XIIIth Meeting on Lattice Parton Physics from Large Momentum Effective Theory (LaMET 2026)

6 Jul 2026, 08:45 → 9 Jul 2026, 19:00 Europe/Warsaw

Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Cracow, Poland

Yizhuang Liu , Maciej A. Nowak (Jagiellonian University)

The XIIIth Meeting on Lattice Parton Physics from Large Momentum Effective Theory (LaMET 2026) will be officially hosted by Jagiellonian University in Cracow, Poland, during July 6-9, 2026. This meeting aims to bring together physicists interested in LaMET and other theoretical approaches with their applications to lattice QCD in the calculation of parton physics.

 

In-person participation is strongly recommended. If you plan to come in person and need an invitation letter to apply for a Polish visa, please contact Maciej A. Nowak (maciej.a.nowak@uj.edu.pl).

 

Important deadlines:

Abstract submission: 10 June 2026

Registration: 24 Jun 2026

 

Each talk will tentatively be given 15 to 25 minutes for presentation and 5 minutes for questions. Talks based on newly published or ongoing works are preferred.

 

The registration fee is 100EUR (420 PLN) for the welcome reception, lunches, coffee breaks, and conference dinner.

 

Note that in the week preceding the meeting, the XVII Quark Confinement and Hadron Spectrum conference will be held at the University of Wrocław, Poland, between June 29th and July 4th, 2026. Also, the 18th International Workshop on Meson Physics will be held in Cracow from the 25th to the 30th of June 2026.

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Previous LaMET Workshops

Center for Fronteris in Nuclear Science, Stony Brook University, US, October 8-10, 2025

University of Maryland, College Park, US, August 11-14, 2024

University of Regensburg, Germany, July 24-26, 2023

Argonne National Laboratory, US, December 1-3, 2022

CNF (SURA), virtual meeting, US, December 7-9, 2021

CNF (SURA) and CFNS (Stony Brook U), virtual Meeting, US, September 7-11, 2020

Brookhaven National Laboratory, US, April 17-19, 2019

University of Maryland, College Park, US, April 6-8, 2018

Peking University, China, July 14-16, 2017

Shanghai Jiao Tong University, China, December 17-18, 2016

University of Maryland, College Park, US, March 30 - April 2, 2014

Shanghai Jiao Tong University, China, November 2-4, 2012

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This workshop is hosted at and supported by the Jagiellonian University.

Monday, 6 July

Registration

Introduction

Morning session

1 Polarized Gluon Helicity Distribution of the Nucleon from Lattice QCD in the Continuum Limit

We present a state-of-the-art lattice QCD calculation of the proton's gluon helicity parton distribution function (PDF) using the large-momentum effective theory (LaMET). The analysis is based on 2+1-flavor CLQCD gauge ensembles at three lattice spacings down to 0.0775 fm and a pion mass of ~300 MeV, with nucleon momenta up to 3.0 GeV. Distillation with momentum smearing is employed to enhance the signal of two-point correlators. A hybrid renormalization scheme is adopted, where self-renormalization is applied to the purely imaginary and antisymmetric matrix elements for the first time. After one-loop perturbative matching, a simultaneous extrapolation to the continuum and infinite-momentum limits is performed. The resulting gluon helicity PDF is compared with global analysis results.

Speaker: Shiyi Zhong (CUHK(SZ))

LaMET2026_Shi-Yi_Zhong 202607.pdf

2 Lattice Calculation on Quark Helicity and Unpolarized PDF with LaMET

In this report, an updated result on both quark helicity and unpolarized colinear PDFs are calculated using CLQCD ensembles within the framework of LaMET. This calculation is dedicated to give one of the newest results with continous extrapolation performed on physical point. NNLO Wilsonian coefficients and matching kernels with leading-renormalon resummation and renormalization group resummation are applied in order to improve the signal-noise ratio. With all these setups and techniques, we hope to obtain higher accuracy results of helicity and unpolarized PDFs comparable with global fits.

Speaker: Lingquan Ma (Institute of Modern Physics, Chinese Academy of Sciences)

3 Parton Distribution Functions from the Large-Momentum Expansion of Current-Current Correlators

This report presents a lattice QCD study of parton distribution functions using current-current correlators within LAME. Unlike conventional quasi-PDF approaches based on Wilson-line operators, current-current correlators have simpler renormalization properties and avoid linear power divergences and associated renormalon ambiguities. We formulate the large-momentum expansion for vector-vector and axial-vector current correlators in momentum-fraction space and derive the corresponding one-loop matching kernel in the (\overline{\mathrm{MS}}) scheme.As a first numerical test, we use existing four-point lattice data from the CLS H102 ensemble and extract the isovector proton PDF. While the current result is limited by statistics, pion mass, and hadron momentum, it demonstrates the feasibility of applying current-current correlators within LaMET.

