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>The BESIII Collaboration recently reported the observation of two new resonances, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>1910</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>2300</mn><mo stretchy="false">)</mo></math>, which have sparked our interest in studying the light hadron family with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>+</mo><mo>−</mo></mrow></msup></math>. In this work, we investigate the mass spectra and Okubo-Zweig-Iizuka (OZI)-allowed two-body strong decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>b</mi><mn>1</mn></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mn>1</mn></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>h</mi><mn>1</mn><mo>′</mo></msubsup></math> using the modified Godfrey-Isgur (MGI) quark model and quark-pair creation (QPC) model with newly fitted parameters. We also explore the possibility of identifying <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>1910</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>2300</mn><mo stretchy="false">)</mo></math> as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mn>1</mn></msub></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>h</mi><mn>1</mn><mo>′</mo></msubsup></math> states. Our numerical results suggest that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>1910</mn><mo stretchy="false">)</mo></math> could be a promising candidate for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>h</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">(</mo><msup><mn>2</mn><mn>1</mn></msup><msub><mi>P</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math> state with quark content <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math>, while the structure of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>2300</mn><mo stretchy="false">)</mo></math> remains uncertain.</p>

Ya-Rong Wang

Xiao-Hai Liu

Cheng-Qun Pang

Hao Chen

New states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>1910</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>2300</mn><mo stretchy="false">)</mo></math> and higher light excited <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>+</mo><mo>−</mo></mrow></msup></math> mesons

We use an effective Lagrangian approach to investigate the production of the anticharmed pentaquark state $$P_{\bar{c}s}^{(*)-}$$ with the minimal quark content $$\bar{c}sudd$$ in the $$\Lambda _b^0$$ decay. In our calculation, the $$P_{\bar{c}s}^{(*)-}$$ is considered as the molecule state of the $$nD_{s0(s1)}^{-}$$ in an wave, and its production and decay occur via triangle loops at the hadron level. With the moderate model parameters, the computed results suggest that the branching fractions of $$\Lambda _b^0\rightarrow P_{\bar{c}s}^{(*)-} D^+ $$ can reach approximately $$10^{-4}$$ . The possible decay modes $$ P_{\bar{c}s}^{(*)-} \rightarrow \Lambda D^{(*)-}$$ and $$ P_{\bar{c}s}^{(*)-} \rightarrow \Sigma D^{(*)-}$$ are also investigated. It is hoped that these predictions could be helpful in searching for the anticharmed-strange pentaquark candidates in future LHCb experiments.

Shi-Dong Liu

Xiao-Yun Wang

Gang Li

Production and decay of anticharmed pentaquark state with quark content $$\bar{c}sudd$$

We investigated the pionic transitions between the <math><msub><mi>X</mi><mn>2</mn></msub></math> [spin-2 partner of the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math>] and <math><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math> using a nonrelativistic effective field theory. The <math><msub><mi>X</mi><mn>2</mn></msub></math> is assumed to be a bound state of the <math><msup><mi>D</mi><mo>*</mo></msup></math> and <math><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> mesons and to decay through several kinds of loops, including the bubble, triangle, and box loops. Within the present model, the widths for the single-pion decays <math><msub><mi>X</mi><mn>2</mn></msub><mo>→</mo><msup><mi>π</mi><mn>0</mn></msup><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> are predicted to be about 3–30 keV. For the dipion decays, the widths are a few keVs. These widths yield a branching fraction of <math><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup><mi>–</mi><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></math>. The ratio <math><msub><mi>R</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><mo>=</mo><mi>Γ</mi><mo>(</mo><msub><mi>X</mi><mn>2</mn></msub><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo>)</mo><mo>/</mo><mi>Γ</mi><mo>(</mo><msub><mi>X</mi><mn>2</mn></msub><mo>→</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo>)</mo><mo>≃</mo><mn>1.6</mn></math>, which is a bit smaller than the expected value of 2, and <math><msub><mi>R</mi><mn>21</mn></msub><mo>=</mo><mi>Γ</mi><mo>(</mo><msub><mi>X</mi><mn>2</mn></msub><mo>→</mo><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>)</mo><mo>/</mo><mi>Γ</mi><mo>(</mo><msub><mi>X</mi><mn>2</mn></msub><mo>→</mo><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>)</mo><mo>≃</mo><mn>0.85</mn></math>. These ratios are nearly independent of the <math><msub><mi>X</mi><mn>2</mn></msub></math> mass and the coupling constants, which might be a good quantity for the experiments. Moreover, the invariant mass spectra of the <math><msup><mi>π</mi><mn>0</mn></msup><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> final state for the dipion processes are presented, showing a cusp structure at the <math><mi>D</mi><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> threshold enhanced and narrowed by the nearby triangle singularity.

