We report the first nucleon gluon parton distribution function (PDF) using Large-Momentum Effective Theory (LaMET). We compute the matching coefficients for the gluon operator with the best signal to perform hybrid-renormalization and matching to the lightcone at the one-loop level. We demonstrate that with the proper Wilson coefficients in place, the counterterms for the renormalization are...
We report on recent progress in calculating gluon parton distribution functions (PDFs) using Large-Momentum Effective Theory (LaMET) combined with a self-renormalization approach to address the renormalization of gluon operators. Our study uses three HISQ ensembles with lattice spacings of $a = \{0.0888, 0.1207, 0.1510\}$ fm and a valence pion mass of $M_\pi \approx$ 310 MeV, with continuum...
We report a lattice QCD calculation of the nucleon gluon parton distribution function in the continuum-limit, employing large-momentum effective theory. The calculation is carried out on the 2+1 flavour CLQCD ensembles with three lattice spacings a = {0.105, 0.0897, 0.0775} fm and pion mass of approximately 300 MeV, covering nulceon momenta up to 1.97 GeV. Distillation technique is applied to...
We use the ensemble C24P29 provided by the CLQCD collaboration, insert the topological current using the proton external state of the momentum smear under the Coulomb gauge of the $5-\mathrm{HYP}$ smear, extract the matrix elements to calculate the gluon helicity under lattice QCD, and the calculation proves that different components of the topological currents $𝐾^\mu$ can be used to give...
I will present the first global proton GPD analysis by Y. Guo et al, with
lattice QCD input. I also comment on LaMET calculations of GPDs.
This work presents a generalization of the asymmetric-frame approach to generalized parton distributions that explicitly includes longitudinal momentum transfer, enabling studies at nonzero skewness $\xi$. The method reorganizes nucleon matrix elements into Lorentz-invariant, frame-independent amplitudes -- an extension of our earlier $\xi=0$ work in unpolarized, helicity, and transversity...
Large-momentum effective theory (LaMET) provides an approach to directly calculate the $x$-dependence of generalized parton distributions (GPDs) on a Euclidean lattice through power expansion and a perturbative matching. When a parton's momentum becomes soft, the corresponding logarithms
in the matching kernel become non-negligible at higher orders of perturbation theory, which requires a...
Momentum conservation in the nucleon is examined in terms of continuous flow of the momentum current density (or in short, momentum flow), which receives contributions from both kinetic motion and interacting forces involving quarks and gluons. While quarks conduct momentum flow through their kinetic motion and the gluon scalar (anomaly) contributes via pure interactions, the gluon stress...
We present updates on gluon GPDs and the hadronic structure of the photon from lattice QCD. The challenges in calculating gluon GPDs will be discussed, along with preliminary results for matrix elements probing the nonperturbative structure of the resolved photon. The lattice QCD calculation of the nonperturbative structure of the photon is being performed on the RBC/UKQCD domain-wall fermion...
We present results for the vector and axial form factors of the isovector nucleon in $2+1$ flavour lattice QCD with Domain Wall fermions. Our pion mass is physical and the lattice spacing is $a=0.114$ fm. We extract the Dirac and Pauli form factors as well as the axial and induced pseudoscalar form factors, and study their momentum transfer dependence over the range $0.05 \lesssim Q^2 \lesssim...
We systematically investigated the inverse discrete Fourier transform of quasi-distributions from the perspective of inverse problem theory. Mathematically, we have demonstrated that this transformation satisfies two of Hadamard’s well-posedness criteria, existence and uniqueness of the solution, but critically violates the stability requirement. To address this instability, we employed and...
The gradient flow has emerged as a powerful tool to enhance the Large Momentum Effective Theory (LaMET) program, offering both conceptual and practical advantages in lattice QCD studies of hadronic structure. In this report, I present our recent progress in applying the gradient flow to baryon light-cone distribution amplitudes (LCDAs) and quasi-parton distribution functions (quasi-PDFs). For...
In this talk, we will present the exact expansions at the next-to-leading order in the $1/N$ expansion for a space-like structure function in the 2D large-N Gross-Neveu model, in the Bjorken and the threshold limits.
The space-like structure function is similar to the lattice-calculable quasi-PDFs. As such, the exact expansion in the Bjorken limit allows a non-trivial first principle...
We present a lattice QCD calculation of the Collins-Soper kernel, which governs the rapidity evolution of transverse-momentum-dependent (TMD) distributions, using Large Momentum Effective Theory (LaMET). Quasi-TMD wave functions are computed with three meson momenta on CLQCD configurations (multiple lattice spacings and pion masses) employing clover quarks and varied hadronic states. HYP...
