinear QCD evolution in accurately modeling the early stages of heavy-ion collisions, as well as its implications for extracting transport properties of the quark-gluon plasma.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Exploring the Nucleon Structure via Deep Electroproduction Processes

Understanding the internal structure of the nucleon is a fundamental goal of modern physics, which aims at a comprehensive framework describing the internal dynamics of quarks and gluons. Among other structure functions, Generalized Parton Distributions (GPDs) offer a powerful framework for describing the nucleon dynamics by correlating the longitudinal momentum and the transverse position of its internal partons. Such a correlation provides a three-dimensional picture of the nucleon and enables access to fundamental properties, including the internal pressure distributions and the parton’s angular momentum contribution to the nucleon's total spin, thereby playing a central role in resolving the nucleon spin puzzle. At the Thomas Jefferson National Facility (JLab), polarized electron beam experiments allow for probing GPDs through the measurement of hard exclusive processes. Among the cleanest experimental channels, we find the electro-production of a real photon through the Deeply Virtual Compton Scattering (DVCS) mechanism. The first data-taking period of the CLAS12 program, taking place in 2018, allowed for unique DVCS Beam Spin Asymmetry (BSA) measurements in the phase space covered by a 10.6 GeV polarized electron beam impinging on an unpolarized liquid hydrogen target. Although detecting all final-state particles ensures exclusivity of the process, conservation laws indicate that it is not mandatory. I adopt an approach omitting the direct detection of the recoil proton, providing a simplified yet effective event selection strategy that boosts statistics and gives access to a larger phase space sensitive to the underlying GPD dynamics through BSA and cross section measurements. The Double DVCS (DDVCS) process promises a dedicated mapping of GPDs. Contributing to the electro-production of a lepton pair cross-section, the DDVCS reaction extends DVCS by allowing the final-state photon to be virtual, enriching the kinematic phase space and providing unique access to the internal correlations encoded by GPDs. A feasibility study is conducted to assess the potential of future DDVCS measurements at Jefferson Lab and the future Electron-Ion Collider (EIC). While Jefferson Lab will provide DDVCS measurements in the valence region through the SoLID$\mu$ and $\mu$CLAS12 experimental projects, in the long term, the EIC will provide complementary measurements in the sea region, both accessing unprecedented information about GPDs in a phase space region otherwise inaccessible. Taken together, these investigations demonstrate both the current capabilities and future opportunities for probing GPDs through exclusive processes. The experimental analysis of DVCS at CLAS12 provides precise measurements within an established framework, while the phenomenological study of DDVCS opens the door to richer and more comprehensive explorations with future detectors and facilities.

Alvarado, Juan [Université Paris-Saclay: Gif-sur-Y↗
DOE OSTI2025

Universality in the Near-Side Energy-Energy Correlator

We investigate the energy-energy correlator (EEC) of hadrons produced on the same side in e + e − annihilation or in leading jets in p p collisions. We observe a remarkable universality of the correlator. Using a nonperturbative transverse momentum dependent (TMD) fragmentation function to model the transition from the “free-hadron” region to the perturbative collinear region, we are able to describe the near-side shapes and peaks over a wide range of energy for both the e + e − annihilation and the p p jet substructure measurements in terms of just two parameters. We present further predictions for the ratio of the projected three-point energy correlator to the EEC. The excellent agreement between our calculations and the experimental data may provide new insights into the role of nonperturbative physics for EECs, and suggests the possibility of exploring nonperturbative TMDs using theoretical tools developed for the energy correlators. Published by the American Physical Society 2025

Liu, Xiaohui (ORCID:0000000277011205)↗
DOE OSTI2025

Study of $\langle {p}_{\text{T}}\rangle$ and its higher moments, and extraction of the speed of sound in Pb-Pb collisions with ALICE

Ultrarelativistic heavy-ion collisions produce a state of hot and dense strongly interacting QCD matter called quark-gluon plasma (QGP). On an event-by-event basis, the volume of the QGP in ultracentral collisions is mostly constant, while its total entropy can vary significantly due to quantum fluctuations, leading to variations in the temperature of the system. Exploiting this unique feature of ultracentral collisions allows for the interpretation of the correlation of the mean transverse momentum ($\langle$p T $\rangle$) of produced charged hadrons and the number of charged hadrons as a measure for the speed of sound, c s . This speed is related to the rate at which compression waves travel in the QGP and is determined by fitting the relative increase in $\langle$p T $\rangle$ with respect to the relative change in the average charged-particle density ($\langle$dN ch /dη$\rangle$) measured at mid-rapidity. This study reports the event-average $\langle$p T $\rangle$ of charged particles as well as the variance, skewness, and kurtosis of the event-by-event transverse momentum per charged particle ([p T ]) distribution in ultracentral Pb-Pb collisions at a center-of-mass energy of 5.02 TeV per nucleon pair using the ALICE detector. Different centrality estimators based on charged-particle multiplicity or the transverse energy of the event are used to select ultracentral collisions. By ensuring a pseudorapidity gap between the region used to define the centrality and the region used to perform the measurement, the influence of biases and their potential effects on the rise of the mean transverse momentum is tested. The measured c$^{2}_{s}$ is found to strongly depend on the exploited centrality estimator and ranges between 0.1146±0.0028 (stat.)±0.0065 (syst.) and 0.4374±0.0006 (stat.)±0.0184 (syst.) in natural units. The self-normalized variance shows a steep decrease towards ultracentral collisions, while the self-normalized skewness variables show a maximum, followed by a fast decrease. These non-Gaussian features are understood in terms of the vanishing of the impact-parameter fluctuations contributing to the event-to-event [p T ] distribution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Unraveling nonperturbative QCD with transverse momentum hadronic structures