Fan Wang

Zhao-Sai Jia

Ju-Jun Xie

Pionic transitions of the spin-2 partner of <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> to <math><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math>

We investigate the weak decays of the triply heavy baryon  $$\Omega _{QQQ}$$  <math> <msub> <mi>Ω</mi> <mrow> <mi>QQQ</mi> </mrow> </msub> </math>   in the light-front quark model. Since  $$\Omega _{QQQ}$$  <math> <msub> <mi>Ω</mi> <mrow> <mi>QQQ</mi> </mrow> </msub> </math>   consists of three indistinguishable identical heavy quarks, the commonly adopted quark–diquark picture does not seem to be valid anymore. Instead, we employ the three-quark picture for baryons where the three quarks are regarded as individual quarks. We calculate the hadronic form factors for the transitions and give predictions for the decay widths of the semi-leptonic decay modes  $$\Omega _{ccc}\rightarrow \Xi _{cc}/ \Omega _{cc}+ l^+\nu _l$$  <math> <mrow> <msub> <mi>Ω</mi> <mrow> <mi>ccc</mi> </mrow> </msub> <mo>→</mo> <msub> <mi>Ξ</mi> <mrow> <mi>cc</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>Ω</mi> <mrow> <mi>cc</mi> </mrow> </msub> <mo>+</mo> <msup> <mi>l</mi> <mo>+</mo> </msup> <msub> <mi>ν</mi> <mi>l</mi> </msub> </mrow> </math>  ,  $$\Omega _{bbb}\rightarrow \Xi _{bb}+ l^-\bar{\nu }_l$$  <math> <mrow> <msub> <mi>Ω</mi> <mrow> <mi>bbb</mi> </mrow> </msub> <mo>→</mo> <msub> <mi>Ξ</mi> <mrow> <mi>bb</mi> </mrow> </msub> <mo>+</mo> <msup> <mi>l</mi> <mo>-</mo> </msup> <msub> <mover> <mrow> <mi>ν</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>l</mi> </msub> </mrow> </math>   and the non-leptonic decay modes  $$\Omega _{ccc}\rightarrow \Xi _{cc}/\Omega _{cc}+ M$$  <math> <mrow> <msub> <mi>Ω</mi> <mrow> <mi>ccc</mi> </mrow> </msub> <mo>→</mo> <msub> <mi>Ξ</mi> <mrow> <mi>cc</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>Ω</mi> <mrow> <mi>cc</mi> </mrow> </msub> <mo>+</mo> <mi>M</mi> </mrow> </math>  ,  $$\Omega _{bbb}\rightarrow \Xi _{bb}+ M$$  <math> <mrow> <msub> <mi>Ω</mi> <mrow> <mi>bbb</mi> </mrow> </msub> <mo>→</mo> <msub> <mi>Ξ</mi> <mrow> <mi>bb</mi> </mrow> </msub> <mo>+</mo> <mi>M</mi> </mrow> </math>  . Our study can be a guide for future experiments to discover the triply heavy baryons.