Recently, a novel approach has been suggested to compute parton distributions through the use of boosted correlators fixed in the Coulomb gauge from lattice QCD, within the framework of Large-Momentum Effective Theory (LaMET). This approach circumvents the need for Wilson lines, potentially enhancing the efficiency and accuracy of lattice QCD calculations significantly. In this study, we...
In this talk, progress in determining the quark Collins–Soper kernel using lattice QCD will be presented as a blueprint for the ongoing gluon kernel determination — to be discussed in the companion talk by Yang Fu.
Numerical results for the quark kernel will also be used to motivate the development of a convolutional transverse-scale–dependent LaMET matching, tailored to the intermediate...
We will present the first lattice QCD calculation of gluon Collins-Soper kernel, which relates the transverse momentum-dependent gluon parton distribution functions at different energy scales.
The Collins-Soper (CS) kernel may be obtained through the TMD soft function by formulating the Wilson line in terms of 1-dimensional auxiliary fermion fields on the lattice. Our computation takes place in the region of the lattice that corresponds to the “spacelike” region in Minkowski space, i.e., Collins' scheme. We explore two methods for obtaining the CS kernel. The "ratio method"; which...
We present a general framework originated from topologically nontrivial configurations, known as instantons in the QCD vacuum, to evaluate the non-perturbative transverse partonic structure of hadrons. Within this approach, we derive the transverse-momentum-dependent parton distribution functions (TMDPDFs) for the pion, kaon, and rho meson, as well as the Collins–Soper (CS) kernel that governs...
Designing good schemes to connect bare operators used in Lattice-QCD to perturbatively defined schemes (such as MSbar) is crucial for Lattice-QCD calculations. Operators containing Wilson Lines (for example those required for a quasi-pdf) contain an additional power divergence in the length of the Wilson Line. In this talk, I'll introduce gauge invariant position-space renormalization schemes...
The lattice QCD computation of parton distributions within the framework of large momentum effective theory (LaMET) constitutes a first-principles approach to studying hadron structures. Building upon preceding studies on meson systems, we have developed and partly implemented lattice methodologies for calculating the leading twist LCDAs of light baryons under the LaMET formalism over the past...
We present the results of lattice QCD calculation of all leading-twist x-dependent Light-cone Distribution Amplitudes (LCDAs) for baryons in light octet, within the framework of Large-momentum Effective Theory (LaMET). We implement a novel Hybrid renormalization scheme for baryon nonlocal operators, and perform simulations at 4 different lattice spacings a = {0.052, 0.068, 0.077, 0.105} fm,...
We determine the leading-twist light-cone distribution amplitude (LCDA) moments of mesons on MILC ensembles using the HYP-smeared clover action, employing both twist-2 local operators and quasi-DA correlators. Based on the twist-2 local operator, we obtain highly precise values for the meson LCDA moments at the physical point and in the continuum limit. By comparing the results from these two...
The pion light-cone distribution amplitude (LCDA) is an essential non-perturbative input for a range of high-energy exclusive processes in quantum chromodynamics. Building upon previous work, I will describe the calculation of the fourth Mellin moment of the pion LCDA in the continuum using the heavy-quark operator product expansion (HOPE) method.
Among other approaches developed in recent years, four-point functions provide access to the $x$ dependence of parton distribution functions (PDFs). One of the corresponding methods is often referred to as the lattice cross section (LCS) approach: in this method, hadronic matrix elements of two local quark-bilinears located at equal time are factorized in terms of a PDF and a perturbative...
We perform the first quantum computation of parton distribution function (PDF) with a real quantum device by calculating the PDF of the lightest positronium in the Schwinger model with IBM quantum computers. The calculation uses 10 qubits for staggered fermions at five spatial sites and one ancillary qubit. The most critical and challenging step is to reduce the number of two-qubit gate depths...
We propose a framework for the reconstruction of parton distribution functions (PDFs) and generalized parton distributions (GPDs) from lattice QCD, utilizing artificial neural networks (ANNs). Our approach combines two complementary methodologies: the Large Momentum Effective Theory (LaMET) and the short-distance operator expansion (SDE). To determine ANN-based PDFs and GPDs, we achieve a...
Parton distribution functions (PDFs) are universal scaling functions essential for probing hadron structure as well as searching for New physics beyond the Standard Model (SM). The large momentum effective theory (LaMET) is a precision-controlled framework for directly calculating the x-dependence of PDFs, based on the first principles of Quantum Chromodynamics (QCD). In this talk, I introduce...
