From C to Parton Sea: Bjorken-x Dependence of the PDFs

Extraction of Next-to-Next-to-Leading-Order PDFs from Lattice QCD Calculations

We present for the first time complete next-to-next-to-leading-order coefficient functions to match flavor non-singlet quark correlation functions in position space, which are calculable in lattice QCD, to parton distribution functions (PDFs). Using PDFs extracted from experimental data and our calculated matching coefficients, we predict valence-quark correlation functions that can be confronted by lattice QCD calculations. The uncertainty of our predictions is greatly reduced with higher order matching coefficients. By performing Fourier transformation, we also obtain matching coefficients f…

PDF in PDFs from Hadronic Tensor and LaMET

We point out a problem of the phenomenological definition of the valence partons as the difference between the partons and antipartons in the context of the NNLO evolution equations. After demonstrating that the classification of the parton degrees of freedom (PDF) of the parton distribution functions (PDFs) are the same in the QCD path-intergral formulations of the hadronic tensor and the quasi-PDF with LaMET, we resolve the problem by showing that the proper definition of the valence should be in terms of those in the connected insertions only. We also prove that the strange partons appear a…

Flavor non-singlet parton distribution functions from lattice QCD at physical quark masses via the pseudo-distribution approach

One of the great challenges of QCD is to determine the partonic structure of the nucleon from first principles. In this work, we provide such a determination of the flavor non-singlet ($u-d$) unpolarized parton distribution function (PDF), utilizing the non-perturbative formulation of QCD on the lattice. We apply Radyushkin's pseudo-distribution approach to lattice results obtained using simulations with the light quark mass fixed to its physical value; this is the first ever attempt for this approach directly at the physical point. The extracted coordinate-space matrix elements are used to fi…

Lattice Nucleon Isovector Unpolarized Parton Distribution in the Physical-Continuum Limit

We present the first lattice-QCD calculation of the nucleon isovector unpolarized parton distribution functions (PDFs) at the physical-continuum limit using Large-Momentum Effective Theory (LaMET). The lattice results are calculated using ensembles with multiple sea pion masses with the lightest one around 135~MeV, 3 lattice spacings $a\in[0.06,0.12]$~fm, and multiple volumes with $M_πL$ ranging 3.3 to 5.5. We perform a simultaneous chiral-continuum extrapolation to obtain RI/MOM renormalized nucleon matrix elements with various Wilson-link displacements in the continuum limit at physical pion…

Machine-Learning Prediction for Quasi-PDF Matrix Elements

There have been rapid developments in the direct calculation in lattice QCD (LQCD) of the Bjorken-$x$ dependence of hadron structure through large-momentum effective theory (LaMET). LaMET overcomes the previous limitation of LQCD to moments (that is, integrals over Bjorken-$x$) of hadron structure, allowing LQCD to directly provide the kinematic regions where the experimental values are least known. LaMET requires large-momentum hadron states to minimize its systematics and allow us to reach small-$x$ reliably. This means that very fine lattice spacing to minimize lattice artifacts at order $(…

用高斯过程处理含噪截断矩问题：在部分子分布函数中的应用

Tackling the noisy truncated moment problem with Gaussian Processes: An application to parton distribution functions

本研究用高斯过程解决含噪截断Hausdorff矩问题，以从矩中重构部分子分布函数，引入均值偏差校正和可学习相关长度核，在5个数据集上验证了稳健性。

质子中横向动量依赖和共线部分子分布首次联合分析

First simultaneous analysis of transverse momentum dependent and collinear parton distributions in the proton

本文首次对质子中的TMD和共线PDFs进行联合全局QCD分析，结合多种实验数据，在次次领头对数精度下改善海夸克部分子分布，提供一致描述。

Connected-Sea Partons

According to the path-integral formalism of the hadronic tensor, the nucleon sea contains two distinct components called connected sea (CS) and disconnected sea (DS). We discuss how the CS and DS are accessed in the lattice QCD calculation of the moments of the parton distributions. We show that the CS and DS components for $\bar u(x) + \bar d(x)$ can be extracted by using recent data on the strangeness parton distribution, the CT10 global fit, and the lattice result of the ratio of the strange to $u(d)$ moments in the disconnected insertion. The extracted CS and DS for $\bar u(x) + \bar d(x)$…

Standard Model $\mathcal{O}(α)$ renormalization of $g_A$ and its impact on new physics searches

We present an $\mathcal{O}(α)$ Standard Model calculation of the inner radiative corrections to Gamow-Teller $β$ decays. We find that \textit{a priori} contributions arise from the photonic vertex correction and $γW$ box diagram. Upon evaluation most elastic contributions vanish due to crossing symmetry or cancellation between isoscalar and isovector photonic contributions, leaving only the polarized parity-odd contribution, i.e., the Gamow-Teller equivalent of the well-known axial $γW$ box contribution for Fermi decays. We show that weak magnetism contributes significantly to the Born amplitu…

The Structure of the Proton in the LHC Precision Era

We review recent progress in the determination of the parton distribution functions (PDFs) of the proton, with emphasis on the applications for precision phenomenology at the Large Hadron Collider (LHC). First of all, we introduce the general theoretical framework underlying the global QCD analysis of the quark and gluon internal structure of protons. We then present a detailed overview of the hard-scattering measurements, and the corresponding theory predictions, that are used in state-of-the-art PDF fits. We emphasize here the role that higher-order QCD and electroweak corrections play in th…