Fang Lu

Hong-Wei Ke

Weak decays of the triply heavy baryons in the three-quark picture with the light-front quark model

The measurements on a few pentaquarks states  $$P_c(4440)$$  <math> <mrow> <msub> <mi>P</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>4440</mn> <mo>)</mo> </mrow> </mrow> </math>  ,  $$P_c(4457)$$  <math> <mrow> <msub> <mi>P</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>4457</mn> <mo>)</mo> </mrow> </mrow> </math>   and  $$P_{cs}(4459)$$  <math> <mrow> <msub> <mi>P</mi> <mrow> <mi>cs</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>4459</mn> <mo>)</mo> </mrow> </mrow> </math>   excite our new interests about their structures. Since the masses of  $$P_c(4440)$$  <math> <mrow> <msub> <mi>P</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>4440</mn> <mo>)</mo> </mrow> </mrow> </math>   and  $$P_c(4457)$$  <math> <mrow> <msub> <mi>P</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>4457</mn> <mo>)</mo> </mrow> </mrow> </math>   are close to the threshold of  $$\Sigma _c{\bar{D}}^*$$  <math> <mrow> <msub> <mi>Σ</mi> <mi>c</mi> </msub> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>  , in the earlier works, they were regarded as molecular states of  $$\Sigma _c{\bar{D}}^*$$  <math> <mrow> <msub> <mi>Σ</mi> <mi>c</mi> </msub> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   with quantum numbers  $$I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$$  <math> <mrow> <mi>I</mi> <mrow> <mo>(</mo> <msup> <mi>J</mi> <mi>P</mi> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msup> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>-</mo> </msup> <mo>)</mo> </mrow> </mrow> </math>   and  $$\frac{1}{2}(\frac{3}{2}^-)$$  <math> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msup> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>-</mo> </msup> <mo>)</mo> </mrow> </mrow> </math>  , respectively. In a similar way  $$P_{cs}(4459)$$  <math> <mrow> <msub> <mi>P</mi> <mrow> <mi>cs</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>4459</mn> <mo>)</mo> </mrow> </mrow> </math>   is naturally considered as a  $$\Xi _c{\bar{D}}^*$$  <math> <mrow> <msub> <mi>Ξ</mi> <mi>c</mi> </msub> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   bound state with  $$I=0$$  <math> <mrow> <mi>I</mi> <mo>=</mo> <mn>0</mn> </mrow> </math>  . Within the Bethe-Salpeter (B-S) framework we systematically study the possible bound states of  $$\Lambda _c\bar{D}^*$$  <math> <mrow> <msub> <mi>Λ</mi> <mi>c</mi> </msub> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>  ,  $$\Sigma _c{\bar{D}}^*$$  <math> <mrow> <msub> <mi>Σ</mi> <mi>c</mi> </msub> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>  ,  $$\Xi _c{\bar{D}}^*$$  <math> <mrow> <msub> <mi>Ξ</mi> <mi>c</mi> </msub> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   and  $$\Xi _c'{\bar{D}}^*$$  <math> <mrow> <msubsup> <mi>Ξ</mi> <mi>c</mi> <mo>′</mo> </msubsup> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>  . Our results indicate that  $$\Sigma _c{\bar{D}}^*$$  <math> <mrow> <msub> <mi>Σ</mi> <mi>c</mi> </msub> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   can form a bound state with  $$I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$$  <math> <mrow> <mi>I</mi> <mrow> <mo>(</mo> <msup> <mi>J</mi> <mi>P</mi> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msup> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>-</mo> </msup> <mo>)</mo> </mrow> </mrow> </math>  , which corresponds to  $$P_c(4440)$$  <math> <mrow> <msub> <mi>P</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>4440</mn> <mo>)</mo> </mrow> </mrow> </math>  . However for the  $$I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$$  <math> <mrow> <mi>I</mi> <mrow> <mo>(</mo> <msup> <mi>J</mi> <mi>P</mi> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msup> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>-</mo> </msup> <mo>)</mo> </mrow> </mrow> </math>   system the attraction between  $$\Sigma _c$$  <math> <msub> <mi>Σ</mi> <mi>c</mi> </msub> </math>   and  $${\bar{D}}^*$$  <math> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </math>   is too weak to constitute a molecule, so  $$P_{c}(4457)$$  <math> <mrow> <msub> <mi>P</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>4457</mn> <mo>)</mo> </mrow> </mrow> </math>   may not be a bound state of  $$\Sigma _c{\bar{D}}^*$$  <math> <mrow> <msub> <mi>Σ</mi> <mi>c</mi> </msub> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   with  $$I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$$  <math> <mrow> <mi>I</mi> <mrow> <mo>(</mo> <msup> <mi>J</mi> <mi>P</mi> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msup> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>-</mo> </msup> <mo>)</mo> </mrow> </mrow> </math>  . As  $$\Xi _c{\bar{D}}^*$$  <math> <mrow> <msub> <mi>Ξ</mi> <mi>c</mi> </msub> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   and  $$\Xi _c'{\bar{D}}^*$$  <math> <mrow> <msubsup> <mi>Ξ</mi> <mi>c</mi> <mo>′</mo> </msubsup> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   systems we take into account of the mixing between  $$\Xi _c$$  <math> <msub> <mi>Ξ</mi> <mi>c</mi> </msub> </math>   and  $$\Xi '_c$$  <math> <msubsup> <mi>Ξ</mi> <mi>c</mi> <mo>′</mo> </msubsup> </math>   and the eigenstets should include two normal bound states  $$\Xi _c{\bar{D}}^*$$  <math> <mrow> <msub> <mi>Ξ</mi> <mi>c</mi> </msub> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   and  $$\Xi _c'{\bar{D}}^*$$  <math> <mrow> <msubsup> <mi>Ξ</mi> <mi>c</mi> <mo>′</mo> </msubsup> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   with  $$I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$$  <math> <mrow> <mi>I</mi> <mrow> <mo>(</mo> <msup> <mi>J</mi> <mi>P</mi> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msup> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>-</mo> </msup> <mo>)</mo> </mrow> </mrow> </math>   and a loosely bound state  $$\Xi _c{\bar{D}}^*$$  <math> <mrow> <msub> <mi>Ξ</mi> <mi>c</mi> </msub> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   with  $$I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$$  <math> <mrow> <mi>I</mi> <mrow> <mo>(</mo> <msup> <mi>J</mi> <mi>P</mi> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msup> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>-</mo> </msup> <mo>)</mo> </mrow> </mrow> </math>  . The conclusion that two  $$\Xi _c{\bar{D}}^*$$  <math> <mrow> <msub> <mi>Ξ</mi> <mi>c</mi> </msub> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   bound states exist, supports the suggestion that the observed peak of  $$P_{cs}(4459)$$  <math> <mrow> <msub> <mi>P</mi> <mrow> <mi>cs</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>4459</mn> <mo>)</mo> </mrow> </mrow> </math>   may hide two states  $$P_{cs}(4455)$$  <math> <mrow> <msub> <mi>P</mi> <mrow> <mi>cs</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>4455</mn> <mo>)</mo> </mrow> </mrow> </math>   and  $$P_{cs}(4468)$$  <math> <mrow> <msub> <mi>P</mi> <mrow> <mi>cs</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>4468</mn> <mo>)</mo> </mrow> </mrow> </math>  . Based on the computations we predict a bound state  $$\Xi _c'{\bar{D}}^*$$  <math> <mrow> <msubsup> <mi>Ξ</mi> <mi>c</mi> <mo>′</mo> </msubsup> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   with  $$I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$$  <math> <mrow> <mi>I</mi> <mrow> <mo>(</mo> <msup> <mi>J</mi> <mi>P</mi> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msup> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>-</mo> </msup> <mo>)</mo> </mrow> </mrow> </math>   but not that with  $$I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$$  <math> <mrow> <mi>I</mi> <mrow> <mo>(</mo> <msup> <mi>J</mi> <mi>P</mi> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msup> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>-</mo> </msup> <mo>)</mo> </mrow> </mrow> </math>  . Further more accurate experiments will test our approach and results.