Speaker: Jialu Zhang (Shanghai Jiao Tong University)

VV current ppt.pdf

4 Recent Progress on Light-Cone Distribution Amplitudes from LaMET

Light-cone distribution amplitudes (LCDAs) are important nonperturbative inputs for understanding the internal structure of hadrons and for studying hard exclusive processes in QCD. In recent years, Large Momentum Effective Theory (LaMET) has provided a practical way to access the full momentum-fraction dependence of LCDAs from lattice QCD.
In this talk, I will reivew recent progress in the study of LCDAs using the LaMET approach, with a focus on light mesons and light baryons. For light mesons, I will discuss recent lattice studies of pseudoscalar and vector meson LCDAs and their implications for hadron structure. For light baryons, I will review recent theoretical and numerical developments in extending LaMET calculations to baryon LCDAs. I will also briefly discuss current challenges, such as systematic uncertainties and the need for higher precision, and outline future prospects for applying LaMET to a wider range of hadronic observables.

Speaker: Jun Hua

JunHua_LaMET.pdf

Session I

5 Proton's isovector PDF with updated analysis of large-momentum lattice data

The proton's unpolarized $u(x)-d(x)$ parton distribution function (PDF) has been studied by a number of lattice QCD groups through large momentum expansion. However, due to lattice artifacts (excited state contaminations, unphysical pion masses, and discretization effects) and less-advanced theoretical analysis (renormalizations, large-distance extrapolations, and large-log resummations), the resulting PDFs cannot be compared strictly with experimental data. By using the state-of-the-art theoretical tools and mitigating the lattice artifacts empirically, we reanalyze the available datasets in the literature and find that the new PDF in physical limits are consistent with global fittings within $1\sigma$. This provides compelling evidence that large momentum expansion is capable of accurately predicting the $x$-dependence of the PDFs when ideal lattice data become available.

Speaker: Yushan Su (University of Maryland, College Park)

Proton_PDF@LaMET2026_V2.pdf

6 Colored noises near UV/IR fixed points

In the presence of "criticality'', in the sense that scale separations become large, non-trivial structures with clean boundaries exists only near a small number of extremely narrow sharp peaks in the logarithmic scale. At the intermediate scales, "colored noises'', or self-similar random fluctuations without clear shapes/boundaries, characterized by simple scaling laws with logarithmic corrections, dominate.

This vast and colored sea of noises, although brutally neglected in many over-simplified QFT narratives based on Lagrangian pictures adopted superficially from the classical physics, actually lies in the origin of local quantum fields, and serves as an amorphous bridge joining smoothly the otherwise divided worlds in the IR and UV, witnessing the matching of EFTs. And if you look deeply into the cloud, you see beauties, such as G(z)\rightarrow\frac{1}{z^{\frac{1}{4}}} or g(L)\rightarrow\frac{16\pi^{2}}{3\ln L}, lasting forever.

Following the above philosophy, this talk presents several examples of asymptotic expansions induced by (marginally) relevant and irrelevant operators near UV and IR fixed points. The examples range from the XXX spin-chain in the IR limit, OPE with condensates in 2D quartic-model/NLSM,to Bjorken asymptotics of lattice correlators in QCD.

We also raise the question regarding boundary of universality, and use the example of a non-inclusive particle number observable in 2D Ising QFT to demonstrate this notation.

Speaker: Yizhuang Liu (UJ)

Talk_O(N).pptx

7 Proton isovector helicity PDF at NNLO and the twist-3 moment $\tilde{d}_2$ from lattice QCD at physical quark masses

We present a lattice quantum chromodynamics calculation of the $x$-dependent isovector quark helicity parton distribution function (PDF) of the proton in the large momentum effective theory (LaMET) framework. Through operator product expansion (OPE) we also extract the $\tilde{d}_2$ moment of the twist-3 PDF $g_T(x)$ for the first time in the $\overline{\rm MS}$ scheme, which is proportional to the average color Lorentz force experienced by the quark in the proton. This calculation is performed on a lattice of spacing $a$ = 0.076 fm at physical quark masses. The quasi-PDF matrix elements are measured in proton states boosted to momenta $P_z=\{0, 0.25, 1.02, 1.53\}$ GeV. We first extract the lowest few helicity PDF moments from the renormalization-group (RG) invariant ratios of the matrix elements with OPE. Combined with the matrix elements relevant for $g_T(x)$, we obtain $\tilde{d}_2^{u-d}(2\ {\rm GeV})=0.0024(46)$ at next-to-leading order in $\overline{\rm MS}$.
Then, the helicity quasi-PDF matrix elements are renormalized in the hybrid scheme with linear renormalon resummation and Fourier transformed to the $x$-space after an asymptotic extrapolation. The quasi-PDF is perturbatively matched to the $\overline{\rm MS}$ PDF with RG and threshold resummations at next-to-leading power and next-to-next-to-leading logarithmic accuracies.
After resummations, we determine the PDF in the region $x\in[0.25,0.75]$. The end-point regions are then parameterized, combined with the LaMET prediction at moderate $x$, and fitted to the short-distance matrix elements in coordinate space.

Speaker: Rui Zhang (MIT)

LaMET_Rui_1.pdf

8 Extracting Vector Mellin Moments for the Pion and Kaon in Lattice QCD

In recent years, the $x$-dependence of parton distribution functions (PDFs) has become accessible through non-local operators of a boosted hadron by utilizing techniques such as large momentum effective theory (LaMET) and short distance factorization (SDF). Embedded in these distribution functions are Mellin moments, which contain information on fundamental properties of hadrons, such as the fraction of the hadron momentum carried by quarks. Moments can be extracted by utilizing SDF, which can then be benchmark of the validity of PDF construction. The pion is particularly interesting to study as it is the lightest hadron, and its SU(3) symmetry counterpart, the kaon, is also of interest. In studying both of these hadrons, we can compare the up and strange quark contributions individually and study SU(3) symmetry breaking. In this work, we study the extraction of the moments at NLO and NNLO accuracy, as well as study DGLAP evolution to study systematics.

