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DOE OSTI2026

Accelerating LHC event generation with simplified pilot runs and fast PDFs

High-precision calculations are an indispensable ingredient for the success of the LHC physics programme, yet their poor computing efficiency has been a growing cause for concern, threatening to become a paralysing bottleneck in the coming years. We present solutions to eliminate the apprehension by focussing on two major components of generalpurpose Monte Carlo event generators: the evaluation of parton distribution functions, and the generation of perturbative matrix elements. We show that for the cost-driving event samples employed by the ATLAS experiment to model omnipresent, irreducible Standard Model backgrounds, such as weak boson or top-quark pair production in association with jets, these computational components dominate the overall run time by up to 80 %. We demonstrate that a reduction of the computing footprint of LHAPDF and SHERPA by factors of around 40 can be achieved for multi-leg NLO event generation.

Bothmann, Enrico [Gottingen U.]↗

DOE OSTI2025

Multidimensional measurements of beam single-spin asymmetries in semi-inclusive deep-inelastic charged-kaon electroproduction off protons in the valence region

Measurements of beam single-spin asymmetries in semi-inclusive deep-inelastic electron scattering (SIDIS) with positively charged kaons off protons have been performed with 10.6 and 10.2 GeV incident electron beams using the CLAS12 spectrometer at Jefferson Lab. We report an analysis of the electroproduction of positively charged kaons over a large kinematic range of fractional energy, Bjorken 𝑥, transverse momentum, and photon virtualities 𝑄 2 ranging from 1 GeV 2 up to 6 GeV 2 . This is the first published multidimensionally binned CLAS12 measurement of a kaon SIDIS single-spin asymmetry in the valence quark regime. The data provide constraints on the structure function ratio $𝐹^{sin \space𝜙}_{𝐿⁢𝑈}$⁡/$𝐹_{𝑈⁢𝑈}$, where $𝐹^{sin \space𝜙}_{𝐿⁢𝑈}$ is a quantity with a leading twist of twist-3 that can reveal novel aspects of the quark-gluon correlations within the nucleon. The impact of the data on understanding the underlying reaction mechanisms and their kinematic variation is explored using theoretical models for the different contributing twist-3 parton-distribution functions (PDFs) and fragmentation functions (FFs).

form factors↗

DOE OSTI2026

New framework for extracting GPDs from exclusive photon electroproduction

Recently, a new framework for studying generic 2 → 3 hard exclusive reactions, referred to as single-diffractive hard exclusive processes, has been introduced to provide a cleaner separation of the underlying physical mechanisms. In this work, we expand this formalism to the case of exclusive real-photon electroproduction off a nucleon, 𝑒⁡(ℓ) +𝑁⁡(𝑝) →𝑒⁡(ℓ′) +𝑁⁡(𝑝′) + 𝛾⁡(𝑞′), which represents the classical channel for accessing generalized parton distributions (GPDs) in nucleons and nuclei. This extension enables a more systematic and physically transparent formulation of the reaction dynamics, paving the way for improved extractions of GPDs from experimental data as compared to existing approaches.

Qiu, Jian-Wei [Thomas Jefferson National Accelerat↗

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

Inverse problem in the large momentum effective theory framework

One proposal to compute parton distributions from first principles is the large momentum effective theory (LaMET), which requires the Fourier transform of matrix elements computed nonperturbatively. Lattice quantum chromodynamics (QCD) provides calculations of these matrix elements over a finite range of Fourier harmonics that are often noisy or unreliable in the largest computed harmonics. It has been suggested that enforcing an exponential decay of the missing harmonics helps alleviate this issue. Using nonperturbative data, we show that the uncertainty introduced by this inverse problem in a realistic setup remains significant without very restrictive assumptions, and that the importance of the exact asymptotic behavior is minimal for values of 𝑥 where the framework is currently applicable. We show that the crux of the inverse problem lies in harmonics of the order of 𝜆 = 𝑧⁢𝑃 𝑧 ∼ 5–15, where the signal in the lattice data is often barely existent in current studies, and the asymptotic behavior is not firmly established. We stress the need for more sophisticated techniques to account for this inverse problem, whether in the LaMET or related frameworks like the short-distance factorization. We also address a misconception that, with available lattice methods, the LaMET framework allows a “direct” computation of the 𝑥-dependence, whereas the alternative short-distance factorization only gives access to moments or fits of the 𝑥-dependence.

