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.

China

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)

Quantum fluctuations in QCD influence nucleon structure and interactions, with pion production serving as a key probe of chiral dynamics. In this Letter, we present a lattice QCD calculation of multipole amplitudes at threshold, related to both pion electroproduction and weak production from a nucleon, using two gauge ensembles near the physical pion mass. We develop a technique for spin projection and construct multiple operators for analyzing the generalized eigenvalue problem in both the nucleon-pion system in the center-of-mass frame and the nucleon system with nonzero momentum. The numerical lattice results are then compared with those extracted from experimental data and predicted by low-energy theorems incorporating one-loop corrections.

Yu-Sheng Gao

Zhao-Long Zhang

Xu Feng

United States

Lu-Chang Jin

Germany

Ulf-G. Meißner

Lattice QCD Study of Pion Electroproduction and Weak Production from a Nucleon

We calculate the s-wave scattering length in the $$0^+$$ sector of $$\eta _c\eta _c$$ and the $$2^+$$ sector of $$J/\psi J/\psi $$ using three $$N_f=2$$ twisted mass gauge ensembles with the pion mass $$300{-}365$$ MeV and lattice spacing $$a=0.0667,0.085,0.098$$ fm, respectively. The scattering lengths are extracted using the conventional Lüscher finite size method. We observe sizable discretization effects and the results after a continuum extrapolation are $$a^{0^+}_{\eta _c\eta _c}=-0.104(09)$$ fm and $$a^{2^+}_{J/\psi J/\psi }=-0.165(16)$$ fm. The slight difference of light quark mass is ignored in this study. Our results indicate that the interaction between the two respective charmonia are repulsive in nature in both cases.

Yu Meng

Xin-Yu Tuo

Haobo Yan

Zhaolong Zhang

Lattice calculation of the $$\eta _c\eta _c$$ and $$J/\psi J/\psi $$ s-wave scattering length

We present the determination of the charm quark mass, the masses, and decay constants of charmed mesons using thirteen <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> flavor gauge ensembles at five different lattice spacings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>∈</mo><mo stretchy="false">[</mo><mn>0.05</mn><mo>,</mo><mn>0.11</mn><mo stretchy="false">]</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>, 8 pion masses <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>130</mn><mo>,</mo><mn>360</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, and several values of the strange quark mass, which allows us to do the chiral and continuum extrapolation. These ensembles are generated through the stout smeared clover fermion action and Symanzik gauge actions with the tadpole improvement. By absorbing the discretization errors into the masses and field normalization of the charm quark, we manage to suppress the discretization error of the charmed meson mass and all the S-wave open charmed meson decay constants to a few percent or even less at lattice spacing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>∼</mo><mn>0.1</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>. Moreover, discretization errors for other quantities are also significantly reduced. The continuum extrapolated charm quark mass, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>c</mi></msub><mo stretchy="false">(</mo><msub><mi>m</mi><mi>c</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mn>1.2933</mn><mo stretchy="false">(</mo><mn>72</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>95</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>MS</mi><mo stretchy="true">¯</mo></mover></math> scheme, is determined using QED-subtracted <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub></math> meson mass and nonperturbative renormalization. Predictions of the open and close charm mesons using this charm quark mass agree with the experimental values at 0.1–0.5% level uncertainty. We obtained <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub></math> decay constants and also by far the most precise <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mo>*</mo></msubsup></math> decay constants <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><msup><mi>D</mi><mo>*</mo></msup></msub><mo>=</mo><mn>0.2292</mn><mo stretchy="false">(</mo><mn>26</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>17</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup></msub><mo>=</mo><mn>0.2691</mn><mo stretchy="false">(</mo><mn>30</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>03</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>.