Speaker: Joshua Miller (Temple University)

LaMET_2026_Miller.pdf

Session II

9 Nucleon Unpolarized PDFs at the Physical Point in the Coulomb Gauge

We present the first Coulomb-gauge calculation of the nucleon unpolarized parton distribution functions (PDFs) at the physical pion mass. Both the isovector and connected isoscalar channels are computed within the large-momentum effective theory (LaMET) framework on a $2+1$ flavor ensemble with lattice spacing $a = 0.076$ fm. By employing kinematically enhanced interpolating operators, we successfully reach nucleon boosts up to $P_z = 2.29$ GeV. The light-cone PDFs are extracted by applying next-to-leading-order (NLO) perturbative matching combined with next-to-leading-logarithmic (NLL) renormalization-group resummation (RGR) and exhibit good convergence between $P_z=1.78$ and 2.29 GeV. The real and imaginary parts of the matrix elements provide access to the valence $q-\bar{q}$ and full $q+\bar{q}$ combinations, respectively, from which we reconstruct the quark and antiquark distributions over the entire kinematic range $x \in [-1, 1]$. The isovector antiquark distribution exhibits a positive $\bar{d} - \bar{u}$ signal consistent with the Gottfried sum rule violation. For the connected isoscalar channel, the RGR substantially mitigates the unphysical excursions of the fixed-order result in the antiquark region, with the residual deviation from NNPDF4.0 expected to arise mainly from the disconnected diagrams not included in this study. Within the reliable moderate window of $0.25 < |x| < 0.65$, our reconstructed NLO+NLL distributions exhibit good agreement with the NNPDF4.0 global analysis.

Speaker: Qi Shi (Kent State University)

slide_QiShi.pdf

10 Progress in the Lattice of Jaffe-Manohar Spin Decomposition

We report a state-of-the-art lattice QCD calculation of the total gluon helicity contribution to the proton spin, $\Delta G$. After extrapolating to the continuum limit, $\Delta G$ is found to be $\Delta G=0.231(17)^{sta.}(44)^{sym.} at the $\overline{\mathrm{MS}}$ scale $\mu^2=10\ \mathrm{GeV}^2$, which constitutes approximately 46(9)% of the proton spin. In addition, we will also provide a theoretical workflow for extracting the total orbital angular momentum without the need for LaMET matching, and provide some numerical results.

Speaker: Dian-Jun Zhao (CUHK(Shenzhen))

2026.07.06.pdf

11 High precision nucleon matrix elements based on the unbiased estimate of all-to-all fermion propagators

We report a high-precision calculation of the nucleon isospin vector charge (g_{S,T}) using the recently proposed “blending” method, which provides high-precision stochastic estimates of the all-to-all fermion propagator. A interpolator basis element that explicitly includes the current is employed to suppress a specific nucleon–meson type of excited-state contamination, whose couples to the current operator and is enhanced by the lattice spatial volume. Based on calculations at five lattice spacings, each with multiple volumes at fixed pion mass (including the physical pion mass), we demonstrate that both the blending method and the current-involved basis are efficient and essential for suppressing excited-state contamination and for revealing hidden systematic uncertainties.

Speaker: Dr Yi-Bo Yang

Yi-Bo Yang 2026.07.06.pdf

12 Gluon Parton Distribution Functions From Boosted Euclidean Correlators in the Coulomb Gauge

Gluon parton distribution functions (PDFs) from large momentum effective theory (LaMET) have remained in poor statistical precision compared to non-singlet PDFs due to their correlators coming solely from disconnected diagrams. One method to improve the long distance signal is to remove the Wilson lines from the correlators, which are present solely to maintain gauge invariance, and compute the new correlators in a gauge fixed calculation. This method has been proven theoretically and numerically in recent quark calculations. The main challenge here is recomputing the perturbative matching for the Coulomb gauge operators. We present our perturbative and numerical results for new Coulomb gauge gluon operators.

Speaker: William Good (Michigan State University)

Good-LaMET-2026-07-05-Updated.pdf

Tuesday, 7 July

Discussion

Morning session

13 Heavy-Hadron Light-Cone Distribution Amplitudes: Heavy-Quark Symmetry, Factorization, and Lattice Access

Light-cone distribution amplitudes (LCDAs) of heavy hadrons play a central role in the QCD description of exclusive processes involving heavy quarks. They encode essential nonperturbative information and provide key inputs for phenomenological analyses based on factorization. In this talk, I will present recent progress on the structure and determination of heavy-hadron LCDAs, with emphasis on both heavy mesons and heavy baryons.

For heavy mesons, I will discuss how heavy-quark spin symmetry can be used to probe and constrain the corresponding LCDAs, clarifying their interrelations and providing new theoretical insights into their nonperturbative structure. I will then turn to the heavy-baryon case and present a factorization formula that connects the LCDA of the baryon in full QCD with its counterpart in boosted heavy-quark effective theory (HQET). This framework establishes a useful bridge between continuum factorization and approaches aimed at accessing light-cone physics from Euclidean observables.

