We study the $$\Lambda _{b}\rightarrow \Lambda _{c}\bar{D}^{0}K^{-}$$ and $$\Lambda _{b}\rightarrow \Lambda _{c}D^{-}\bar{K}^{0}$$ decays which proceed via a Cabibbo and $$N_c$$ favored process of external emission, and we determine the $$\bar{D}^{0}K^{-}$$ and $$D^{-}\bar{K}^{0}$$ mass distributions close to the $$\bar{D} \bar{K}$$ threshold. For this, we use the tree level contribution plus the rescattering of the meson-meson components, using the extension of the local hidden gauge approach to the charm sector that produces the $$D^*_{s0}(2317)$$ resonance. We observe a large enhancement of the mass distributions close to threshold due to the presence of this resonance below threshold. Next we undertake the inverse problem of extracting the maximum information on the interaction of the $$\bar{D} \bar{K}$$ channels from these distributions, and using the resampling method we find that from these data one can obtain precise values of the scattering lengths and effective ranges, the existence of an $$I=0$$ bound state with a precision of about $$4 \;\mathrm MeV$$ in the mass, plus the $$\bar{D} \bar{K}$$ molecular probability of this state with reasonable precision. Given the fact that the $$\Lambda _{b}\rightarrow \Lambda _{c}\bar{D}^{0}K^{-}$$ decay is already measured by the LHCb collaboration, it is expected that in the next runs with more statistics of the decay, these mass distributions can be measured with precision and the method proposed here can be used to determine the nature of the $$D^*_{s0}(2317)$$ , which is still an issue of debate.

China

Hai-Peng Li

Wei-Hong Liang

Chu-Wen Xiao

Ju-Jun Xie

Spain

Eulogio Oset

Determination of the binding and $\textit{DK}$ probability of the $$D^{*}_{s0}(2317)$$ from the $$(\bar{D}\bar{K})^-$$ mass distributions in $$\Lambda _{b}\rightarrow \Lambda _{c} (\bar{D}\bar{K})^-$$ decays

We study the scattering parameters of the $$K^+\bar{K}^0$$ system through the analysis of the $$D^+\rightarrow \bar{K}^0\pi ^+\eta $$ reaction, aiming at determining the scattering length $$a$$ and effective range $$r_0$$ of the $$K^+\bar{K}^0$$ interaction. These parameters are extracted by analyzing and fitting the mass distributions of the pairs in the final $$\bar{K}^0\pi ^+\eta $$ state. To ensure the reliability of the results, we apply resampling techniques to evaluate statistical uncertainties and improve the precision of the scattering parameters. The obtained results are compared with previous theoretical predictions and experimental data, providing new insights into the $$K^+\bar{K}^0$$ interaction at low energies.

Jing Song

Determination of the $$K^+\bar{K}^0$$ scattering length and effective range from the $$D^+\rightarrow \bar{K}^0\pi ^+\eta $$ reaction

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 report on the reactions $$\psi (3770)\rightarrow \bar{\Omega }^+ \bar{K} \Xi $$ and $$\psi (3770)\rightarrow \bar{\Omega }^+ \bar{K}\Xi ^*(1530) \;(\Xi ^*(1530)\rightarrow \pi \Xi $$ ), and calculate the mass distributions $$\frac{\textrm{d}\Gamma }{\textrm{d}M_\text {inv}(\bar{K}\Xi )}$$ and $$\frac{\textrm{d}\Gamma }{\textrm{d}M_\text {inv}(\bar{K}\Xi ^*)}$$ , respectively. We obtain clear peaks corresponding to the $$\Omega (2012)$$ . From the decay of $$\psi (3770)\rightarrow \bar{\Omega }^+ \bar{K}\Xi ^*$$ , we also get a second, broader, peak around $$2035\,\mathrm MeV$$ , which comes from the $$\Omega (2012)$$ decay to $$\bar{K}\Xi ^*$$ . This second peak is closely tied to the molecular picture of the $$\Omega (2012)$$ with the $$\bar{K}\Xi ^*(1530)$$ and $$\eta \Omega $$ components. Its observation would provide a boost to the molecular picture of the $$\Omega (2012)$$ .

