General one-loop formulas for loop-induced processes $gg/\gamma \gamma \rightarrow \phi_i\phi_j$ with $\phi_i\phi_j = hh,~hH,~HH$ are presented in this paper. The analytic expressions evaluated in this study are valid for a class of Higgs Extensions of the Standard Model, $\textit{e.g.,}$ Inert Doublet Higgs, Two Higgs Doublet, Zee-Babu, and Triplet Higgs Models$\textit{.}$ Analytic expressions for one-loop form factors are expressesd in terms of the basic scalar one-loop two-, three-, and four-point functions following the output format of the packages $ {\tt LoopTools}$ and $ {\tt Collier}$ . Hence, physical results can be evaluated numerically using one of these packages. The analytic results are tested using several checks such as the ultraviolet finiteness and infrared finiteness of the one-loop amplitudes. Furthermore, the amplitudes obey the ward identity due to massless gauge bosons in the initial states. This identity is also verified numerically. Regarding applications, we present the phenomenological results for the investigated processes in the Zee-Babu model as a typical example. In particular, production cross-sections for the processes $\gamma \gamma\rightarrow hh$ are scanned over the parameter space of the Zee-Babu Model.

Vietnam

Khiem Hong Phan

Dzung Tri Tran

Thanh Huy Nguyen

One-loop analytical expressions for $\textit{gg}$/$\textit{γγ}$ → ϕ$_{i}$ϕ$_{j}$ in Higgs extensions of the standard model and their applications * This research is supported by Vietnam National Foundation for Science and Technology Development (103.01-2023.16). Khiem Hong Phan and Dzung Tri Tran express their gratitude to all the valuable support from Duy Tan University, for the 30th anniversary of establishment (Nov. 11, 1994 - Nov. 11, 2024) towards ''Integral, Sustainable and Stable Development''

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.