Dutrieux, Hervé [Aix-Marseille Université, Marseil↗

DOE OSTI2026

Collins-Soper kernel and reduced soft function in lattice QCD

We evaluate the Collins-Soper kernel and the reduced soft function in lattice QCD, incorporating 𝒪⁡(𝛼 𝑠 ) matching corrections. The calculation relies on the evaluation of the quasitransverse momentum–dependent wave function with asymmetric staple-shaped quark bilinear operators and four-point meson form factors. These quantities are computed nonperturbatively using two 𝑁 𝑓 =2 + 1 + 1 twisted-mass fermion ensembles with the same lattice spacing of 𝑎 = 0.093 fm: the first ensemble has a lattice size of 24 3 × 48 and a pion mass of 346 MeV, and the second one has a lattice size of 32 3 × 64 and a pion mass of 261 MeV. The Collins-Soper kernel and the soft function are needed for the determination of the transverse momentum–dependent parton distribution functions.

Lattice QCD↗

DOE OSTI2026

Determination of proton PDF uncertainties with Markov chain Monte Carlo

We present an analysis of parton distribution functions (PDFs) of the proton using Markov chain Monte Carlo (MCMC) methods. The MCMC approach naturally implements Bayes’ theorem and, thus, provides a means to directly sample the underlying probability distribution—in this case, the probability distribution of the PDF parameters. This allows for a straightforward propagation of the resulting uncertainties into any PDF-dependent observable, preserving their simple probabilistic interpretation. In our analysis we include a broad set of deep inelastic scattering data from HERA, BCDMS and NMC experiments along with the Drell-Yan, 𝑊 and 𝑍 boson data from LHC and Tevatron experiments, which combined with theoretical calculations at next-to-next-to-leading order in QCD allow for realistic determination of PDFs. The main focus of this analysis is to explore alternative methods for PDF uncertainty estimation that are more firmly grounded in statistical principles. We show that the flexibility of the Bayes framework, allowing one, e.g., to account for non-Gaussianity or inconsistencies of datasets, is crucial to extract realistic uncertainties when such assumptions are not fulfilled. We also demonstrate that MCMC allows one to determine the Δ⁢𝜒 2 value corresponding to a given confidence level in the sample, which can, in turn, be used as a statistically well-founded tolerance criterion used in the Hessian method, thus addressing one of its main long-standing drawbacks.

Risse, Peter Clemens [Universität Münster (Germany↗

DOE OSTI2026

Determination of nuclear PDFs using Markov chain Monte Carlo methods

Global QCD analyses of nuclear parton distribution functions (nPDFs) have traditionally relied on the Hessian method for uncertainty estimation. However, the inherent Gaussian approximation and reliance on local curvature often prove insufficient for nPDF fits, which are frequently characterized by limited data constraints and non-Gaussian likelihoods. In this paper, we present the first nPDF determination based on Markov Chain Monte Carlo (MCMC) techniques, implemented within the nCTEQ framework using an adaptive Metropolis-Hastings algorithm. The MCMC approach enables a direct mapping of the posterior distribution and reveals a highly nontrivial parameter-space structure, including multiple modes and pronounced non-Gaussian behavior, particularly for the valence PDFs. We perform the first single-nucleus global analysis of lead PDFs using exclusively lead data and compare it to a multi-nuclei fit employing a standard analytic A dependence. The inclusion of lighter nuclei reduces quark uncertainties and modifies the shape of the lead PDFs, while leaving the gluon distribution largely unaffected. A complementary Hessian analysis exposes systematic limitations of the Gaussian approximation. Our results demonstrate that MCMC methods provide a more reliable framework for uncertainty quantification in nPDF determinations.

