The Collins-Soper (CS) kernel governs the rapidity evolution of transverse-momentum-dependent (TMD) parton distributions, a cornerstone for QCD factorization and linking nucleon structure data across scales. Its nonperturbative behavior at large transverse separations (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>b</mi><mo>⊥</mo></msub></math>) remains weakly constrained due to phenomenological model dependencies. We present a first-principles determination of the CS kernel at the continuum limit and physical pion mass from lattice QCD in the large-momentum effective theory framework. Using (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor configurations (lattice spacings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>∈</mo><mo stretchy="false">[</mo><mn>0.052</mn><mo>,</mo><mn>0.105</mn><mo stretchy="false">]</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>, and pion mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>≈</mo><mo stretchy="false">(</mo><mn>136</mn><mo>,</mo><mn>230</mn><mo>,</mo><mn>300</mn><mo>,</mo><mn>320</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>), we simulating the nonlocal equal-time correlation function and extract the quasi-TMD wave functions. Taking into account systematic improvements including hypercubic smearing, nonperturbative renormalization, and a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>b</mi><mo>⊥</mo></msub></math>-unexpanded matching kernel, we obtain the CS kernel at the continuum, chiral, and infinite-momentum limits. Our results are determined up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>b</mi><mo>⊥</mo></msub><mo>∼</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>, with controllable uncertainties, and agree with perturbative QCD at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>b</mi><mo>⊥</mo></msub></math> and global TMD phenomenological extractions. We conduct a global analysis integrated with phenomenological fits and demonstrate the impact of our results on such fits. This work yields the most precise nonperturbative constraint on the CS kernel’s long-distance behavior from lattice QCD, which not only bridges lattice QCD, perturbation theory, and nucleon structure experiments for TMD studies, but also boosts the utility of our constraint for future global TMD analyses.

China

Jin-Xin Tan

Zhi-Chao Gong

Jun Hua

United States

Xiangdong Ji

Xiangyu Jiang

Hang Liu

Germany

Andreas Schäfer

Yushan Su

Han-Zhang Wang

Wei Wang

Yi-Bo Yang

Jun Zeng

Jian-Hui Zhang

Jia-Lu Zhang

Qi-An Zhang

Lattice QCD determination of the Collins-Soper kernel in the continuum and physical mass limits

Momentum current density (MCD) <italic>Tij</italic> is a general physics concept describing the momentum conservation through momentum flow generated from both the kinetic motion of particles and the interacting forces among them. It has been suggested by M. Polyakov et al. that the MCD in the nucleon, characterized by the form factor <italic>C</italic>/ <italic>D</italic> of the QCD energy-momentum tensor, can be interpreted as the pressure and shear forces between adjacent parts of the system because the nucleon interior approximates a continuous medium. While intuitively appealing, we find that the interpretation is hard to justify from a detailed examination of the physical mechanisms for the momentum flow in QCD. After reviewing through a broad range of classical and quantum systems, we find that while thermal and/or quantum average of isotropic motion contributes to kinetic MCD a pressure term proportional to <italic>&#948;ij</italic>, when there is an anisotropic motion, the pressure cannot simply be identified from the MCD tensor. Furthermore, kinetic pressure cannot be considered as the surface force between adjacent parts of a system. More importantly, at the scale of the nucleon dimension, the color forces among quarks and gluons is by no means short-ranged as in a continuous medium, and the resulting interaction MCD cannot be interpreted as normal or shear &#8220;stress&#8221; force, although an isotropic term from the QCD trace anomaly may be interpreted as a &#8220;vacuum pressure.&#8221; Following our previous study of force densities through divergences of kinetic MCDs, we affirm that the vacuum pressure term provides a confining potential on the quarks through color Lorentz forces.

Chen Yang

A journey of seeking pressure and forces in the nucleon

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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> within a range of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">[</mo><msub><mi>x</mi><mi>min</mi></msub><mo>,</mo><msub><mi>x</mi><mi>max</mi></msub><mo stretchy="false">]</mo></math>. 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.

Taiwan

Jiunn-Wei Chen

Xiang Gao

Jinchen He

Rui Zhang

Yong Zhao

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

We report the first global extraction of generalized parton distributions, GUMP 1.0, by combining deeply virtual Compton scattering and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ρ</mi></mrow></math>-meson production data from Jefferson Lab and the Hadron-Electron Ring Accelerator with global fits of parton distribution functions, charge form factors, and lattice quantum chromodynamics simulations. Using a conformal moment space parametrization, we achieve a unified description across low- and high-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> regions at next to leading order accuracy in perturbative corrections. The results provide state-of-the-art generalized parton distributions consistent with almost all known facts, enabling three-dimensional nucleon imaging in impact parameter space and, at the same time, establishing a benchmark for future theoretical and experimental studies of the nucleon structure.

