We study the inelastic charmonium ( $ J/\psi $ , $ \psi(2S) $ ) and bottomonium ( $ \Upsilon(nS) $ ) photoproduction and fragmentation processes in $\textit{p}$-$\textit{p}$ and $ \rm Pb$ - $\rm Pb$ collisions at LHC energies, where the ultra-incoherent photon emission is included. Using the NRQCD factorization approach, an exact treatment is developed. This approach recovers the Weizsäcker-Williams approximation (WWA) near the $ Q^{2}\sim0 $ region, where the Martin-Ryskin and BCCKL methods are used to avoid double counting. We calculated the $ Q^{2} $ , $\textit{y}$, $\textit{z}$, $ \sqrt{s} $ , and $ p_{T} $ dependent and total cross sections. Inelastic photoproduction and fragmentation were observed to contribute to heavy quarkonium production, particularly at large $ p_{T} $ . In addition, the contribution of the ultra-incoherent photon channel, which increases rapidly with quarkonium mass, is significant and begins to dominate the photoproduction processes for large $ p_{T} $ . We also obtained the complete WWA validity scopes of inelastic heavy quarkonium photoproduction in heavy-ion collisions. The WWA had high accuracy at high energies and for $\rm Pb $ - $\rm Pb $ collisions. However, current photon spectra are derived beyond the WWA scope, and double counting can occur when considering different channels simultaneously.

China

Zhi-Lei Ma

Zhun Lu

Hao Liu

Li Zhang

Inelastic heavy quarkonium photoproduction in $\textit{p}$-$\textit{p}$ and Pb-Pb collisions at LHC energies * Supported in part by the National Natural Science Foundation of China (12305092, 12233006, 12150013), the Xingdian Talent Support Program for Youth Project, and by the Yunnan Fundamental Research Projects (202401AU070206). Hao Liu is supported by the Scientific Research and Innovation Project of Postgraduate Students in the Academic Degree of YunNan University (KC-242410212)

The neutrino floor, a theoretical sensitivity limit for dark matter (DM) direct detection, is being redefined as the boundary of a dynamic ''neutrino fog,'' where neutrino signals become inevitable, obscuring DM detection due to statistical and systematic uncertainties. This study provides the first site-specific analysis of the neutrino floor at China Jinping Underground Laboratory (CJPL), leveraging its unique geographic and environmental characteristics. We quantify how CJPL’s suppressed atmospheric neutrino flux (approximately 30% lower than that of Laboratori Nazionali del Gran Sasso (LNGS)) reshapes the neutrino floor, thereby enabling improved sensitivity to high-mass WIMPs (mass > 10 GeV). Using a gradient-based framework, we derive the CJPL’s neutrino floor and estimate the detection prospects for the PandaX-xT experiment. Our results demonstrate that a 500 tonne-year exposure with PandaX-xT could reach the floor, probing spin independent cross-sections down to $ \sigma_{n}\sim 3\times 10^{-49}\; {\rm{cm}}^2$ at a DM mass of 70 GeV/$\textit{c}$ $^{2}$.

Yingjie Fan

Xuewen Liu

Ning Zhou

Characterizing the CJPL’s site-specific neutrino floor as the neutrino fog boundary * Xuewen Liu is supported by the Project of Shandong Province Higher Educational Science and Technology Program (2022KJ271). Ning Zhou is supported by National Science Foundation of China (12325505)

We analyzed two-loop planar contributions to a three-body form factor at next-to-leading power in the high-energy limit, where the masses of the external particles are much smaller than their energies. Calculations were performed by exploiting differential equations for the expansion coefficients, both to facilitate linear relations among them and to derive their analytic expressions. The results are expressed in terms of generalized polylogarithms involving a few simple symbol letters. Our method can readily be applied to calculations of non-planar contributions as well. Our results provide crucial information for establishing sub-leading factorization theorems for massive scattering amplitudes in the high-energy limit.