Hai-Yang Du

Bolun Hu

Mengchu Cai

Ying Chen

Heng-Tong Ding

Xiangyu Jiang

Ji-Hao Wang

Yi-Bo Yang

Dian-Jun Zhao

Charmed meson masses and decay constants in the continuum limit from the tadpole improved clover ensembles

The subtraction function plays a pivotal role in calculations involving the forward Compton amplitude, which is crucial for predicting the Lamb shift in muonic atoms, as well as the proton-neutron mass difference. In this Letter, we present a lattice QCD calculation of the subtraction function using two domain wall fermion gauge ensembles near the physical pion mass. We utilize a recently proposed subtraction point, demonstrating its advantage in mitigating statistical and systematic uncertainties by eliminating the need for ground-state subtraction. Our results reveal significant contributions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mi>π</mi></math> intermediate states to the subtraction function. Incorporating these contributions, we compute the proton, neutron, and nucleon isovector subtraction functions at photon momentum transfer <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>∈</mo><mo stretchy="false">[</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo stretchy="false">]</mo><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>. For the proton subtraction function, we compare our lattice results with chiral perturbation theory prediction at low <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup></math> and with the results from the perturbative operator-product expansion at high <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup></math>. Finally, using these subtraction functions as input, we determine their contribution to two-photon exchange effects in the Lamb shift and isovector nucleon electromagnetic self-energy.

Yang Fu

Shi-Da Wen

Lattice QCD Calculation of the Subtraction Function in Forward Compton Amplitude

We present a model-independent method to calculate the radiative transition without the momentum extrapolation for the off shell transition factors. The on shell transition factor is directly obtained from the lattice hadronic function. We apply the method to calculate the charmonium radiative transition <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msub><mi>η</mi><mi>c</mi></msub></math>. After a continuous extrapolation under three lattice spacings, we obtain the on shell transition factor as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mn>1.90</mn><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo></math>, where the error is the statistical error that already takes into account the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>a</mi><mn>2</mn></msup></math> error in the continuous extrapolation. Finally, we determine the branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msub><mi>η</mi><mi>c</mi></msub></math> as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Br</mi><mo stretchy="false">(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mn>2.49</mn><mo stretchy="false">(</mo><mn>11</mn><msub><mo stretchy="false">)</mo><mi>lat</mi></msub><mo stretchy="false">(</mo><mn>5</mn><msub><mo stretchy="false">)</mo><mi>exp</mi></msub><mo>%</mo></math>, where the second error comes from the uncertainty of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> total decay width 92.6(1.7) keV.

Teng Wang

Lattice study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msub><mi>η</mi><mi>c</mi></msub></math> using a method without momentum extrapolation

Lattice QCD results for isospin <math><mrow><mi>I</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math> <math><mi>D</mi><mi>π</mi></math> scattering are presented. Utilizing a series of <math><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></math> Wilson-Clover ensembles with pion masses of <math><msub><mi>m</mi><mi>π</mi></msub><mo>≈</mo><mn>133</mn></math>, 208, 305, and 317 MeV, various two-particle operators are constructed, and the corresponding finite-volume spectra are determined. The <math><mi>S</mi></math>- and <math><mi>P</mi></math>-wave scattering phase shifts are extracted using the Lüscher approach. A clear trend for the motion of the <math><msubsup><mi>D</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>2300</mn><mo>)</mo></math> pole is identified. With the physical pion mass configurations also included, this calculation constitutes the first lattice calculation in which the pion mass dependence of the <math><msubsup><mi>D</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>2300</mn><mo>)</mo></math> pole is investigated and the scattering lengths are extrapolated/interpolated to the physical pion mass in <math><mi>D</mi><mi>π</mi></math> scattering.

Pion mass dependence in <math><mi>D</mi><mi>π</mi></math> scattering and the <math><msubsup><mi>D</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>2300</mn><mo>)</mo></math> resonance from lattice QCD

Many excited states in the hadron spectrum have large branching ratios to three-hadron final states. Understanding such particles from first principles QCD requires input from lattice QCD with one-, two-, and three-meson interpolators as well as a reliable three-body formalism relating finite-volume spectra at unphysical pion mass values to the scattering amplitudes at the physical point. In this work, we provide the first-ever calculation of the resonance parameters of the <math><mi>ω</mi></math> meson from lattice QCD, including an update of the formalism through matching to effective field theories. The main result of this pioneering study, the pole position of the <math><mi>ω</mi></math> meson at <math><msqrt><msub><mi>s</mi><mi>ω</mi></msub></msqrt><mo>=</mo><mo>(</mo><mn>778.0</mn><mo>(</mo><mn>11.2</mn><mo>)</mo><mo>−</mo><mi>i</mi><mn>3.0</mn><mo>(</mo><mn>5</mn><mo>)</mo><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, agrees reasonably well with experiment. In addition we provide an estimate of the <math><mi>ω</mi><mo>−</mo><mi>ρ</mi></math> mass difference as 29(15) MeV.