China

Fang Lu

Hong-Wei Ke

Xiao-Hai Liu

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

Recently, the LHCb Collaboration has observed the decays <math><mrow><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup></mrow></math> and <math><mrow><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup></mrow></math>. They measured the relative branching fractions times the ratio of beauty-baryon production cross sections <math><mrow><mi>R</mi><mo>(</mo><mfrac><mrow><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow><mrow><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub></mrow></mfrac><mo>)</mo><mo>≡</mo><mfrac><mrow><mi>σ</mi><mo>(</mo><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>)</mo></mrow><mrow><mi>σ</mi><mo>(</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>)</mo></mrow></mfrac><mo>×</mo><mfrac><mrow><mi>B</mi><mo>(</mo><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>)</mo></mrow><mrow><mi>B</mi><mo>(</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>)</mo></mrow></mfrac></mrow></math> and <math><mrow><mi>R</mi><mo>(</mo><mfrac><mrow><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mo>−</mo></mrow></msubsup></mrow><mrow><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub></mrow></mfrac><mo>)</mo><mo>≡</mo><mfrac><mrow><mi>σ</mi><mo>(</mo><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>)</mo></mrow><mrow><mi>σ</mi><mo>(</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>)</mo></mrow></mfrac><mo>×</mo><mfrac><mrow><mi>B</mi><mo>(</mo><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>)</mo></mrow><mrow><mi>B</mi><mo>(</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>)</mo></mrow></mfrac></mrow></math>. Once the ratio <math><mrow><mfrac><mrow><mi>σ</mi><mo>(</mo><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>)</mo></mrow><mrow><mi>σ</mi><mo>(</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>)</mo></mrow></mfrac></mrow></math> or <math><mfrac><mrow><mi>σ</mi><mo>(</mo><msubsup><mi>Ξ</mi><mi>b</mi><mo>−</mo></msubsup><mo>)</mo></mrow><mrow><mi>σ</mi><mo>(</mo><msubsup><mi>Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo>)</mo></mrow></mfrac></math> is known, one can determine the relative branching fractions which can be used to exam the mixing of <math><msub><mi>Ξ</mi><mi>c</mi></msub></math> and <math><msubsup><mi>Ξ</mi><mi>c</mi><mo>′</mo></msubsup></math>. In previous literature, <math><msub><mi>Ξ</mi><mi>c</mi></msub></math> and <math><msubsup><mi>Ξ</mi><mi>c</mi><mo>′</mo></msubsup></math> were assumed to belong to <math><mrow><msub><mrow><mi>SU</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mi>F</mi></msub></mrow></math> antitriple and sextet, respectively. However, recent experimental measurements, such as the ratio <math><mrow><mi>Γ</mi><mo>(</mo><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>→</mo><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo><mo>/</mo><mi>Γ</mi><mo>(</mo><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>→</mo><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo></mrow></msubsup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></mrow></math>, indicate the spin-flavor structures of <math><msub><mi>Ξ</mi><mi>c</mi></msub></math> and <math><msubsup><mi>Ξ</mi><mi>c</mi><mo>′</mo></msubsup></math> are a mixture of <math><msubsup><mi>Ξ</mi><mi>c</mi><mover><mn>3</mn><mo>¯</mo></mover></msubsup></math> and <math><msubsup><mi>Ξ</mi><mi>c</mi><mn>6</mn></msubsup></math>. The exact value of mixing angle <math><mi>θ</mi></math> is still under debate. In theoretical models, the mixing angle was fitted to be about <math><mrow><mn>16.2</mn><mn>7</mn><mi>°</mi><mo>±</mo><mn>2.3</mn><mn>0</mn><mi>°</mi></mrow></math> or <math><mrow><mn>85.5</mn><mn>4</mn><mi>°</mi><mo>±</mo><mn>2.3</mn><mn>0</mn><mi>°</mi></mrow></math> based on decay channels <math><msub><mi>Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>→</mo><msubsup><mi>Ξ</mi><mi>c</mi><mrow><msup><mo>(</mo><mo>′</mo></msup><mo>)</mo></mrow></msubsup></math>. While in lattice calculation, a small angle (<math><mrow><mn>1.2</mn><mi>°</mi><mo>±</mo><mn>0.1</mn><mi>°</mi></mrow></math>) is preferred. To address such discrepancy and test the mixing of <math><msub><mi>Ξ</mi><mi>c</mi></msub></math> and <math><msubsup><mi>Ξ</mi><mi>c</mi><mo>′</mo></msubsup></math>, here we propose the analysis of semileptonic and nonleptonic decays of <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>→</mo><msub><mi>Ξ</mi><mi>c</mi></msub></math> and <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Ξ</mi><mi>c</mi><mo>′</mo></msubsup></math>. We calculate the decay rate of <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>→</mo><msub><mi>Ξ</mi><mi>c</mi></msub></math> and <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Ξ</mi><mi>c</mi><mo>′</mo></msubsup></math> based on the light-front quark model and study the effect of the mixing angle on the ratios of weak decays <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>→</mo><msub><mi>Ξ</mi><mi>c</mi></msub></math> and <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Ξ</mi><mi>c</mi><mo>′</mo></msubsup></math>. In particular, we find the transition <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Ξ</mi><mi>c</mi><mo>′</mo></msubsup></math> can be an ideal channel to verify the mixing and extract the mixing angle because in theory, the decay rate would be extremely tiny without mixing. Our calculation suggests a measurement of <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Ξ</mi><mi>c</mi><mo>′</mo></msubsup></math> can be feasible in the near future, which will help to test flavor mixing angle <math><mi>θ</mi></math> and elucidate the mechanism of decay of heavy baryons.

Gang-Yang Fang

United States

Yan-Liang Shi

Study on the mixing of <math><msub><mi>Ξ</mi><mi>c</mi></msub></math> and <math><msubsup><mi>Ξ</mi><mi>c</mi><mo>′</mo></msubsup></math> by the transition <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Ξ</mi><mi>c</mi><mrow><msup><mo>(</mo><mo>′</mo></msup><mo>)</mo></mrow></msubsup></math>

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>

The identification of jets originating from quarks and gluons, often referred to as quark/gluon tagging, plays an important role in various analyses performed at the Large Hadron Collider, as Standard Model measurements and searches for new particles decaying to quarks often rely on suppressing a large gluon-induced background. This paper describes the measurement of the efficiencies of quark/gluon taggers developed within the ATLAS Collaboration, using $\sqrt{s} = 13$ TeV proton–proton collision data with an integrated luminosity of 140 fb $^{-1}$ collected by the ATLAS experiment. Two taggers with high performances in rejecting jets from gluon over jets from quarks are studied: one tagger is based on requirements on the number of inner-detector tracks associated with the jet, and the other combines several jet substructure observables using a boosted decision tree. A method is established to determine the quark/gluon fraction in data, by using quark/gluon-enriched subsamples defined by the jet pseudorapidity. Differences in tagging efficiency between data and simulation are provided for jets with transverse momentum between 500 GeV and 2 TeV and for multiple tagger working points.