Yishuai Guo

Zhi-Feng Liu

Mingming Lu

Tianya Xia

Li-Lin Yang

A three-body form factor at sub-leading power in the high-energy limit: planar contributions * Supported in part by the National Natural Science Foundation of China Sunder (12375097, 12347103) and the Fundamental Research Funds for the Central Universities. Zhi-Feng Liu was supported by the China Postdoctoral Science Foundation (2023M733123, 2023TQ0282) and the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation

We present the first lattice result of the near threshold $ \Lambda_c\Lambda_c $ scattering with $ I(J^P) = 0(0^+) $ . The calculation is performed on two $ N_f = 2+1 $ Wilson-Clover ensembles with pion mass $ m_\pi \sim 303 $ MeV and lattice spacing $ a = 0.07746 $ fm. Lüscher's finite volume method is utilized to extract the scattering parameters from the finite-volume spectrum. The coupled channel $ \Xi_{cc}N $ is ignored in the scattering analysis based on the observation that the energy levels computed from the $ \Lambda_c\Lambda_c $ and $ \Xi_{cc}N $ operators do not mix. The $ \Sigma_c\Sigma_c $ channel is not included either since the energy range explored in this study is well below its threshold. Our results indicate that the interaction in the $ \Lambda_c\Lambda_c $ single channel is repulsive, and the scattering length is determined to be $ a_0 = -0.21(4)(8) $ fm, where the first error is statistical and the second is systematic.

Hanyang Xing

Yiqi Geng

Chuan Liu

Liuming Liu

Peng Sun

Jiajun Wu

Zhicheng Yan

Ruilin Zhu

Lattice QCD study of Λ $\textit{c}$ Λ $\textit{c}$ scattering * Supported by NSFC (12293060, 12293061, 12293063, 12175279, 12435002, 12322503, 12175239). L. Liu also acknowledges the Strategic Priority Research Program of the Chinese Academy of Sciences with (XDB34030301) and Guangdong Major Project of Basic and Applied Basic Research (2020B0301030008). We also acknowledge the Science and Education Integration Young Faculty Project of University of Chinese Academy of Sciences (YSBR-101)

A new thermal regime of QCD, featuring decoupled scale-invariant infrared glue, has been proposed to exist both in pure-glue (N f =0) and “real-world” (N f =2+1 at physical quark masses) QCD. In this IR phase, elementary degrees of freedom flood the infrared, forming a distinct component independent from the bulk. This behavior necessitates non-analyticities in the theory. In pure-glue QCD, such non-analyticities have been shown to arise via Anderson-like mobility edges in Dirac spectra (λ IR = 0, ±λ A ≠ 0), as manifested in the dimension function d IR(λ). Here, we present the first evidence, based on lattice QCD calculation at a=0.105 fm, that this mechanism is also at work in real-world QCD, thus supporting the existence of the proposed IR regime in nature. An important aspect of our results is that, while at T = 234 MeV we find a dimensional jump between zero modes and lowest near-zero modes very close to unity (d IR = 3 to d IR ≃ 2), similar to the IR phase of pure-glue QCD, at T = 187 MeV we observe a continuous λ-dependence. This suggests that thermal states just above the chiral crossover are non-analytically (in T) connected to thermal state at T = 234 MeV, supporting the key original proposition that the transition into the IR regime occurs at a temperature strictly above the chiral crossover.

Xiao-Lan Meng

United States

Andrei Alexandru

Czechia

Ivan Horváth

Keh-Fei Liu

France

Gen Wang

Yi-Bo Yang

Separation of infrared and bulk in thermal QCD

Decay constants of pseudoscalar mesons D,   $ D_s $  ,   $ D_s $   and vector mesons   $ D_s $  ,   $ D_s $  ,   $ D_s $   are determined from the   $ D_s $   lattice QCD at a lattice spacing   $ D_s $   fm. For vector mesons, the decay constants defined by tensor currents are given in the   $ D_s $   scheme at   $ D_s $   GeV. The calculation is performed on domain wall fermion configurations generated by the RBC-UKQCD collaborations and the overlap fermion action is used for the valence quarks. Comparing the current results with our previous results at a coarser lattice spacing   $ D_s $   fm provides a better understanding of the discretization error. We obtain   $ D_s $   with a better precision than our previous result. Combining our   $ D_s $   MeV with the total width of   $ D_s $   determined in a recent study gives a branching fraction   $ D_s $   for   $ D_s $   leptonic decay.