Hai Pang

Xue-Qian Li

Study on the possible molecular states composed of  $$\Lambda _c{\bar{D}}^*$$  <math> <mrow> <msub> <mi>Λ</mi> <mi>c</mi> </msub> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>  ,  $$\Sigma _c{\bar{D}}^*$$  <math> <mrow> <msub> <mi>Σ</mi> <mi>c</mi> </msub> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>  ,  $$\Xi _c{\bar{D}}^*$$  <math> <mrow> <msub> <mi>Ξ</mi> <mi>c</mi> </msub> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   and  $$\Xi _c'{\bar{D}}^*$$  <math> <mrow> <msubsup> <mi>Ξ</mi> <mi>c</mi> <mo>′</mo> </msubsup> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   in the Bethe–Salpeter frame based on the pentaquark states  $$P_c(4440)$$  <math> <mrow> <msub> <mi>P</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>4440</mn> <mo>)</mo> </mrow> </mrow> </math>  ,  $$P_c(4457)$$  <math> <mrow> <msub> <mi>P</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>4457</mn> <mo>)</mo> </mrow> </mrow> </math>   and  $$P_{cs}(4459)$$  <math> <mrow> <msub> <mi>P</mi> <mrow> <mi>cs</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>4459</mn> <mo>)</mo> </mrow> </mrow> </math>