Derakhshanian, N. [Institute of Nuclear Physics Po↗

DOE OSTI2025

Global QCD analysis of spin PDFs in the proton with high-𝑥 and lattice constraints

We perform a comprehensive global QCD analysis of spin-dependent parton distribution functions (PDFs), combining all available data on inclusive and semi-inclusive deep-inelastic scattering (DIS), as well as inclusive weak boson and jet production in polarized 𝑝⁢𝑝 collisions, simultaneously extracting spin-averaged PDFs and fragmentation functions. Including recent Jefferson Lab DIS data at high 𝑥, together with subleading power corrections to the leading-twist framework, allows us to verify the stability of the PDFs for 𝑊 2 ≥ 4 GeV 2 and quantify the uncertainties on the spin structure functions more reliably. We explore the use of new lattice QCD data on gluonic pseudo-Ioffe time distributions, which, together with jet production and high-𝑥 DIS data, improve the constraints on the polarized gluon PDF. The expanded kinematic reach afforded by the data into the high-𝑥 region allows us to refine the bounds on higher-twist contributions to the spin structure functions, and test the validity of the Bjorken sum rule.

Perturbative QCD↗

DOE OSTI2026

Charm quark evolution in the early stages of heavy-ion collisions

Heavy quarks are predominantly generated at the initial stage of relativistic heavy-ion collisions such that heavy flavor observables have the potential to provide information on the pre-equilibrium medium dynamics. In this study, we investigate the sensitivity of D-meson $R_{AA}$ and $v_2$ to early-time charm quark dynamics in Pb+Pb collisions at $\sqrt{s_{NN}}$=5.02 TeV. We employ the IP-Glasma+MUSIC+UrQMD framework to model the evolution of the bulk medium. Charm quarks are generated using PYTHIA with nuclear parton distribution functions and evolved using Langevin dynamics within MARTINI. We observe that even though there is significant momentum broadening in the earliest stage, D-meson $R_{AA}$ and $v_2$ are only weakly sensitive to pre-equilibrium interactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Strangeness in the proton from $W+$ charm production and SIDIS data

We perform a global QCD analysis of unpolarized parton distribution functions (PDFs) in the proton, including new 𝑊+⁢ charm production data from 𝑝⁢𝑝 collisions at the LHC and semi-inclusive pion and kaon production data in lepton-nucleon deep-inelastic scattering, both of which have been suggested for constraining the strange quark PDF. Compared with a baseline global fit that does not include these datasets, the new analysis reduces the uncertainty on the strange quark distribution over the range 0.01 < 𝑥 < 0.3, and provides a consistent description of processes sensitive to strangeness in the proton. Including the new datasets, the ratio of strange to nonstrange sea quark distributions is $R_s = (s + \bar{s})/(\bar{u} +\bar{d})$ $=$ {$0.7⁢2^{+0.52}_{−0.34}, 0.4⁢6^{+0.30}_{−0.20}, 0.3⁢2^{+0.23}_{−0.15}$} for 𝑥 ={$0.01, 0.04, 0.1$} at 𝑄 2 $=$ 4 GeV 2 . The data place more stringent constraints on the strange asymmetry $(s - \bar{s})$, which is found to be consistent with zero in this range.