Yuxun Guo

Fatma P. Aslan

M. Gabriel Santiago

First Global Extraction of Generalized Parton Distributions from Experiment and Lattice Data with Next-to-Leading-Order Accuracy

Light cone distribution amplitudes for a light baryon can be extracted through the simulation of the quasi-distribution amplitudes (quasi-DAs) on the lattice. We implement the hybrid renormalization for the quasi-DAs of light baryons. Lattice simulations are performed using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></math> stout-smeared clover fermions and a tree-level Symanzik-improved gauge action, with three lattice spacings of 0.105, 0.077, 0.052 fm. By analyzing zero-momentum matrix elements for different lattice spacings, we extract the linear divergence associated with the Wilson-line self-energy. Matching to perturbative matrix elements in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>MS</mi><mo stretchy="true">¯</mo></mover></math> scheme yields the residual self-renormalization factors. Using these factors, we renormalize the quasi-DAs within the hybrid scheme, which combines self-renormalization at large separations and the ratio scheme at short distances. The renormalized results demonstrate effective cancellation of linear divergences and yield smooth, continuumlike coordinate-space distributions suitable for subsequent Fourier transformation and perturbative matching. These results establish the viability of both self- and hybrid-renormalization frameworks for light baryon quasi-DAs, providing a robust foundation for LaMET-based determinations of light cone distribution amplitudes in future.

Haoyang Bai

Jian Liang

JiaLu Zhang

Mu-Hua Zhang

Hybrid renormalization for distribution amplitude of a light baryon in large momentum effective theory

We present a search for light dark matter particles through their interactions with atomic electrons and nucleons, utilizing PandaX-4T data with an effective exposure of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1.04</mn><mtext> </mtext><mtext> </mtext><mi>tonne</mi><mo>·</mo><mi>year</mi></mrow></math> for ionization-only data and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1.20</mn><mtext> </mtext><mtext> </mtext><mi>tonne</mi><mo>·</mo><mi>year</mi></mrow></math> for paired data. Our analysis focuses on the energy range (efficiency <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>&gt;</mo><mn>0.01</mn></math>) of approximately 0.33 to 3 keV for nuclear recoils and from 0.04 to 0.39 keV for electronic recoils. We establish the most stringent constraints on spin-independent dark matter-nucleon interactions within a mass range of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2.5</mn><mi>–</mi><mn>5.0</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, spin-dependent neutron-only interactions within <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1.0</mn><mi>–</mi><mn>5.6</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, and spin-dependent proton-only interactions within <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1.0</mn><mi>–</mi><mn>4.1</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>. Their corresponding limits at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1.1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>43</mn></mrow></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>8.4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>40</mn></mrow></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2.8</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>38</mn></mrow></msup><mtext> </mtext><mtext> </mtext><msup><mrow><mi>cm</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, respectively. Additionally, our results improve the upper limits on the dark matter-electron scattering cross section by a factor of 1.5 and 9.3 for heavy and light mediator scenarios, respectively, within <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>50</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math>, compared with previous best results. The improved limits reach <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1.5</mn><mo>×</mo><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>41</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>5.6</mn><mo>×</mo><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>37</mn></mrow></msup><mtext> </mtext><mtext> </mtext><msup><mrow><mi>cm</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>200</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math> for the heavy and light mediators, respectively.