Taken together, these developments advance our understanding of heavy-hadron LCDAs and help lay the foundation for more systematic nonperturbative determinations, including future studies in lattice QCD.

Speaker: Jun Zeng (Hainan Normal University)

Heavy-Hadron LCDA_Jun Zeng.pdf

14 First-principles QCD Inputs for Precision Studies of B and D Decays

Heavy meson light-cone distribution amplitudes (LCDAs) are essential nonperturbative quantities that characterize the internal dynamics of heavy mesons. They play a crucial role in the theoretical description of heavy meson (B or D) exclusive decays. However, due to the intrinsic challenges of nonperturbative QCD, first-principles calculations of heavy meson LCDAs have been notoriously difficult, with most studies relying on phenomenological models. We proposed a sequential effective theory approach to compute heavy meson LCDAs from first principles using lattice QCD. In this talk, we will present our results for heavy meson LCDAs obtained from lattice QCD calculations extrapolated to the continuum limit.

Speaker: Qi-An Zhang (BUAA)

QianZhang_LaMET2026.pdf

15 Complete leading-twist baryon light-cone distribution amplitudes from lattice QCD

We present the first lattice QCD calculation of all components of the leading-twist light-cone distribution amplitudes (LCDAs) of baryons at the physical pion mass and in the continuum limit, within the Large-Momentum Effective Theory (LaMET) framework.
This work provides a systematic first-principles determination of baryon LCDAs beyond moment-based approaches, enabling direct access to their full momentum dependence. In this work, we develop and implement the key ingredients that make such a calculation possible, including a hybrid renormalization strategy to remove linear divergences, HQET-guided analytic extrapolation of quasi-DAs, as well as controlled matching to the $\overline{\mathrm{MS}}$ scheme and reliable extrapolations to the physical and continuum limits.
These advances establish a comprehensive framework for precision studies of baryon structure from lattice QCD, paving the way for future high-precision investigations of hadron structure.

Speaker: Mu-Hua Zhang (Shanghai Jiao Tong University)

Baryon LCDA from LQCD - LaMET2026.pdf

16 LCDA moments from local and non-local matrix elements

We determine the leading-twist light-cone distribution amplitude (LCDA) moments of mesons using the HYP-smeared clover action on MILC ensembles, employing both twist-2 local operators and the LaMET approach. From the twist-2 local operators, we obtain high-precision values for the meson LCDA moments at the physical point and in the continuum limit. A comparison between the two methods shows good agreement for most moments. Furthermore, we improve the accuracy of the LCDA predictions by combining the results from both methods.

Speaker: Ji-Hao Wang (Institute of Theoretical Physics，Chinese Academy of Sciences)

WangJiHao_LaMET2026.pdf

Session I

17 Constraints on light travel and partons from quantum mechanics

I will consider in the effective field theory framework how UV quantum fluctuations destroy the concept of light travel and partons, unless in an asymptotic free theory.

Speaker: Xiangdong Ji (Shanghai Jiao Tong University)

18 Direct calculation of parton distributions in momentum space from lattice QCD

Coulomb-gauge quasi-parton distributions can be computed directly in momentum space on a finite lattice, enabled by the commutativity of their renormalization and Fourier transform. This approach removes the formal inverse problem in coordinate-space methods. Our momentum-space pion quasi-distributions agree with coordinate-space results Fourier transformed with asymptotic extrapolation, indicating that the formal inverse problem in the latter is not a practical concern here. We further extend the framework to higher dimensions and obtain the first 3D image of the pion directly from lattice QCD.

Speaker: Rui Zhang (MIT)

Lamet_Rui_2.pdf

19 Quantum Simulation of Generalized Parton Distributions: A Qudit-Based Approach

With the future Electron Ion Collider on the horizon, Generalized Parton Distributions (GPDs) have attracted significant interest over the past years. As a tool to map out the three-dimensional structure of hadrons, they offer unique opportunities to study Quantum Chromodynamics (QCD) and complex partonic correlators at non-perturbative scales. However, their experimental extraction is complicated by the deconvolution problem, model dependence, and the limited reach of current lattice calculations. Quantum computers, including qudit-based architectures, offer a potential route to study such observables in a controlled setting.

In this talk, I present an 8-dimensional qudit formulation of the $SU(3)$ color structure of QCD$_{1+1}$ on a lattice. After introducing the baryon and boost operators, I show how the off-forward matrix elements relevant for GPDs can be measured directly on quantum hardware, avoiding an explicit deconvolution step in this framework. I validate the approach using state-of-the-art tensor network simulations, estimate the resource requirements, and feasibility of the required measurements on current and near-term quantum devices.