Brazil

Jorgivan Dias

Testing the molecular nature of the $$\Omega (2012)$$ with the $$\psi (3770) \rightarrow \bar{\Omega } \bar{K} \Xi $$ and $$\psi (3770) \rightarrow \bar{\Omega } \bar{K} \Xi ^*(1530) (\bar{\Omega } \bar{K} \pi \Xi )$$ reactions

We calculate the correlation functions for the <math><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup><mi>p</mi><mo>,</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>Σ</mi><mn>0</mn></msup><mo>,</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>Σ</mi><mo>+</mo></msup><mo>,</mo><msup><mi>π</mi><mo>+</mo></msup><mi>Λ</mi></math>, and <math><mi>η</mi><msup><mi>Σ</mi><mo>+</mo></msup></math> states, which in the chiral unitary approach predict an excited <math><msup><mi>Σ</mi><mo>*</mo></msup><mo>(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>)</mo></math> state at the <math><mover><mi>K</mi><mo>¯</mo></mover><mi>N</mi></math> threshold, recently observed by the Belle Collaboration. Once this is done, we tackle the inverse problem of seeing how much information one can obtain from these correlation functions. With the resampling method, one can determine the scattering parameters of all the channels with relative precision, by means of the analysis in a general framework, and find a clear cusplike structure corresponding to the <math><msup><mi>Σ</mi><mo>*</mo></msup><mo>(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>)</mo></math> in the different amplitudes at the <math><mover><mi>K</mi><mo>¯</mo></mover><mi>N</mi></math> threshold.

Jia-Jun Wu

En Wang

How to unravel the nature of the <math><mrow><msup><mrow><mi>Σ</mi></mrow><mrow><mo>*</mo></mrow></msup><mo>(</mo><mn>1430</mn><mo>)</mo><mo>(</mo><mn>1</mn><mo>/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></mrow></math> state from correlation functions

We start from a recently favored picture in which the <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2940</mn><mo>)</mo></math> and <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2910</mn><mo>)</mo></math> correspond mostly to <math><mi>N</mi><msup><mi>D</mi><mo>*</mo></msup></math> bound states with <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> respectively, and then add a <math><mi>D</mi></math> as a third particle, looking for the possible binding of the <math><mi>D</mi><mi>N</mi><msup><mi>D</mi><mo>*</mo></msup></math> three-body system within the framework of the fixed center approximation. We find that the system is bound with respect to the corresponding <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2940</mn><mo>)</mo><mi>D</mi></math>, <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2910</mn><mo>)</mo><mi>D</mi></math> thresholds with a binding of about 60 MeV and a width of about 90 MeV. Alternatively we assume a cluster of <math><mi>N</mi><mi>D</mi></math> and a <math><msup><mi>D</mi><mo>*</mo></msup></math> meson interacting with the cluster, and we find similar results. The observation of these states of <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup><mo>,</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></math> would provide new and valuable information concerning the <math><mi>D</mi><mi>N</mi></math> and <math><msup><mi>D</mi><mo>*</mo></msup><mi>N</mi></math> interaction, an issue of current debate.

Victor Montesinos

Juan Nieves

Miguel Albaladejo

Study of possible <math><mrow><mi>D</mi><mi>N</mi><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> bound states

We propose the reaction  $$\psi (3686) \rightarrow \bar{\Xi }^+ \bar{K}^0 \Sigma ^{*-}$$  <math> <mrow> <mi>ψ</mi> <mrow> <mo>(</mo> <mn>3686</mn> <mo>)</mo> </mrow> <mo>→</mo> <msup> <mover> <mrow> <mi>Ξ</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mo>+</mo> </msup> <msup> <mrow> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mn>0</mn> </msup> <mmultiscripts> <mi>Σ</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mo>-</mo> </mrow> </mmultiscripts> </mrow> </math>  , with the  $$\Sigma ^{*-}$$  <math> <mmultiscripts> <mi>Σ</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mo>-</mo> </mrow> </mmultiscripts> </math>   decaying to  $$\pi ^- \Lambda $$  <math> <mrow> <msup> <mi>π</mi> <mo>-</mo> </msup> <mi>Λ</mi> </mrow> </math>   in order to show evidence for the existence of two  $$\Xi (1820)$$  <math> <mrow> <mi>Ξ</mi> <mo>(</mo> <mn>1820</mn> <mo>)</mo> </mrow> </math>   states, one around 1824 MeV and narrow, and another one around 1875 MeV and wide. The phase space for  $$\bar{K}^0 \Sigma ^{*-}$$  <math> <mrow> <msup> <mrow> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mn>0</mn> </msup> <mmultiscripts> <mi>Σ</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mo>-</mo> </mrow> </mmultiscripts> </mrow> </math>   production reduces the effect of the lower mass resonance, magnifying the effect of the higher mass resonance that shows clearly over the phase space. The estimated rate of the production is bigger than the one of the  $$\psi (3686) \rightarrow \bar{\Xi }^+ K^- \Lambda $$  <math> <mrow> <mi>ψ</mi> <mrow> <mo>(</mo> <mn>3686</mn> <mo>)</mo> </mrow> <mo>→</mo> <msup> <mover> <mrow> <mi>Ξ</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mo>+</mo> </msup> <msup> <mi>K</mi> <mo>-</mo> </msup> <mi>Λ</mi> </mrow> </math>   reaction, where a clear peak for  $$\Xi (1820)$$  <math> <mrow> <mi>Ξ</mi> <mo>(</mo> <mn>1820</mn> <mo>)</mo> </mrow> </math>   was observed by the BESIII collaboration, what makes the Beijing facility ideal to carry out the reaction proposed.