Minzhen Zhang

Zihao Bo

Wei Chen

Xun Chen

Yunhua Chen

Chen Cheng

Xiangyi Cui

Manna Deng

Yingjie Fan

Deqing Fang

Xuanye Fu

Zhixing Gao

Yujie Ge

Lisheng Geng

Karl Giboni

Xunan Guo

Xuyuan Guo

Zichao Guo

Chencheng Han

Ke Han

Changda He

Jinrong He

Houqi Huang

Junting Huang

Yule Huang

Ruquan Hou

Yonglin Ju

Xiaorun Lan

Chenxiang Li

Jiafu Li

Mingchuan Li

Peiyuan Li

Shuaijie Li

Tao Li

Yangdong Li

Zhiyuan Li

Qing Lin

Jianglai Liu

Yuanchun Liu

Congcong Lu

Xiaoying Lu

Lingyin Luo

Yunyang Luo

Yugang Ma

Yajun Mao

Yue Meng

Binyu Pang

Ningchun Qi

Zhicheng Qian

Xiangxiang Ren

Dong Shan

Xiaofeng Shang

Xiyuan Shao

Guofang Shen

Manbin Shen

Wenliang Sun

Xuyan Sun

Yi Tao

Yueqiang Tian

Yuxin Tian

Anqing Wang

Guanbo Wang

Hao Wang

Haoyu Wang

Jiamin Wang

Lei Wang

Meng Wang

Qiuhong Wang

Shaobo Wang

Shibo Wang

Siguang Wang

Xu Wang

Zhou Wang

Yuehuan Wei

Weihao Wu

Yuan Wu

Mengjiao Xiao

Xiang Xiao

Kaizhi Xiong

Jianqin Xu

Yifan Xu

Shunyu Yao

Binbin Yan

Xiyu Yan

Yong Yang

Peihua Ye

Chunxu Yu

Ying Yuan

Zhe Yuan

Youhui Yun

Xinning Zeng

Peng Zhang

Shibo Zhang

Siyuan Zhang

Shu Zhang

Tao Zhang

Wei Zhang

Yang Zhang

Search for Light Dark Matter with 259 Days of Data in PandaX-4T

We phenomenologically constrain the small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> and small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ξ</mi></math> gluon generalized parton distributions (GPDs) with the deeply virtual <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>DV</mi><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">P</mi></mrow></math>) in the framework of GPDs through universal moment parameterization (GUMP). We use a hybrid cross-section formula combining collinear factorization to the next-to-leading order (NLO) accuracy of the strong coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math>, with corrections from nonrelativistic QCD to account for the power corrections due to the heavy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> mass. We reach reasonable fit to the measured differential cross sections of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>DV</mi><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">P</mi></mrow></math> by H1 at the Hadron-Electron Ring Accelerator as well as forward gluon parton distribution functions (PDFs) from JAM22 global analysis. We find that both NLO and nonrelativistic corrections are significant for heavy vector meson productions. Of course, the gluon GPD we obtain still contains considerable freedom in need of inputs from other constraints, particularly in the distribution-amplitude-like region.

Jinghong Yang

Hao-Cheng Zhang

Small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> gluon GPD constrained from deeply virtual <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production and gluon PDF through universal-moment parametrization

Light-cone distribution amplitudes (LCDAs) of heavy meson within heavy quark effective theory (HQET) are crucial for predicting physical observables in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> decays, but unfortunately there is no first-principle result due to severe challenges. After analyzing these challenges, we propose a realistic method to determine heavy meson LCDA. We utilize equal-time correlations and incorporate a dynamic quark field for a fast moving heavy quark. To verify this method, we make use of lattice QCD simulation on a lattice ensemble with spacing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>=</mo><mn>0.05187</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>. The preliminary findings for HQET LCDAs qualitatively align with phenomenological models, and the fitted result for the first inverse moment <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>λ</mi><mi>B</mi><mrow><mo>−</mo><mn>1</mn></mrow></msubsup></math> is consistent with the experimentally constrained region from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>γ</mi><mo>ℓ</mo><msub><mi>ν</mi><mo>ℓ</mo></msub></math>. We explore how our findings can reduce model uncertainties in predictions of heavy-to-light form factors at large recoil. These results demonstrate the promise of our method in providing first-principle predictions for heavy meson LCDAs.

Xue-Ying Han

Cai-Dian Lü

Ji Xu

Shuai Zhao

Realistic method to access heavy meson light-cone distribution amplitudes from first-principle

Detailed studies of two-neutrino double electron capture (2$\textit{ν}$DEC) is a crucial step towards searching for the neutrinoless mode to explore the Majorana nature of neutrinos. We have measured precisely the half-life of the 2$\textit{ν}$DEC process in Xe, utilizing a total exposure of 1.73 tonne year from the commissioning run and the first science run of the PandaX-4T experiment. A time-dependent background model in the $$ \mathcal{O} $$ (10 keV) energy is constructed for the first time in PandaX-4T data. With an unbinned maximum likelihood fit, we determine the half-life of the 2$\textit{ν}$DEC process to be (1.03 ± 0.15 ± 0.08 ) × 10 yr. Furthermore, we have evaluated the capture fraction for both electrons captured from the $\textit{K}$ shell ($\textit{KK}$) to be (65 ± 5)%, which aligns with the Xe nuclear model calculations within 1.8 $\textit{σ}$.

Zhaokan Cheng

Di Huang

Yu Hou

Xiangpan Ji

Wenbo Ma

Xuyang Ning

Xiuli Wang

Yingxin Zhang

Yuanyuan Zhang

Li Zhao

Jifang Zhou

Jiaxu Zhou

Jiayi Zhou

Ning Zhou

Xiaopeng Zhou

Yubo Zhou

Measurement of two-neutrino double electron capture half-life of

We perform a search of double beta decay of Xe to the excited state, $$ {0}_1^{+} $$ , of Ba (2$\textit{νββ}$- $$ {0}_1^{+} $$ ), using the dual-phase xenon detector of PandaX-4T with the first 94.9-day commissioning data. The multi-site events are reconstructed up to the MeV energy scale, which helps to improve the background model significantly. The background contribution from the stainless steel platform outside PandaX-4T cryostat is evaluated for the first time. No significant evidence for 2$\textit{νββ}$- $$ {0}_1^{+} $$ is observed, resulting in a lower limit on half-life of 7$\textit{.}$5 × 10 yr at the 90% confidence level. This is the first experimental limit on such a rare decay in a natural xenon-based detector.

Zhizhen Zhou

Search for double beta decay of