Switzerland

Maxim Mai

Marco Garofalo

Carsten Urbach

<math><mi>ω</mi></math> Meson from Lattice QCD

We perform the first lattice calculation on the semileptonic decay of <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> using the (<math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor Wilson-clover gauge ensembles generated by CLQCD collaboration. Three gauge ensembles with different lattice spacings, from 0.0519 to 0.1053 fm, and pion masses, <math><msub><mi>m</mi><mi>π</mi></msub><mo>∼</mo><mn>300</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, are utilized. After a naive continuum extrapolation using three lattice spacings, we obtain <math><mi>Br</mi><mo>(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msub><mi>D</mi><mi>s</mi></msub><mi>e</mi><msub><mi>ν</mi><mi>e</mi></msub><mo>)</mo><mo>=</mo><mn>1.90</mn><mo>(</mo><mn>6</mn><mo>)</mo><mo>(</mo><mn>5</mn><msub><mo>)</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub></msub><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>10</mn></mrow></msup></math> and <math><mi>Br</mi><mo>(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>D</mi><mi>e</mi><msub><mi>ν</mi><mi>e</mi></msub><mo>)</mo><mo>=</mo><mn>1.21</mn><mo>(</mo><mn>6</mn><mo>)</mo><mo>(</mo><mn>9</mn><msub><mo>)</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>d</mi></mrow></msub></msub><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>11</mn></mrow></msup></math>, where the first errors are statistical, and the second come from the uncertainties of Cabibbo-Kobayashi-Maskawa matrix element <math><msub><mi>V</mi><mrow><mi>c</mi><mi>s</mi><mo>(</mo><mi>d</mi><mo>)</mo></mrow></msub></math>. The ratios of the branching fractions between lepton <math><mi>μ</mi></math> and <math><mi>e</mi></math> are also calculated as <math><msub><mi>R</mi><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>(</mo><msub><mi>D</mi><mi>s</mi></msub><mo>)</mo><mo>=</mo><mn>0.97002</mn><mo>(</mo><mn>8</mn><mo>)</mo></math> and <math><msub><mi>R</mi><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>(</mo><mi>D</mi><mo>)</mo><mo>=</mo><mn>0.97423</mn><mo>(</mo><mn>15</mn><mo>)</mo></math> after performing a continuum limit including only <math><msup><mi>a</mi><mn>2</mn></msup></math> term. The ratios provide necessary theoretical support for the future experimental test of lepton flavor universality.

Jin-Long Dang

Ke-Long Zhang

First lattice QCD calculation of <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> semileptonic decay containing <math><mi>D</mi></math> and <math><msub><mi>D</mi><mi>s</mi></msub></math> particles

We present a lattice QCD calculation of the nucleon electric polarizabilities at the physical pion mass. Our findings reveal the substantial contributions of the <math><mi>N</mi><mi>π</mi></math> states to these polarizabilities. Without considering these contributions, the lattice results fall significantly below the experimental values, consistent with previous lattice studies. This observation has motivated us to compute both the parity-negative <math><mi>N</mi><mi>π</mi></math> scattering up to a nucleon momentum of <math><mrow><mo>∼</mo><mn>0.5</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math> in the center-of-mass frame and corresponding <math><mrow><mi>N</mi><msup><mrow><mi>γ</mi></mrow><mrow><mo>*</mo></mrow></msup><mo>→</mo><mi>N</mi><mi>π</mi></mrow></math> matrix elements using lattice QCD. Our results confirm that incorporating dynamic <math><mi>N</mi><mi>π</mi></math> contributions is crucial for a reliable determination of the polarizabilities from lattice QCD. This methodology lays the groundwork for future lattice QCD investigations into various other polarizabilities.

Xuan-He Wang

Xiong-Hui Cao

Cong-Ling Fan

Nucleon Electric Polarizabilities and Nucleon-Pion Scattering at the Physical Pion Mass