Speaker: Florian Hechenberger (Stony Brook Universtiy)

qudit_gpds_lamet.pdf

20 One-loop matching for Coulomb-gauge quasi generalized parton distributions

We present a one-loop matching calculation for flavor-nonsinglet Coulomb-gauge quasi generalized parton distributions within large-momentum effective theory. Using nonforward quark matrix elements at large hadron momentum, we derive the perturbative kernel relating the Coulomb-gauge equal-time correlator to the corresponding light-cone nonsinglet GPD. We show that the infrared singularities of the quasi and light-cone distributions agree, so that their difference defines a short-distance matching coefficient. The resulting kernel depends on the momentum fraction and skewness, reduces to the known Coulomb-gauge quasi-PDF matching coefficient in the forward limit, and yields the corresponding Coulomb-gauge quasi-DA matching coefficient in the distribution-amplitude limit. We also discuss a distinctive feature of the coordinate-space result: the Coulomb-gauge no-link correlator can retain nontrivial dependence on the partonic longitudinal momentum through combinations such as (z p_z), making its connection to the conventional local moment OPE less direct.

Speaker: Fei Yao

GPD_mtch_fei.pdf

Session II

21 Finite-t and target mass corrections for the short-distance expansion of quasi- GPDs

We calculate the ``kinematic'' corrections $t/P_z^2$ and $m_N^2/P_z^2$ to the short distance expansion of gauge-invariant nonlocal quark-antiquark operators sandwiched between nucleon states with different momenta. Here $t$ is the momentum transfer, $m_N$ is the nucleon mass and $P_z$ is the momentum component in the direction of the quark-antiquark separation, which is assumed to be large.
These matrix elements can be calculated in lattice QCD and, at leading twist, expressed in terms of moments of the generalized parton distrubutions (GPDs). Our results allow one to control one of principal uncertainties in such calculations and extend their region of applicability to larger momentum transfers, which is important in the quest to access the three-dimension image of the proton.
The calculated corrections turn out to be significant for a realistic lattice QCD setup.

Speaker: Prof. Vladimir Braun (University of Regensburg)

kinematic4.pdf

22 Pion GPD moments from nonlocal lattice correlators in LaMET

We present lattice QCD calculations of the odd Mellin moments of pion valence-quark generalized parton distribution (GPD) up to fifth order, $\langle x^4\rangle$, and for the skewness range $[-0.33, 0]$ using operator product expansion of bilocal quark-bilinear operators. The calculations are performed on an ensemble with lattice spacing $a=0.04~\mathrm{fm}$ and valence pion mass $300~\mathrm{MeV}$, employing boosted pion states with momenta up to 2.428~GeV and momentum transfers reaching 2.748~GeV$^2$. We employ ratio-scheme renormalization and next-to-leading-logarithmic resummed perturbative matching. At zero skewness, our results are consistent with previous lattice studies. By combining matrix elements at multiple values of skewness and momentum transfer, skewness-dependent moments are obtained through simultaneous polynomiality-constrained fits.

Speaker: Fei Yao

GPD_mmts_fei.pdf

23 Mellin moments of proton unpolarized GPDs at nonzero skewness from lattice QCD with neural networks

This talk presents an extraction of Mellin moments of the proton unpolarized generalized parton distributions (GPDs) at nonzero skewness from lattice QCD. The analysis builds on the recent studies of GPDs at nonzero skewness, which, together with the polynomiality relations and short-distance factorization matching, connect the moments to generalized form factors. The present method uses artificial neural networks to parameterize the generalized form factors as functions of the invariant momentum transfer and to determine them from lattice data.

Speaker: Manuel Colaço (Adam Mickiewicz University)

gpd_mellin_moments_Manuel_Colaco.pdf

24 Controlling Systematic Uncertainties in Lattice QCD Calculations of Proton Unpolarized GPDs

Understanding and controlling systematic uncertainties is one of the main challenges in lattice QCD calculations. In this work, we investigate the momentum transfer ($t$) dependence of Mellin moments for unpolarized proton generalized parton distributions (GPDs) at zero skewness. The ground-state matrix elements are extracted using plateau fits and subsequently renormalized using the double ratio method. In this framework, we employ Artificial Neural Network (ANN) to establish the $t$-dependence of the Mellin moments, where the training is performed with the Ioffe-time distribution of GPDs via short-distance factorization. Using this framework, we investigate discretization effects in the matrix elements and the moments. The effect of excited states is investigated using two-state fits. This method enables us to account for the contribution from the first excited state in the underlying matrix elements.

Speaker: Arif Sarkar (Faculty of Physics and Astronomy, Adam Mickiewicz University)

LaMET26_Arif.pdf

25 Mellin Moments of the Unpolarized Gluon PDF in the Proton from Nonlocal Operators in Lattice QCD

We present a lattice QCD determination of the Mellin moments of the unpolarized gluon parton distribution function in the proton. The analysis is based on matrix elements of nonlocal gluon operators coupled to momentum-boosted proton states. The calculation relies on an $N_f=2+1+1$ ensemble of maximally twisted mass fermions with clover improvement and the Iwasaki-improved gauge action, at a pion mass of approximately 260 MeV. Working within the short-distance operator product expansion (OPE) of the reduced gluon Ioffe-time distribution, we extract ratios of higher-order gluon moments, $\langle x^n\rangle$ with $n>1$, to the gluon momentum fraction, $\langle x\rangle$. We investigate systematic effects associated with the truncation of the order of moment in the OPE, the choice of minimum and maximum Wilson-line separations entering the analysis, and the treatment of mixing with the quark-singlet under perturbative matching. The stability of the extracted moments is further studied under scale evolution using DGLAP equations, allowing us to assess uncertainties related to perturbative truncation by varying the scale. Our work provides a determination of the ratio $\langle x^3\rangle_g/\langle x\rangle_g$ at a scale of 2 GeV, with uncertainties that account for both statistical and the dominant theoretical systematic uncertainties.