The main purpose of this thesis is to investigate the theoretical foundations of the factorization theorems that involve transverse quark and gluon momentum distributions, and to better understand the interface between foundational questions and phenomenological applications. Many of these applications involve using transverse parton momentum dependent (TMD) correlation functions as tools for probing the complex nonperturbative structures of the hadrons. We first introduce the concepts of collinear and TMD factorization in a toy-model theory and, by leveraging the comparative simplicity of such a model, we test the range of validity and limitations of the factorization approach. At the same time, we introduce the conventional approaches that are adopted for the phenomenological extractions of the TMD distributions, and catalog the advantages and disadvantages. Following the general theoretical framework of factorization, we then develop a different approach to TMD phenomenology that is able to systematically integrate the perturbative and non perturbative information in parametrizations of TMD distributions, while being completely consistent with their operator definitions and the predictions of QCD, including their nontrivial evolution. The name Hadron Structure Oriented approach, or HSO, is coined in order to emphasize the central role of the nonperturbative nature of QCD and its relation to the partonic structure of hadrons. Finally, we provide a first phenomenological implementation of the HSO approach by extracting TMD distributions relying on low-to-moderate energy Drell-Yan data. The quality and robustness of the results are then compared against higher energy processes like high-Q2 Z0 boson production. Our analysis demonstrates the feasibility of this novel approach and points the way toward the improvements it can achieve in future applications.

Rainaldi, Tommaso [Old Dominion Univ., Norfolk, VA↗
DOE OSTI2026

QCD Theory and Transverse Momentum Dependent Physics

A major challenge for QCD theorists is to understand how to different categories of QCD physics contribute to a single observable. This is the goal of QCD factorization theory. Today, QCD physicists are tasked with describing increasingly detailed properties of transverse momentum dependent particle distributions, including their shapes and normalizations, their variation with energy and other kinematical variables, the identity of particles involved, correlations with spin, and the relationship between transverse momentum distributions in different processes. Embedded within that broad effort are specific fundamental questions at the heart of QCD theory. Namely, how does one give precise, quantitative meaning to quark and gluon concepts in hard scattering events, and what are the limits of those concepts? In the past two decades, there has been a renaissance in TMD QCD, with a broad spectrum of motivations driving the study of TMD observables. TMD QCD studies are in a transformative stage; subfields that traditionally progressed nearly independently of one other, such as hadronic structure studies and the study of perturbative QCD gluon radiation in high-energy collisions, are becoming intertwined. It is thus becoming increasingly clear that unified approaches -- those that incorporate all the relevant phenomena into a single formalism rooted in QCD fundamentals -- will be critical to the mission to expand the current understanding of QCD nuclear/hadronic dynamics. TMD QCD factorization theorems and their generalizations will be central to these efforts. The factorization theorems, in addition, provide the practical prescription for applying specific calculations to phenomenology. The goal of this project was to unify and push the boundaries of traditional TMD research and prepare it for use in future phenomenological applications.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Jet charge with global event shapes: Probing quark flavor dynamics

We propose measuring the jet electric charge of jet regions, defined within the framework of global event shapes, as a probe of quark flavor dynamics within the nucleon and the hadronization process. In particular, we consider a measurement of the jet region charge while simultaneously keeping track of the energy flow throughout the event, as characterized by the global event shape. As a concrete example, we focus on the measurement of the (Q), the jet charge of the jet region (𝐽) defined within the framework of the 1-Jettiness global event shape (𝜏 1 ) for the Deep Inelastic Scattering (DIS) process, 𝑒 − +𝑝→𝑒 − +𝐽+𝑋, with unpolarized or longitudinally polarized protons. The 1-Jettiness distribution, binned according to jet charge, allows for enhanced quark flavor separation of the initial state unpolarized or polarized PDFs. On the other hand, the jet charge distribution binned by 1-Jettiness can serve as a probe of quark flavor dynamics in the final state hadronization process. We derive a factorization theorem for simultaneous measurements of 𝜏 1 and Q in the resummation region, 𝜏 1 ≪𝑃 𝐽 𝑇 , where 𝑃 𝐽 𝑇 denotes the transverse momentum of the jet region. The correlation between the jet region charge and the charge of the struck quark is expected to be the strongest in the resummation region. The factorization theorem contains a new universal , generalizing the standard jet function to include a jet charge measurement. Therefore these universal functions can be extracted from a global analysis of N-jettiness and thrust at 𝑒 + ⁢𝑒 − colliders. We provide simulation studies to demonstrate the sensitivity of the 1-Jettiness jet charge observable to quark flavor dynamics in nucleon structure and explore the possibility of probing the final state hadronization process. This observable is well-suited for applications with existing HERA data and the future Electron-Ion Collider (EIC).

Mantry, Sonny [University of North Georgia, Dahlon↗
DOE OSTI2025

Investigating the Transverse Structure of Hadrons Using Parton Pseudodistributions

Within the pseudo-PDF framework, we investigate the perturbative contributions to correlators that are used to study transverse momentum dependent parton distributions (TMDs) on the lattice. Our results contain the full perturbative corrections which arise as artifacts from performing the calculation for a Euclidean separation between the parton fields, as well as the corrections which yield the evolution equations for the TMDs. This gives a path to extraction of the genuine non-perturbative features of the three-dimensional structure of the hadrons from lattice calculations.

Santiago, Melvin Gabriel [Old Dominion Univ., Norf↗