In this work, we study the weak decay between two heavy baryons  $${\mathcal {B}}_i(\frac{1}{2}^+)\rightarrow {\mathcal {B}}_f(\frac{3}{2}^+)$$  <math> <mrow> <msub> <mi>B</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>+</mo> </msup> <mo>)</mo> </mrow> <mo>→</mo> <msub> <mi>B</mi> <mi>f</mi> </msub> <mrow> <mo>(</mo> <msup> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>+</mo> </msup> <mo>)</mo> </mrow> </mrow> </math>   in the light-front quark model where three-quark picture is employed for baryon. We derive general form of transition amplitude of  $$ {\mathcal {B}}_i(\frac{1}{2}^+)\rightarrow {\mathcal {B}}_f(\frac{3}{2}^+)$$  <math> <mrow> <msub> <mi>B</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>+</mo> </msup> <mo>)</mo> </mrow> <mo>→</mo> <msub> <mi>B</mi> <mi>f</mi> </msub> <mrow> <mo>(</mo> <msup> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>+</mo> </msup> <mo>)</mo> </mrow> </mrow> </math>  , and analyze two specific cases of transitions: the weak decays of single heavy baryon  $$\Sigma _{b} \rightarrow \Sigma _{c}^*$$  <math> <mrow> <msub> <mi>Σ</mi> <mi>b</mi> </msub> <mo>→</mo> <msubsup> <mi>Σ</mi> <mrow> <mi>c</mi> </mrow> <mo>∗</mo> </msubsup> </mrow> </math>   and the decays of double-charmed baryon  $$\Xi _{cc}\rightarrow \Sigma _{c}^*(\Xi _{c}^*)$$  <math> <mrow> <msub> <mi>Ξ</mi> <mrow> <mi>cc</mi> </mrow> </msub> <mo>→</mo> <msubsup> <mi>Σ</mi> <mrow> <mi>c</mi> </mrow> <mo>∗</mo> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>Ξ</mi> <mrow> <mi>c</mi> </mrow> <mo>∗</mo> </msubsup> <mo>)</mo> </mrow> </mrow> </math>  . We compute the hadronic form factors for the transitions and apply them to study the decay widths of the semi-leptonic  $${\mathcal {B}}_i(\frac{1}{2}^+)\rightarrow {\mathcal {B}}_f(\frac{3}{2}^+) l\bar{\nu }_l$$  <math> <mrow> <msub> <mi>B</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>+</mo> </msup> <mo>)</mo> </mrow> <mo>→</mo> <msub> <mi>B</mi> <mi>f</mi> </msub> <mrow> <mo>(</mo> <msup> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>+</mo> </msup> <mo>)</mo> </mrow> <mi>l</mi> <msub> <mover> <mrow> <mi>ν</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>l</mi> </msub> </mrow> </math>   and non-leptonic  $${\mathcal {B}}_i(\frac{1}{2}^+)\rightarrow {\mathcal {B}}_f(\frac{3}{2}^+)M$$  <math> <mrow> <msub> <mi>B</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>+</mo> </msup> <mo>)</mo> </mrow> <mo>→</mo> <msub> <mi>B</mi> <mi>f</mi> </msub> <mrow> <mo>(</mo> <msup> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>+</mo> </msup> <mo>)</mo> </mrow> <mi>M</mi> </mrow> </math>  . Previously we studied the transition  $$\Sigma _{b} \rightarrow \Sigma _{c}^*$$  <math> <mrow> <msub> <mi>Σ</mi> <mi>b</mi> </msub> <mo>→</mo> <msubsup> <mi>Σ</mi> <mrow> <mi>c</mi> </mrow> <mo>∗</mo> </msubsup> </mrow> </math>   with the quark–diquark picture of baryon in the light-front quark model. Here we revisit this transition with three-quark picture of baryon. At the quark level, the transition  $$\Sigma _{b} \rightarrow \Sigma _{c}^*$$  <math> <mrow> <msub> <mi>Σ</mi> <mi>b</mi> </msub> <mo>→</mo> <msubsup> <mi>Σ</mi> <mrow> <mi>c</mi> </mrow> <mo>∗</mo> </msubsup> </mrow> </math>   is induced by the  $$b\rightarrow c$$  <math> <mrow> <mi>b</mi> <mo>→</mo> <mi>c</mi> </mrow> </math>   transition.The subsystem of the two unchanged light quarks which possesses definite and same spin in initial and final state can be viewed as a spectator, so the spectator approximation can be applied directly. For the weak decay of doubly charmed baryon  $$\Xi _{cc}$$  <math> <msub> <mi>Ξ</mi> <mrow> <mi>cc</mi> </mrow> </msub> </math>  , a c quark decays to a light quark  $$q_1$$  <math> <msub> <mi>q</mi> <mn>1</mn> </msub> </math>  , so both the initial state cc and final state  $$q_1q_2$$  <math> <mrow> <msub> <mi>q</mi> <mn>1</mn> </msub> <msub> <mi>q</mi> <mn>2</mn> </msub> </mrow> </math>   ( $$q_1$$  <math> <msub> <mi>q</mi> <mn>1</mn> </msub> </math>   and the original  $$q_2$$  <math> <msub> <mi>q</mi> <mn>2</mn> </msub> </math>   in initial state may be the same flavor quarks) which possess definite spin are no longer spectators. A rearrangement of quarks for initial and final states is adopted to isolate the unchanged subsystem  $$cq_2$$  <math> <mrow> <mi>c</mi> <msub> <mi>q</mi> <mn>2</mn> </msub> </mrow> </math>   which can be viewed as the spectator approximately. Future measurements on these channels will constrain the nonperturbative parameter in the wavefunctions and test the model predictions.

United States

Yan-Liang Shi

Study on the weak decay between two heavy baryons  $${\mathcal {B}}_i(\frac{1}{2}^+)\rightarrow {\mathcal {B}}_f(\frac{3}{2}^+)$$  <math> <mrow> <msub> <mi>B</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>+</mo> </msup> <mo>)</mo> </mrow> <mo>→</mo> <msub> <mi>B</mi> <mi>f</mi> </msub> <mrow> <mo>(</mo> <msup> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>+</mo> </msup> <mo>)</mo> </mrow> </mrow> </math>   in the light-front quark model