Speaker: Joseph Delmar (Argonne National Laboratory)

Delmar_LaMET2026.pdf

Conference Dinner

Wednesday, 8 July

Discussion

Morning session

26 Lattice QCD Determination of the TMDPDFs

The transverse-momentum-dependent parton distribution function (TMDPDF) encodes essential information on the three-dimensional momentum structure of hadrons and plays a central role in QCD factorization for semi-inclusive processes. A first-principles determination of TMDPDFs remains highly challenging because of their intrinsically nonperturbative nature and the presence of both ultraviolet and rapidity divergences. In this work, we present a lattice QCD study of the TMDPDF within the large-momentum effective theory framework. Starting from suitably constructed nonlocal equal-time matrix elements, we extract the quasi-TMDPDF and investigate its dependence on the hadron momentum, Wilson-line geometry, and transverse separation $b_\perp$. Special attention is paid to the treatment of the intrinsic soft function, which captures the long-distance nonperturbative structure associated with TMD factorization on the lattice.

Our calculation employs gauge ensembles with multiple lattice spacings, volumes, and pion masses, enabling systematic control over discretization and chiral effects. We implement nonperturbative renormalization and matching procedures to connect the lattice observables to the physical TMDPDF. This study demonstrates the feasibility of accessing TMDPDFs directly from lattice QCD and provides new first-principles insight into the transverse momentum structure of hadrons. It also lays the foundation for a quantitative connection between lattice calculations and experimental measurements of semi-inclusive processes, advancing our understanding of hadron structure in QCD.

Speaker: Jin-Xin Tan (Shanghai Jiao Tong University)

TMD_JX.pdf

27 Obtaining the Collins-Soper Kernel and Intrinsic Soft Function with Lattice QCD

TMD quantities, such as TMDPDFs, provide essential information on the three-dimensional structure of hadrons and serve as key nonperturbative inputs for high-energy scattering processes, including SIDIS and Drell–Yan production. Unlike collinear PDFs, TMDs involve near-light-cone Wilson lines and therefore suffer from rapidity divergences arising from the separation of soft and collinear dynamics. A properly defined soft subtraction is required to remove these divergences, while the rapidity-scale dependence of TMDs is governed by the Collins–Soper kernel. In addition, the intrinsic soft function encodes the rapidity-independent, long-distance soft-gluon contribution that is essential for a complete nonperturbative description of TMD factorization.

In this presentation, I will first introduce the theoretical role of the Collins–Soper kernel and the intrinsic soft function in TMD physics. I will then discuss how these quantities can be accessed from lattice QCD within the LaMET framework. Finally, I will present our recent extension of this program, including improved lattice calculations, next-to-leading-order matching, controlled extrapolations toward the continuum and physical pion-mass limits, and the determination of the intrinsic soft function at transverse separations up to about 1 fm.

Speaker: Mr Zhi-Chao Gong (Shanghai Jiaotong University)

CS Kernel and Intrinsic Soft Function.pdf

28 The Collins-Soper kernel from a vacuum soft function

We present the results of the first lattice calculation of the Collins-Soper (CS) kernel from a vacuum soft function, which is constructed from space-like Wilson lines with complex direction vectors. Employing three ensembles of pure SU(3) gauge configurations at fine lattice spacings, we achieve high statistical precision in computing the soft function, whose rapidity dependence is well described by CS evolution across a wide range of rapidity differences. Although the uncertainties in the extracted CS kernel are dominated by perturbative matching systematics, they are comparable to those achieved in state-of-the-art lattice calculations based on hadronic observables. Notably, the kernel exhibits saturation at large transverse Wilson-line separations, which provides an important constraint for TMD phenomenology.

Speaker: Wayne Morris (National Yang Ming Chiao Tung University)

morris_lamet2026.pdf

29 Intrinsic soft function in the Coulomb-gauge approach

At large hadron momentum, quasi-transverse-momentum-dependent distributions (quasi-TMDs) defined from Coulomb-gauge correlators can be expanded and perturbatively matched to the light-cone TMDs up to the subtraction of an intrinsic soft function. In this talk, I will discuss the derivation of the operator definition of this soft function, as well as the method to extract it from a meson form factor on the lattice. The results obtained from our recent lattice calculation at next-to-leading order shows reasonably good agreement with perturbation theory at short transverse separations and a slower-than-Gaussian decay in the non-perturbative region.

Speaker: Yong Zhao (Argonne National Laboratory)

LaMET2026_Zhao.pdf

Session I

30 Toward a Continuum-Extrapolated Collins–Soper Kernel from Physical-Point Lattice QCD

We present a preliminary lattice-QCD calculation of the Collins–Soper kernel from pion quasi-TMD wave functions toward the continuum limit. The calculation uses Coulomb-gauge-fixed quasi-TMDWFs without an explicit gauge link, computed with Clover valence fermions on physical-pion-mass HISQ ensembles with lattice spacings $a$=0.040–0.076 fm. After ratio-scheme renormalization and a Fourier transform to $x$ space, the Collins–Soper kernel is extracted from the momentum dependence of quasi-TMDWFs with next-to-leading logarithmic matching. The use of multiple lattice spacings, spatial volumes, and pion momenta enables an assessment of discretization, finite-volume, and large-momentum systematics.

