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)

<p>We report a lattice QCD calculation of the parton distribution function (PDF) of a deuteronlike dibaryon system using large-momentum effective theory. The calculation is done on three Wilson-clover ensembles with a fixed lattice spacing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>a</mi><mo>=</mo><mn>0.105</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></mrow></math> and two pion masses. The lattice matrix elements are computed at proton momenta up to 2.46 GeV, with the signal of high-momentum modes being improved by applying the momentum smearing technique. The state-of-the-art renormalization, matching, and extrapolation are then applied to obtain the final result of the light-cone PDF. A comparison between the result of the dibaryon system and the sum of the proton and neutron PDFs is also given.</p>

Chen Chen

Yi-Bo Yang

Fei Yao

Jian-Hui Zhang

Kuan Zhang

Parton distribution function of a deuteronlike dibaryon system from lattice QCD

<p>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>.</p>

Hai-Yang Du

Bolun Hu

Mengchu Cai

Ying Chen

Heng-Tong Ding

Xiangyu Jiang

Yu Meng

Ji-Hao Wang

Dian-Jun Zhao

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

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.

Haobo Yan

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.

Germany

Switzerland

United States

Maxim Mai

Marco Garofalo

Ulf-G. Meißner

Carsten Urbach

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

We present the light-flavor quark masses and low-energy constants using the <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> flavor full-QCD ensembles with stout smeared-clover fermion action and Symanzik gauge action. Both the fermion and gauge actions are tadpole improved self-consistently. The simulations are performed on 11 ensembles at three lattice spacings <math><mi>a</mi><mo>∈</mo><mo>[</mo><mn>0.05</mn><mo>,</mo><mn>0.11</mn><mo>]</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>, four spatial sizes <math><mi>L</mi><mo>∈</mo><mo>[</mo><mn>2.5</mn><mo>,</mo><mn>5.1</mn><mo>]</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>, seven pion masses <math><msub><mi>m</mi><mi>π</mi></msub><mo>∈</mo><mo>[</mo><mn>135</mn><mo>,</mo><mn>350</mn><mo>]</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, and several values of the strange quark mass. The quark mass is defined through the partially conserved axial current relation and renormalized to <math><mrow><mover><mrow><mi>MS</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>(</mo><mn>2</mn><mtext> </mtext><mi>GeV</mi><mo>)</mo></mrow></math> through the intermediate regularization independent momentum subtraction scheme. The systematic uncertainty of using the symmetric momentum subtraction scheme is also included. Eventually, we predict <math><msub><mi>m</mi><mi>u</mi></msub><mo>=</mo><mn>2.45</mn><mo>(</mo><mn>22</mn><mo>)</mo><mo>(</mo><mn>20</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, <math><msub><mi>m</mi><mi>d</mi></msub><mo>=</mo><mn>4.74</mn><mo>(</mo><mn>11</mn><mo>)</mo><mo>(</mo><mn>09</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, and <math><msub><mi>m</mi><mi>s</mi></msub><mo>=</mo><mn>98.8</mn><mo>(</mo><mn>2.9</mn><mo>)</mo><mo>(</mo><mn>4.7</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> with the systematic uncertainties from lattice spacing determination, continuum extrapolation and renormalization constant included. We also obtain the chiral condensate <math><msup><mi>Σ</mi><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup><mo>=</mo><mn>268.6</mn><mo>(</mo><mn>3.6</mn><mo>)</mo><mo>(</mo><mn>0.7</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> and the pion decay constant <math><mi>F</mi><mo>=</mo><mn>86.6</mn><mo>(</mo><mn>7</mn><mo>)</mo><mo>(</mo><mn>1.4</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> in the <math><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn></math> chiral limit, and the next-to-leading order low-energy constants <math><msub><mo>ℓ</mo><mn>3</mn></msub><mo>=</mo><mn>2.43</mn><mo>(</mo><mn>54</mn><mo>)</mo><mo>(</mo><mn>05</mn><mo>)</mo></math> and <math><msub><mo>ℓ</mo><mn>4</mn></msub><mo>=</mo><mn>4.322</mn><mo>(</mo><mn>75</mn><mo>)</mo><mo>(</mo><mn>96</mn><mo>)</mo></math>.

Zhi-Cheng Hu

Bo-Lun Hu

Ming Gong

Guoming Liu

Wei Sun

Wei Wang

Quark masses and low-energy constants in the continuum from the tadpole-improved clover ensembles

In heavy quark limit, the lowest-lying charmed baryons with two light quarks can form an SU(3) triplet and sextet. The <math><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> in the SU(3) triplet and <math><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo></mrow></msubsup></math> in the sextet have the same <math><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msup></math> quantum number and can mix due to the finite charm quark mass and the fact the strange quark is heavier than the up/down quark. We explore the <math><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub></math>–<math><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo></mrow></msubsup></math> mixing by calculating the two-point correlation functions of the <math><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> and <math><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo></mrow></msubsup></math> baryons from lattice QCD. Based on the lattice data, we adopt two independent methods to determine the mixing angle between <math><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> and <math><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo></mrow></msubsup></math>. After making the chiral and continuum extrapolation, it is found that the mixing angle θ is <math><msup><mrow><mn>1.2</mn></mrow><mrow><mo>∘</mo></mrow></msup><mo>±</mo><msup><mrow><mn>0.1</mn></mrow><mrow><mo>∘</mo></mrow></msup></math>, which seems insufficient to account for the large SU(3) symmetry breaking effects found in weak decays of charmed baryons.