Anderson, Trey [College of William and Mary, Willi↗

DOE OSTI2025

Off forward non- s -channel helicity conserving contributions to exclusive vector quarkonium production from the spin dependent BFKL Pomeron

A novel contribution to off forward, exclusive vector quarkonium production, γ(*)+p → V+p, at high energy is derived which corresponds to a t-channel exchange of a Balitsky-Fadin-Kuraev-Lipatov (BFKL) hard Pomeron, with a helicity flip of the proton. This “spin-dependent BFKL Pomeron” is required in a consistent expansion in powers of the momentum transfer t ≈−Δ$^{2}_{⊥}$ beyond first order. The spin-dependent Pomeron violates s-channel helicity conservation at O(Δ$^{2}_{⊥}$), and beyond. Expanding to leading twist only, it corresponds to generalized parton distributions E g (x,t) for vanishing skewness. We derive explicit expressions for the eikonal BFKL amplitudes, to all orders in dipole size times momentum transfer, for all helicity configurations of the particles in the initial and final states. We also provide numerical estimates of the helicity flip two gluon exchange amplitude at moderate x from a light cone quark model of the proton. The spin dependent BFKL Pomeron could, in principle, be discovered via double spin asymmetries in e+p → e+p+J/ψ with a transversely polarized proton and longitudinally polarized electron in the initial state.

Deep inelastic scattering↗

DOE OSTI2026

Final SeaQuest Results on the Flavor Asymmetry of the Proton Light-Quark Sea with Proton-Induced Drell-Yan Process

The Fermilab E906/SeaQuest collaboration performed measurements of the Drell-Yan process using 120 GeV proton beams bombarding liquid hydrogen and liquid deuterium targets. A combined analysis of all collected data was performed to obtain the final results for the 𝜎 𝑝⁢𝑑 /2⁢𝜎 𝑝⁢𝑝 Drell-Yan cross section ratio covering the kinematic region of 0.13 < 𝑥 <0.45. The 𝑥 dependencies of $\bar{d}$(𝑥)/$\bar{𝑢}$⁡(𝑥) and $\bar{d}$(𝑥) $-$ $\bar{𝑢}$⁡(𝑥) are extracted from these cross section ratios. It is found that $\bar{d}$(𝑥) is greater than $\bar{𝑢}$⁡(𝑥) over the entire measured 𝑥 range, with improved statistical accuracy compared to previous measurements. The new results on $\bar{d}$(𝑥)/$\bar{𝑢}$⁡(𝑥) and $\bar{d}$(𝑥) $-$ $\bar{𝑢}$⁡(𝑥) are compared to various parton distribution functions and theoretical calculations.

Leung, C. H. [University of Illinois at Urbana-Cha↗

DOE OSTI2026

Large-momentum effective theory’s asymptotic extrapolation vs the inverse problem

Large-momentum effective theory is a physics-guided systematic expansion to calculate light-cone parton distributions, including collinear (PDFs) and transverse-momentum-dependent ones, at any fixed momentum fraction 𝑥 within a range of [𝑥 min , 𝑥 max ]. It theoretically solves the ill-posed inverse problem that afflicts other theoretical approaches to collinear PDFs, such as short-distance factorizations. Recently, Dutrieux et al. raised practical concerns about whether current or even future lattice data will have sufficient precision in the subasymptotic correlation region to support an error-controlled extrapolation—and if not, whether it becomes an inverse problem where the relevant uncertainties cannot be properly quantified. While we agree that not all current lattice data have the desired precision to qualify for an asymptotic extrapolation, some calculations do, and more are expected in the future. We comment on the analysis and results in Dutrieux et al. and argue that a physics-based systematic extrapolation still provides the most reliable error estimates, even when the data quality is not ideal. In contrast, reframing the long-distance asymptotic extrapolation as a data-driven-only inverse problem with ad hoc mathematical conditioning could lead to unnecessarily conservative errors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Study of deeply virtual Compton scattering at the future electron-ion collider

This study presents the impact of future measurements of deeply virtual Compton scattering (DVCS) with the ePIC detector at the electron-ion collider (EIC), currently under construction at Brookhaven National Laboratory. The considered process is sensitive to generalized parton distributions (GPDs), the understanding of which is a cornerstone of the EIC physics program. Our study marks a milestone in the preparation of DVCS measurements at EIC and provides a reference point for future analyses. In addition to presenting distributions of basic kinematic variables obtained with the latest ePIC design and simulation software, we examine the impact of future measurements on the understanding of nucleon tomography and DVCS Compton form factors, which are directly linked to GPDs. We also assess the impact of radiative corrections and background contribution arising from exclusive π 0 production.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Small-𝑥 asymptotics of the leading-twist flavor-singlet quark TMDs