Speaker: Xiang Gao (BNL)

CSkernel_XG.pdf

31 Gluon Collins-Soper kernel from lattice QCD

We will present the first lattice QCD calculation of the gluon Collins-Soper kernel, which governs the rapidity evolution of transverse-momentum-dependent gluon distributions. The calculation is performed at a near-physical pion-mass m_\pi = 172(3) MeV with lattice spacing a = 0.15 fm, using next-to-next-to-leading logarithmic matching in Large Momentum Effective Theory, covering transverse separations up to b_T = 0.60 fm. These results represent the first step toward a controlled determination of the gluon Collins-Soper kernel in QCD, with eventual phenomenological import and relevance to present and future experiments sensitive to the gluon structure of hadronic matter.

Speaker: Yang Fu (MIT)

LaMET2026.pdf

32 Three-dimensional Imaging of Transversely Polarized Proton in Momentum Space

We present a lattice quantum chromodynamics (QCD) calculation of the proton valence-quark transverse-momentum-dependent parton distribution function (TMDPDF) in three polarization channels 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 proton with the chiral-symmetry-preserving domain wall fermion, the physical valence pion mass, and a lattice spacing of $a = 0.0836$ fm. The intrinsic soft function required in the CG framework is extracted from large-momentum-transfer form factors, and we also determine the associated Collins-Soper (CS) kernel as a direct result. Both the soft function and the CS kernel show agreement with perturbative results at small transverse quark separations ($b_\perp$). At larger values of $b_\perp$, the CS kernel remains compatible with recent findings based on CG and gauge-invariant (GI) TMD correlators in the literature. By applying next-to-leading logarithmic (NLL) factorization to both the quasi-TMD beam function and the soft function, we extract the $x$ dependence of the proton quark TMDPDFs in three polarization channels, extending to transverse separations $b_\perp > 1$ fm.

Speaker: Jinchen He (University of Maryland)

LaMET2026-Jinchen.pdf

33 Aspects of Coulomb-gauge renormalisation

The recent proposal to use nonlocal, Coulomb gauge-fixed operators in a LaMET framework to measure hadron structure properties has seen great success, as it circumvents poor signal-to-noise issues present with Wilson line operators. In this contribution, I will discuss nonperturbative renormalization schemes for Coulomb gauge-fixed operators, including RI'-MOM schemes adapted to only use spatial momenta.

Speaker: Joshua Lin (Argonne National Laboratory)

Session II

34 Kinematic enhancement for nucleon interpolators

We study kinematically enhanced nucleon interpolators using the example of unpolarized isovector nucleon quark matrix elements extracted at large source--sink separations, where excited-state artifacts are significantly suppressed. We find that the precision of the renormalized nucleon matrix elements is typically improved by an order of magnitude at momenta of approximately 2.5 GeV. By comparing results from three CLS ensembles with different lattice spacings but similar pion masses, we observe no statistically significant lattice-spacing dependence in the renormalized matrix elements at nearly identical boost momenta.

Speaker: Daniel Reitinger

35 Hadron Mass and Trace-Anomaly Decompositions from Gradient-Flow-Based Renormalization of the QCD EMT

We present a lattice-QCD validation of multiple sum rules associated with quark–gluon decomposition of hadron mass by computing all relevant tensor components of the quark and gluon energy--momentum tensor matrix elements from first principles. We achieve this through nonperturbative renormalization of the QCD energy–momentum tensor, including its trace, in a gradient-flow scheme, followed by continuum extrapolations, two-loop matching to the $\overline{\rm MS}$ scheme, and zero-flow-time extrapolations. These ingredients enable a direct and simultaneous verification, in a common renormalization scheme and scale, of multiple energy-density-based and trace-based mass decomposition sum rules proposed in the literature. We demonstrate the framework for the $\eta_c$ and $J/\psi$ charmonia using three fine lattice spacings with a physical strange-quark and near-physical up- and down-quark masses. The method is general and can be straightforwardly adopted for lattice-QCD calculations of mass and spin decompositions as well as gravitational form factors of other hadrons and nuclei.

Speaker: Xiang Gao (BNL)

GFF_XG.pdf

36 Topological QCD Vacuum and Hadron Structure

Speaker: Ismail Zahed (Stony Brook University)

POLAND-02-07-2026-Ismail-Zahed.pptx

37 Instantons from Lattice QCD using Gradient Flow in Pion Form Factors

The instanton liquid model is believed to capture the main features of vacuum QCD dynamics. Recently, multiple predictions for hadron structure functions have been derived and compared with experimental measurements and lattice QCD calculations, showing general agreement. In order to explore the precision of the instanton liquid model, one has to compare its predictions with non-perturbative simulations in a regime dominated by instanton dynamics.

This has been performed for two gluon-sensitive observables: the gluon Green’s function and the strong running coupling constant [1]. In this contribution, we propose to study a fermionic observable, the pion vector form factor, for which instanton liquid model predictions have been discussed in [1]. We use the Wilson flow to single out the dominant instanton contribution from lattice QCD gauge-field configurations. We describe the details of our numerical setup and present first preliminary results.