In this work, we propose to search for the exotic doubly charmed meson  $$T_{cc}^+$$  <math> <msubsup> <mi>T</mi> <mrow> <mi>cc</mi> </mrow> <mo>+</mo> </msubsup> </math>   and its analog  $$T_{cc\bar{s}}^+$$  <math> <msubsup> <mi>T</mi> <mrow> <mi>c</mi> <mi>c</mi> <mover> <mrow> <mi>s</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>+</mo> </msubsup> </math>   in  $$B_c^+$$  <math> <msubsup> <mi>B</mi> <mi>c</mi> <mo>+</mo> </msubsup> </math>   decays, which provide a good environment for the formation of the exotic state containing double charm quarks. Within the molecular scheme, the production of  $$T_{cc}^+$$  <math> <msubsup> <mi>T</mi> <mrow> <mi>cc</mi> </mrow> <mo>+</mo> </msubsup> </math>   and  $$T_{cc\bar{s}}^+$$  <math> <msubsup> <mi>T</mi> <mrow> <mi>c</mi> <mi>c</mi> <mover> <mrow> <mi>s</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>+</mo> </msubsup> </math>   through various rescattering processes with different intermediate states are investigated. For the moderate values of model parameters, the branching ratios of  $$B_c^+$$  <math> <msubsup> <mi>B</mi> <mi>c</mi> <mo>+</mo> </msubsup> </math>   decaying into  $$T_{cc}^+ \bar{D}^{0}$$  <math> <mrow> <msubsup> <mi>T</mi> <mrow> <mi>cc</mi> </mrow> <mo>+</mo> </msubsup> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mn>0</mn> </msup> </mrow> </math>  ,  $$T_{cc}^+ \bar{D}^{*0}$$  <math> <mrow> <msubsup> <mi>T</mi> <mrow> <mi>cc</mi> </mrow> <mo>+</mo> </msubsup> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> </mrow> </math>  ,  $$T_{cc\bar{s}}^+ \bar{D}^{0}$$  <math> <mrow> <msubsup> <mi>T</mi> <mrow> <mi>c</mi> <mi>c</mi> <mover> <mrow> <mi>s</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>+</mo> </msubsup> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mn>0</mn> </msup> </mrow> </math>   and  $$T_{cc\bar{s}}^+ \bar{D}^{*0}$$  <math> <mrow> <msubsup> <mi>T</mi> <mrow> <mi>c</mi> <mi>c</mi> <mover> <mrow> <mi>s</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>+</mo> </msubsup> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> </mrow> </math>   are estimated to be of the order of  $$10^{-7}$$  <math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>7</mn> </mrow> </msup> </math>  ,  $$10^{-5}$$  <math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </msup> </math>  ,  $$10^{-6}$$  <math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> </math>   and  $$10^{-4}$$  <math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </msup> </math>  , respectively, which may be tested by future experiments.

Yuan Li

Ying-Bo He

Baoyi Chen

Searching for doubly charmed tetraquark candidates  $$T_{cc}$$  <math> <msub> <mi>T</mi> <mrow> <mi>cc</mi> </mrow> </msub> </math>   and  $$T_{cc\bar{s}}$$  <math> <msub> <mi>T</mi> <mrow> <mi>c</mi> <mi>c</mi> <mover> <mrow> <mi>s</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </msub> </math>   in  $$B_c$$  <math> <msub> <mi>B</mi> <mi>c</mi> </msub> </math>   decays

We use the spectral lag catalog of 46 short GRBs aggregated by Xiao et al. (Astrophys J Lett 924:L29, 2022), to carry out an independent search for Lorentz invariance violation (LIV). For this purpose, we use a power-law model as a function of energy for the intrinsic astrophysical induced spectral lags. The expansion history of the universe needed for constraining LIV was obtained in a non-parametric method using cosmic chronometers. We use Bayesian model comparison to determine if the aforementioned spectral lags show evidence for LIV as compared to only astrophysically induced lags. We do not find any evidence for LIV, and obtain 95% CL lower limits on the corresponding energy scale to be  $$4 \times 10^{15}$$  <math> <mrow> <mn>4</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>15</mn> </msup> </mrow> </math>   GeV and  $$6.8 \times 10^{9}$$  <math> <mrow> <mn>6.8</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>9</mn> </msup> </mrow> </math>   GeV for the linear and quadratic LIV models respectively. Our results obtained by using the flat  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM model for characterizing the cosmic expansion history are consistent with those obtained using chronometers.