France

G. Aad

B. Abbott

Germany

K. Abeling

N.J. Abicht

S.H. Abidi

Morocco

A. Aboulhorma

Israel

H. Abramowicz

H. Abreu

Y. Abulaiti

Italy

United Kingdom

B.S. Acharya

C. Adam Bourdarios

Poland

L. Adamczyk

S.V. Addepalli

M.J. Addison

J. Adelman

A. Adiguzel

T. Adye

A.A. Affolder

Switzerland

Y. Afik

Spain

M.N. Agaras

J. Agarwala

A. Aggarwal

Romania

C. Agheorghiesei

A. Ahmad

Azerbaijan

F. Ahmadov

Canada

W.S. Ahmed

S. Ahuja

X. Ai

G. Aielli

A. Aikot

M. Ait Tamlihat

B. Aitbenchikh

I. Aizenberg

M. Akbiyik

Sweden

T.P.A. Åkesson

A.V. Akimov

Japan

D. Akiyama

N.N. Akolkar

K. Al Khoury

G.L. Alberghi

J. Albert

P. Albicocco

G.L. Albouy

S. Alderweireldt

M. Aleksa

I.N. Aleksandrov

C. Alexa

Greece

T. Alexopoulos

F. Alfonsi

M. Algren

M. Alhroob

Czechia

B. Ali

H.M.J. Ali

S. Ali

S.W. Alibocus

M. Aliev

G. Alimonti

W. Alkakhi

C. Allaire

B.M.M. Allbrooke

J.F. Allen

Chile

C.A. Allendes Flores

P.P. Allport

A. Aloisio

Argentina

F. Alonso

C. Alpigiani

M. Alvarez Estevez

A. Alvarez Fernandez

M. Alves Cardoso

M.G. Alviggi

M. Aly

Brazil

Y. Amaral Coutinho

A. Ambler

C. Amelung

M. Amerl

C.G. Ames

D. Amidei

Portugal

S.P. Amor Dos Santos

K.R. Amos

Norway

V. Ananiev

C. Anastopoulos

T. Andeen

J.K. Anders

S.Y. Andrean

A. Andreazza

S. Angelidakis

A. Angerami

A.V. Anisenkov

A. Annovi

C. Antel

M.T. Anthony

E. Antipov

M. Antonelli

F. Anulli

M. Aoki

T. Aoki

J.A. Aparisi Pozo

M.A. Aparo

L. Aperio Bella

C. Appelt

Performance and calibration of quark/gluon-jet taggers using 140 fb$^{−1}$ of $\textit{pp}$ collisions at ${{\sqrt{\boldsymbol s}\bf = 13}}$ TeV with the ATLAS detector * We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; ANID, Chile; CAS, MOST and NSFC, China; Minciencias, Colombia; MEYS CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS and CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF and MPG, Germany; GSRI, Greece; RGC and Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MEiN, Poland; FCT, Portugal; MNE/IFA, Romania; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DSI/NRF, South Africa; MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taipei; TENMAK, Türkiye; STFC, United Kingdom; DOE and NSF, United States of America. In addition, individual groups and members have received support from BCKDF, CANARIE, CRC and DRAC, Canada; PRIMUS 21/SCI/017 and UNCE SCI/013, Czech Republic; COST, ERC, ERDF, Horizon 2020, ICSC-Next Generation EU and Marie Skłodowska-Curie Actions, European Union; Investissements d'Avenir Labex, Investissements d'Avenir Idex and ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and MINERVA, Israel; Norwegian Financial Mechanism 2014-2021, Norway; NCN and NAWA, Poland; La Caixa Banking Foundation, CERCA Programme Generalitat de Catalunya and PROMETEO and GenT Programmes Generalitat Valenciana, Spain; Göran Gustafssons Stiftelse, Sweden; The Royal Society and Leverhulme Trust, United Kingdom.

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.