Dong-Hao Li

Ying Chen

Ming Gong

Zhaofeng Liu

Ting-Xiao Wang

(χQCD Collaboration) 

Charm physics with overlap fermions on 2+1-flavor domain wall fermion configurations  

We compute the overlap Dirac spectrum on three gauge ensembles generated using <math><mn>2</mn><mo>+</mo><mn>1</mn></math>-flavor domain wall fermions. The three ensembles have different lattice spacings, and two of them have quark masses tuned to the physical point. The spectral density is determined up to <math><mi>λ</mi><mo>∼</mo><mn>100</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> with subpercentage statistical uncertainty. We find that the density is close to a constant below <math><mi>λ</mi><mo>∼</mo><mn>20</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> as predicted by chiral perturbative theory (<math><mi>χ</mi><mi>PT</mi></math>) and then increases linearly due to the strange quark mass. By fitting to the next-to-leading order <math><mi>χ</mi><mi>PT</mi></math> form and using the nonperturbative renormalization using the regularization independent momentum subtraction scheme, the SU(2) (keeping the strange quark mass at the physical point) and SU(3) chiral condensates at <math><mrow><mover><mrow><mi>MS</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> 2 GeV are determined to be <math><mi>Σ</mi><mo>=</mo><mo>(</mo><mn>265.4</mn><mo>(</mo><mn>0.5</mn><mo>)</mo><mo>(</mo><mn>4.2</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><msup><mo>)</mo><mn>3</mn></msup></math> and <math><msub><mi>Σ</mi><mn>0</mn></msub><mo>=</mo><mo>(</mo><mn>234.3</mn><mo>(</mo><mn>0.5</mn><mo>)</mo><mo>(</mo><mn>25.8</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><msup><mo>)</mo><mn>3</mn></msup></math>, respectively. The pion decay constants are also determined to be <math><mi>F</mi><mo>=</mo><mn>84.1</mn><mo>(</mo><mn>1.9</mn><mo>)</mo><mo>(</mo><mn>8.0</mn><mo>)</mo></math> and <math><msub><mi>F</mi><mn>0</mn></msub><mo>=</mo><mn>58.6</mn><mo>(</mo><mn>0.5</mn><mo>)</mo><mo>(</mo><mn>10.0</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The systematic errors are carefully estimated including the effects of fitting ranges and the uncertainty of low-energy constant <math><msub><mi>L</mi><mn>6</mn></msub></math>. We also show that one can resolve the sea flavor content of the sea quarks and constrain their masses with <math><mrow><mo>∼</mo><mn>10</mn><mo>%</mo><mi>–</mi><mn>20</mn><mo>%</mo></mrow></math> statistical uncertainties using the Dirac spectral density.

Jian Liang

Yu-Jiang Bi

Terrence Draper

Detecting the flavor content of the vacuum using the Dirac operator spectrum

The hadron mass can be obtained through the calculation of the trace of the energy-momentum tensor in the hadron which includes the trace anomaly and sigma terms. The anomaly due to conformal symmetry breaking is believed to be an important ingredient for hadron mass generation and confinement. In this work, we will present the calculation of the glue part of the trace anomaly form factors of the pion up to <math><msup><mi>Q</mi><mn>2</mn></msup><mo>∼</mo><mn>4.3</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></math> and the nucleon up to <math><msup><mi>Q</mi><mn>2</mn></msup><mo>∼</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></math>. The calculations are performed on a domain wall fermion ensemble with overlap valence quarks at seven valence pion masses varying from <math><mo>∼</mo><mn>250</mn></math> to <math><mo>∼</mo><mn>540</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, including the unitary point <math><mo>∼</mo><mn>340</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. We calculate the radius of the glue trace anomaly for the pion and the nucleon from the <math><mi>z</mi></math> expansion. By performing a two-dimensional Fourier transform on the glue trace anomaly form factors in the infinite momentum frame with no energy transfer, we also obtain their spatial distributions for several valence quark masses. The results are qualitatively extrapolated to the physical valence pion mass with systematic errors from the unphysical sea quark mass, discretization effects in the renormalization sum rule, and finite-volume effects to be addressed in the future. We find the pion’s form factor changes sign, as does its spatial distribution, for light quark masses. This explains how the trace anomaly contribution to the pion mass approaches zero toward the chiral limit.