India

Shantanu Desai

Rajdeep Agrawal

Germany

Haveesh Singirikonda

Search for Lorentz invariance violation using Bayesian model comparison applied to Xiao et al. GRB spectral lag catalog

Two isosinglet hadron states <math><msub><mi>X</mi><mn>0</mn></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math> and <math><msub><mi>X</mi><mn>1</mn></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math> with <math><mi>J</mi><mo>=</mo><mn>0</mn></math> and 1, respectively, discovered by the LHCb collaboration in 2020, are identified as molecular bound states of <math><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math>. Recently two structures <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>s</mi><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><msup><mo>)</mo><mn>0</mn></msup></math> and <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>s</mi><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><msup><mo>)</mo><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> have been observed at the hadron spectra, and one would suspect if they also are molecular states of <math><msup><mi>D</mi><mo>*</mo></msup></math> and <math><msup><mi>K</mi><mo>*</mo></msup></math>. As long as they are of the molecular structures of <math><msup><mi>D</mi><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math>, the hadron states must be in an isovector, namely <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>s</mi><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><msup><mo>)</mo><mn>0</mn></msup></math> and <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>s</mi><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><msup><mo>)</mo><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> are <math><msub><mi>I</mi><mn>3</mn></msub><mo>=</mo><mo>−</mo><mn>1</mn></math>, 1 components of the isovector. If it is the case, then the corresponding <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>s</mi><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><msup><mo>)</mo><mo>+</mo></msup></math> of <math><mi>I</mi><mo>=</mo><mn>1</mn><mo>,</mo><msub><mi>I</mi><mn>3</mn></msub><mo>=</mo><mn>0</mn></math>, and <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>s</mi><mn>0</mn></mrow><mrow><mo>′</mo><mi>a</mi></mrow></msubsup><mo>(</mo><mn>2900</mn><msup><mo>)</mo><mo>+</mo></msup></math> of <math><mi>I</mi><mo>=</mo><mn>0</mn><mo>,</mo><msub><mi>I</mi><mn>3</mn></msub><mo>=</mo><mn>0</mn></math> so far have evaded experimental observation, but should be found by the future experiments. To testify this ansatz, in this paper we study the possible molecular structures of <math><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math> and <math><msup><mi>D</mi><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math> within the Bethe-Salpeter framework. With reasonable input parameters it is found that <math><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math> isoscalar systems with <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>0</mn><mo>+</mo></msup></math> and <math><msup><mn>1</mn><mo>+</mo></msup></math> have solutions. The result supports the ansatz of <math><msub><mi>X</mi><mn>0</mn></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math> and <math><msub><mi>X</mi><mn>1</mn></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math> being molecular states of <math><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math>. Whereas for the system of <math><msup><mi>D</mi><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math> with <math><mi>I</mi><mo>=</mo><mn>1</mn></math> the corresponding Bethe-Salpeter equation has no solution. Thus we can draw a clear conclusion that <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>s</mi><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><msup><mo>)</mo><mn>0</mn></msup></math> and <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>s</mi><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><msup><mo>)</mo><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> should not be bound states of <math><msup><mi>D</mi><mo>*</mo></msup></math> and <math><msup><mi>K</mi><mo>*</mo></msup></math>. The two structures observed by the LHCb collaboration may be caused by dynamics, such as the well-recognized triangle anomalies or other mechanisms.

Yi-Fan Shi

Possible molecular states of <math><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math> (<math><msup><mi>D</mi><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math>) and new exotic states <math><msub><mi>X</mi><mn>0</mn></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math>, <math><msub><mi>X</mi><mn>1</mn></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math>, <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>s</mi><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><msup><mo>)</mo><mn>0</mn></msup></math> and <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>s</mi><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><msup><mo>)</mo><mrow><mo>+</mo><mo>+</mo></mrow></msup></math>