In this paper, we investigate the small-𝑥 behavior of the flavor-singlet, leading-twist quark transverse-momentum-dependent parton distribution functions (TMDs) using the light-cone operator treatment. This formalism allows us to express TMD operators at small 𝑥 in terms of polarized dipole amplitudes, enabling a systematic approach to their small-𝑥 evolution. We derive the evolution equations for these TMDs and solve them within the large-𝑁 𝑐 approximation under the linearized, double-logarithmic approximation, where 𝑁 𝑐 represents the number of quark colors. Expanding on previous work on unpolarized and helicity TMDs, we present the small-𝑥 asymptotics for a comprehensive set of TMDs, including the Sivers function, helicity worm-gear, transversity, pretzelosity, Boer-Mulders, and transversity worm-gear distributions. Our results provide a complete picture of the small-𝑥 asymptotic behavior for all leading-twist flavor-singlet quark TMDs. We also discuss the implications of our findings for phenomenological applications and outline potential avenues for further research, particularly in understanding nonlinear effects and extending beyond the double-logarithmic approximation and large-𝑁 𝑐 approximations.

Adamiak, Daniel [Thomas Jefferson National Acceler↗

DOE OSTI2025

Transverse-momentum-dependent pion structures from lattice QCD: Collins-Soper kernel, soft factor, TMDWF, and TMDPDF

We present the first lattice quantum chromodynamics (QCD) calculation of the pion valence-quark transverse-momentum-dependent parton distribution function (TMDPDF) within the framework of large-momentum effective theory (LaMET). Using correlators fixed in the Coulomb gauge (CG), we computed the quasi-TMD beam function for a pion with a mass of 300 MeV, a fine lattice spacing of 𝑎 =0.06 fm, and multiple large momenta up to 3 GeV. The intrinsic soft functions in the CG approach are extracted from form factors with large momentum transfer, and as a byproduct, we also obtain the corresponding Collins-Soper (CS) kernel. Our determinations of both the soft function and the CS kernel agree with perturbation theory at small transverse separations (𝑏 ⊥ ) between the quarks. At larger 𝑏 ⊥ , the CS kernel remains consistent with recent results obtained using both CG and gauge-invariant TMD correlators in the literature. By combining next-to-leading logarithmic factorization of the quasi-TMD beam function and the soft function, we obtain an 𝑥-dependent pion valence-quark TMDPDF for transverse separations 𝑏 ⊥ ≳1 fm. Interestingly, we find that the 𝑏 ⊥ dependence of the phenomenological parametrizations of TMDPDF for moderate values of 𝑥 are in reasonable agreement with our QCD determinations. In addition, we present results for the transverse-momentum-dependent wave function for a heavier pion with 670 MeV mass.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Significance of radiative corrections on measurements of the EMC effect

Deep inelastic scattering (DIS) from nuclear targets probes the parton distribution functions (PDFs) in nuclei. Comparisons of the PDFs from heavy nuclei and the deuteron show deviations that demonstrate a non-trivial nuclear dependence to these distributions, referred to as the EMC effect. A global analysis of the worlds data on the EMC effect reveals tensions between different extractions. Precise measurements at Jefferson Lab, studying the dependence on both the quark momentum fraction, x, and nuclear mass, show systematic discrepancies among experiments, making the extraction of the A dependence of the EMC effect sensitive to the selection of datasets. Further, by comparing various methods and assumptions used to calculate radiative corrections, we have identified differences that, while not large, significantly impact the EMC ratios and show that using a consistent radiative correction procedure resolves this discrepancy, leading to a more coherent global picture, and allowing for a more robust extraction of the EMC effect for infinite nuclear matter.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