Bigeng Wang

Fangcheng He

Trace anomaly form factors from lattice QCD

We present the first lattice QCD calculation of the universal axial <math><mrow><mi>γ</mi><mi>W</mi></mrow></math>-box contribution <math><mrow><msubsup><mrow><mo>□</mo></mrow><mrow><mi>γ</mi><mi>W</mi></mrow><mrow><mi>V</mi><mi>A</mi></mrow></msubsup></mrow></math> to both superallowed nuclear and neutron beta decays. This contribution emerges as a significant component within the theoretical uncertainties surrounding the extraction of <math><mo>|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>d</mi></mrow></msub><mo>|</mo></math> from superallowed decays. Our calculation is conducted using two domain wall fermion ensembles at the physical pion mass. To construct the nucleon four-point correlation functions, we employ the random sparsening field technique. Furthermore, we incorporate long-distance contributions to the hadronic function using the infinite-volume reconstruction method. Upon performing the continuum extrapolation, we arrive at <math><mrow><msubsup><mrow><mo>□</mo></mrow><mrow><mi>γ</mi><mi>W</mi></mrow><mrow><mi>V</mi><mi>A</mi></mrow></msubsup><mo>=</mo><mn>3.65</mn><mo>(</mo><mn>7</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>lat</mi></mrow></msub><mo>(</mo><mn>1</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>PT</mi></mrow></msub><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>. Consequently, this yields a slightly higher value of <math><mrow><mo>|</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>u</mi><mi>d</mi></mrow></msub><mo>|</mo><mo>=</mo><mn>0.973</mn><mtext> </mtext><mn>86</mn><mo>(</mo><mn>11</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>exp</mi></mrow></msub><mo>(</mo><mn>9</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>RC</mi></mrow></msub><mo>(</mo><mn>27</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>NS</mi></mrow></msub></mrow></math>, reducing the previous <math><mn>2.1</mn><mi>σ</mi></math> tension with the CKM unitarity to <math><mn>1.8</mn><mi>σ</mi></math>. Additionally, we calculate the vector <math><mi>γ</mi><mi>W</mi></math>-box contribution to the axial charge <math><msub><mi>g</mi><mi>A</mi></msub></math>, denoted as <math><msubsup><mo>□</mo><mrow><mi>γ</mi><mi>W</mi></mrow><mrow><mi>V</mi><mi>V</mi></mrow></msubsup></math>, and explore its potential implications.

Peng-Xiang Ma

Xu Feng

Germany

Mikhail Gorchtein

Lu-Chang Jin

Chien-Yeah Seng

Bi-Geng Wang

Zhao-Long Zhang

Lattice QCD Calculation of Electroweak Box Contributions to Superallowed Nuclear and Neutron Beta Decays

We explore the roles of the trace anomaly in several hadron properties. We derive the scale invariant expression for the pressure from the gravitational form factors (GFF) of QCD which results in consistent results for the mass and rest energy from the GFF and those from the trace and the Hamiltonian of the energy-momentum tensor (EMT) operators. It is shown that the energy-equilibrium correspondence of hadrons infers an equation of state where the trace anomaly matrix element, emerging from the glue condensate in the vacuum, gives a negative constant pressure that leads to confinement, much like the confinement mechanism for the vortices in type II superconductors where the negative constant pressure is due to the cost of depleting the superconducting condensate. We also note that both the trace anomaly in the QCD energy-momentum tensor and the cosmological constant in Einstein's equation are associated with the metric term which contributes to both energy and pressure. Their difference in terms of the role the pressure plays is discussed. Finally, we note that a lattice calculation of the trace anomaly distribution in the pion has addressed a question about the trace anomaly contribution to the pion mass and suggests that there might be a connection between the conformal symmetry breaking and chiral symmetry breaking in this case.

Hadrons, superconductor vortices, and cosmological constant