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

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>

We investigate the process  $$B\rightarrow \bar{D}D_s \pi $$  <math> <mrow> <mi>B</mi> <mo>→</mo> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <msub> <mi>D</mi> <mi>s</mi> </msub> <mi>π</mi> </mrow> </math>   via several rescattering processes. It is shown that the triangle singularity (TS) peak around the  $$D^*K^*$$  <math> <mrow> <msup> <mi>D</mi> <mo>∗</mo> </msup> <msup> <mi>K</mi> <mo>∗</mo> </msup> </mrow> </math>   threshold generated from the  $$\chi _{c1}K^* D^*$$  <math> <mrow> <msub> <mi>χ</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> <msup> <mi>K</mi> <mo>∗</mo> </msup> <msup> <mi>D</mi> <mo>∗</mo> </msup> </mrow> </math>   loop is relatively narrow, which may simulate the resonance-like structure  $$T_{c\bar{s}}(2900)$$  <math> <mrow> <msub> <mi>T</mi> <mrow> <mi>c</mi> <mover> <mrow> <mi>s</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math>   recently observed by LHCb in the  $$D_s\pi $$  <math> <mrow> <msub> <mi>D</mi> <mi>s</mi> </msub> <mi>π</mi> </mrow> </math>   spectrum. However, the TS peak around the  $$D_s^*\rho $$  <math> <mrow> <msubsup> <mi>D</mi> <mi>s</mi> <mo>∗</mo> </msubsup> <mi>ρ</mi> </mrow> </math>   threshold generated from the  $$D^{**} D_s^* \rho $$  <math> <mrow> <msup> <mi>D</mi> <mrow> <mrow></mrow> <mo>∗</mo> <mrow></mrow> <mo>∗</mo> </mrow> </msup> <msubsup> <mi>D</mi> <mi>s</mi> <mo>∗</mo> </msubsup> <mi>ρ</mi> </mrow> </math>   loop is smoothed by the broad width of  $$\rho $$  <math> <mi>ρ</mi> </math>  , which itself can hardly describe the  $$T_{c\bar{s}}(2900)$$  <math> <mrow> <msub> <mi>T</mi> <mrow> <mi>c</mi> <mover> <mrow> <mi>s</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math>   structure. A non-resonance TS signal around the DK threshold generated from the  $$\chi _{c0}K D $$  <math> <mrow> <msub> <mi>χ</mi> <mrow> <mi>c</mi> <mn>0</mn> </mrow> </msub> <mi>K</mi> <mi>D</mi> </mrow> </math>   loop is also predicted.

Ying-Hui Ge

Possibility of  $$T_{c\bar{s}}(2900)$$  <math> <mrow> <msub> <mi>T</mi> <mrow> <mi>c</mi> <mover> <mrow> <mi>s</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math>   as the resonance-like structure induced by threshold effects

Recently the LHCb Collaboration reported a new exotic state <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> which is conjectured to be a molecular state of <math><msup><mi>D</mi><mn>0</mn></msup><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup></math> (or <math><msup><mi>D</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mi>D</mi><mo>+</mo></msup></math>) theoretically. Belle Collaboration also searched for tetraquark state <math><msub><mi>X</mi><mrow><mi>c</mi><mi>c</mi><mi>s</mi><mi>s</mi></mrow></msub></math> in <math><msub><mi>D</mi><mi>s</mi></msub><msub><mi>D</mi><mi>s</mi></msub></math> (<math><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup></math>) final states but no significant signals were observed, which did not rule out the existence of <math><msub><mi>X</mi><mrow><mi>c</mi><mi>c</mi><mi>s</mi><mi>s</mi></mrow></msub></math> as a molecular state of <math><msub><mi>D</mi><mi>s</mi></msub><msub><mi>D</mi><mi>s</mi></msub></math> (<math><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo></mrow></msubsup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo></mrow></msubsup></mrow></math>). Inspired by these experimental results on double charmed exotic state, in this paper we study whether the molecular bound states of <math><msubsup><mi>D</mi><mi>s</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup><msubsup><mi>D</mi><mi>s</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup></math> and <math><msubsup><mi>B</mi><mi>s</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup><msubsup><mi>B</mi><mi>s</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup></math> can exist with the Bethe-Salpeter (BS) equation approach. We employ heavy meson chiral perturbation theory and one-boson-exchange approximation to calculate the interaction kernels in the BS equations. Our numerical results suggest that two <math><msubsup><mi>B</mi><mi>s</mi><mo>*</mo></msubsup></math> mesons perhaps form a <math><msup><mn>0</mn><mo>+</mo></msup></math> molecular state. Future experimental search for <math><msub><mi>X</mi><mrow><mi>c</mi><mi>c</mi><mi>s</mi><mi>s</mi></mrow></msub></math> and <math><msub><mi>X</mi><mrow><mi>b</mi><mi>b</mi><mi>s</mi><mi>s</mi></mrow></msub></math> states in other decay channels may shed light on the structure of double charmed exotic state.

Study of possible molecular states of <math><msubsup><mi>D</mi><mi>s</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup><msubsup><mi>D</mi><mi>s</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup></math> and <math><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup><msubsup><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup></mrow></math>