Interestingly, we find that at positive Wilson flow time the statistical signal for hadronic matrix elements, particularly at higher momentum transfer, is significantly improved. This suggests that Wilson flow may provide a useful way to access fermionic observables in a regime where instanton-dominated dynamics can be more clearly isolated.

Reference

[1] Wei-Yang Liu, Edward Shuryak, and Ismail Zahed, Phys. Rev. D 109, 074029 (2024). doi:10.1103/PhysRevD.109.074029

Speaker: Vaibhav Chahar (Jagiellonian University, Poland)

Instantons_gf_lamet_2026.pdf

38 Parton Structure from the QCD Vacuum and Its Connection to LaMET

Partons provide a natural language for hadron structure at high energies in QCD. However, direct light-front (LF) quantization leads to severe infrared singularities. These divergences reflect the absence of an intrinsic IR scale and nontrivial vacuum structure, thus placing QCD at a critical point. As a result, well-defined parton distributions are constructed through renormalization prior to the infinite momentum limit $P_z\rightarrow\infty$. To address this, we propose a gradient-flow framework based on the instanton liquid model (ILM), an effective UV-finite QCD ensemble emerging at a finite flow-time resolution scale $t$. In this approach, the UV modes are removed by renormalization at the corresponding scale $\mu_0\sim 1/(8t)^{-1/2}$, yielding a well-defined light-front formalism with key nonperturbative phenomena well addressed, including chiral symmetry breaking, anomalies, and confinement. Thus, parton observables can be systematically computed at $\mu_0$ in ILM, matched to the MS bar scheme with small-flow-time expansion, and then evolved to high energy perturbatively. This construction parallels LaMET, where finite $P_z$ plays an analogous role to $t$, providing a different Wilsonian description of parton structure that well addresses the topological origin for nonperturbative QCD.

Speaker: Wei-Yang Liu (Stony Brook University)

Parton_Structure_from_the_QCD_Vacuum_and_Its_Connection_to_LaMET__LaMET2026_ (1).pdf

Thursday, 9 July

Discussion

Morning session

39 Parton physics from a heavy-quark operator product expansion: Dynamical lattice QCD calculation of moments of the pion and kaon light-cone distribution amplitude

The light-cone distribution amplitude (LCDA) is a non-perturbative quantity for understanding hadron structure and exclusive scattering processes. We present on our calculation of moments of the pion and kaon LCDAs using the heavy-quark operator product expansion (HOPE) framework. This method employs an OPE analysis of hadronic amplitudes through the inclusion of a fictitious valence heavy quark.
Our previous work has successfully applied this framework to determine the second and fourth Mellin moments of the pion LCDA in the quenched approximation. In this work, we extend the application of HOPE to dynamical lattice QCD calculations using CLS ensembles. We present preliminary results for the first three nontrivial Mellin moments of the kaon LCDA and the second moment of the pion LCDA. These results demonstrate the feasibility of the HOPE method for accessing higher moments of meson LCDAs from dynamical lattice QCD.

Speaker: Alex Chang (Institute of Physics, National Yang Ming Chiao Tung University)

HOPEAlex_LM.pdf

40 Parton structure from Hamiltonian lattice gauge theory

Calculating parton functions from first principles remains a major challenge: they require matrix elements with a Wilson line along a light-like direction, which are not directly accessible in the Euclidean lattice formulation underlying conventional Monte Carlo simulations. In contrast, the Hamiltonian formalism allows for a direct treatment of light-cone dynamics, complementing indirect Euclidean methods. Recent developments in quantum computing and tensor network approaches enable efficient representations of states in Hilbert space. We developed a framework to extract light-cone matrix elements from a time evolution in Minkowski space and demonstrate the approach in a tensor-network calculation in the massive Schwinger model. We present PDFs and LCDAs of the Schwinger model with different fermion masses with controlled uncertainties.

Speaker: Manuel Schneider (National Yang Ming Chiao Tung University, Taiwan)

ManuelSchneider_LaMET2026.pdf

41 Towards Distribution Amplitude and GPD Calculations on a Quantum Computer

I will describe our attempts to compute the meson lightcone distribution amplitude and a meson GPD on a quantum computer.

Speaker: Jiunn-Wei Chen (National Taiwan University)

LaMET 2026 07092026.pdf

42 Asymptotic Long-Distance Expansion of Euclidean Correlators in Lattice Parton Applications

Bilinear Euclidean quark and gluon correlators with Wilson links have been used widely for applications of large-momentum effective field theories to computing non-perturbative collinear and soft parton physics. Due to color confinement, these correlators decay exponentially at large spatial distances, a behavior crucial for computing momentum-space Fourier transformations with controlled errors from lattice QCD data. Using heavy-quark effective theory reduction, dispersive analysis, Lorentz symmetry, and heavy-flavor spectra, we determine the leading and next-to-leading asymptotic behaviors and relate the expansion parameters to binding energies of heavy-flavor hadrons. We demonstrate the results through two-loop calculations in $\phi^3$ theory and from the perspective of locality and analyticity. We also study the impact of the asymptotic analysis on realistic lattice QCD data and demonstrate reliable error estimates.

Speaker: Yizhuang Liu (UJ)

decay.pptx

Excursion