Hang Liu

Jin-Xin Tan

Qi-An Zhang

mixing from lattice QCD

We calculate the nucleon isovector scalar charge in lattice QCD using overlap fermions on five ensembles of gauge configurations generated by the RBC/UKQCD collaboration using the domain-wall quark action with <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> dynamical flavors. The five ensembles cover five pion masses, <math><msub><mi>m</mi><mi>π</mi></msub><mo>≈</mo><mn>139</mn></math>, 171, 302, 337 and 371 MeV, and four lattice spacings, <math><mi>a</mi><mo>≈</mo><mn>0.06</mn></math>, 0.08, 0.11 and 0.14 fm. Three to six valence quark masses are computed on each ensemble to investigate the pion mass dependence. The extrapolation to the physical pion mass, continuum and infinite volume limits is obtained by a global fit of all data to a formula originated from partially quenched chiral perturbation theory. The excited-states contamination is carefully analyzed with 3–5 sink-source separations and multi-state fits. Our final result, in the <math><mrow><mover><mrow><mi>MS</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> scheme at 2 GeV, is <math><mrow><msubsup><mrow><mi>g</mi></mrow><mrow><mi>S</mi></mrow><mrow><mi>u</mi><mo>−</mo><mi>d</mi></mrow></msubsup><mo>=</mo><mn>0.94</mn><mo>(</mo><mn>10</mn><msub><mrow><mo>)</mo></mrow><mrow><mtext>stat</mtext></mrow></msub><mo>(</mo><mn>8</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>sys</mi></mrow></msub></mrow></math>, where the first error is the statistical error and the second is the systematic error.

Ting Chen

Terrence Draper

Jian Liang

Keh-Fei Liu

Geng Wang

Nucleon isovector scalar charge from overlap fermions

We present the first direct  $$N_f=2$$  <math> <mrow> <msub> <mi>N</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>2</mn> </mrow> </math>   lattice QCD computation of two- and three- $$\pi ^+$$  <math> <msup> <mi>π</mi> <mo>+</mo> </msup> </math>   scattering quantities that includes an ensemble at the physical point. We study the quark mass dependence of the two-pion phase shift, and the three-particle interaction parameters. We also compare to phenomenology and chiral perturbation theory (ChPT). In the two-particle sector, we observe good agreement to the phenomenological fits in s- and d-wave, and obtain  $$M_\pi a_0 = -0.0481(86)$$  <math> <mrow> <msub> <mi>M</mi> <mi>π</mi> </msub> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>-</mo> <mn>0.0481</mn> <mrow> <mo>(</mo> <mn>86</mn> <mo>)</mo> </mrow> </mrow> </math>   at the physical point from a direct computation. In the three-particle sector, we observe reasonable agreement at threshold to the leading order chiral expansion, i.e. a mildly attractive three-particle contact term. In contrast, we observe that the energy-dependent part of the three-particle quasilocal scattering quantity is not well described by leading order ChPT.

Matthias Fischer

Bartosz Kostrzewa

Spain

Fernando Romero-López

Martin Ueding

Scattering of two and three physical pions at maximal isospin from lattice QCD

This exploratory study computes two-photon decay widths of pseudo-scalar (
					) and scalar (
					) charmonium using two ensembles of 
					 twisted mass lattice QCD gauge configurations. The simulation is performed using two lattice ensembles with lattice spacings 
					 fm with size 
					 and 
					 fm with size 
					. The decay widths for the two charmonia are obtained within the expected ballpark, but are however smaller than the experimental ones. Possible reasons for these discrepancies are discussed.
				

Ning Li

Yu-Bin Liu

Zhaofeng Liu

Jian-Ping Ma

Chao Xiong

Ke-Long Zhang

Lattice study of two-photon decay widths for scalar and pseudo-scalar charmonium This work is supported in part by the National Science Foundation of China (NSFC) (11335001, 11275169, 11405178, 11935017, 11575196, 11875169, 11775229). It is also supported in part by the DFG and the NSFC (11261130311) through funds provided to the Sino-Germen CRC 110 symmetries and the Emergence of Structure in QCD. This work is also funded in part by National Basic Research Program of China (973 Program) (2015CB856700). M. Gong and Z. Liu are partially supported by the Youth Innovation Promotion Association of CAS (2013013). This work is also supported by the Scientific Research Program Funded by Shaanxi Provincial Education Department (19JK0391) andNatural Science Basic Research Plan in Shaanxi Province of China (2019JM-001)