Man-Yu Duan

E. Oset

On the search for the two poles of the  $$\Xi (1820)$$  <math> <mrow> <mi>Ξ</mi> <mo>(</mo> <mn>1820</mn> <mo>)</mo> </mrow> </math>   in the  $$\psi (3686) \rightarrow \bar{\Xi }^+ \bar{K}^0 \Sigma ^{*-}(\pi ^- \Lambda )$$  <math> <mrow> <mi>ψ</mi> <mrow> <mo>(</mo> <mn>3686</mn> <mo>)</mo> </mrow> <mo>→</mo> <msup> <mover> <mrow> <mi>Ξ</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mo>+</mo> </msup> <msup> <mrow> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mn>0</mn> </msup> <mmultiscripts> <mi>Σ</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mo>-</mo> </mrow> </mmultiscripts> <mrow> <mo>(</mo> <msup> <mi>π</mi> <mo>-</mo> </msup> <mi>Λ</mi> <mo>)</mo> </mrow> </mrow> </math>   decay

We have studied the <math><mrow><msub><mrow><mi>Ω</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>,</mo><mi>η</mi><mo>)</mo><mi>π</mi><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> and <math><mrow><msub><mrow><mi>Ω</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>,</mo><mi>η</mi><mo>)</mo><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover><msup><mrow><mi>Σ</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> decays, where the final <math><mi>π</mi><msup><mi>Ξ</mi><mo>*</mo></msup></math> or <math><mover><mi>K</mi><mo>¯</mo></mover><msup><mi>Σ</mi><mo>*</mo></msup></math> comes from the decay of two resonances around the nominal <math><mi>Ξ</mi><mo>(</mo><mn>1820</mn><mo>)</mo></math>, which are generated from the interaction of coupled channels made of a pseudoscalar and a baryon of the decuplet. The <math><mi>π</mi><msup><mi>Ξ</mi><mo>*</mo></msup></math> mass distributions obtained in the six different reactions studied are quite different, and we single out four of them, which are free of a tree level contribution, showing more clearly the effect of the resonances. The lower mass resonance is clearly seen as a sharp peak, but the higher mass resonance manifests itself through an interference with the lower one that leads to a dip in the mass distribution around 1850 MeV. Such a feature is similar to the dip observed in the <math><mi>S</mi></math>-wave <math><mi>π</mi><mi>π</mi></math> cross section around the 980 MeV coming from the interference of the <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>500</mn><mo>)</mo></math> and <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> resonances. Its observation in coming upgrades of present facilities will shed light on the existence of these two resonances and their nature. On the other hand, when the <math><mrow><msub><mrow><mi>Ω</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>,</mo><mi>η</mi><mo>)</mo><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover><msup><mrow><mi>Σ</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> reactions are studied, both peaks are observed.

Raquel Molina

<math><mrow><msub><mrow><mi>Ω</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>,</mo><mi>η</mi><mo>)</mo><mi>π</mi><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math>, <math><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>,</mo><mi>η</mi><mo>)</mo><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover><msup><mrow><mi>Σ</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> reactions and the two <math><mi>Ξ</mi><mo>(</mo><mn>1820</mn><mo>)</mo></math> states

We recall that the chiral unitary approach for the interaction of pseudoscalar mesons with the baryons of the decuplet predicts two states for the <math><mi>Ξ</mi><mo>(</mo><mn>1820</mn><mo>)</mo></math> resonance, one with a narrow width and the other one with a large width. We contrast this fact with the recent BESIII measurement of the <math><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>Λ</mi></math> mass distribution in the <math><mi>ψ</mi><mo>(</mo><mn>3686</mn><mo>)</mo></math> decay to <math><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>Λ</mi><msup><mrow><mover><mrow><mi>Ξ</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>+</mo></mrow></msup></math>, which demands a width much larger than the average of the PDG, and show how the consideration of the two <math><mi>Ξ</mi><mo>(</mo><mn>1820</mn><mo>)</mo></math> states provides a natural explanation to the experimental data.

R. Molina

Zhi-Feng Sun

Two states for the Ξ(1820) resonance

In this work we compare the predictions for the scattering length and effective range of the channels  $$K^0 \Sigma ^+, K^+ \Sigma ^0, K^+ \Lambda $$  <math> <mrow> <msup> <mi>K</mi> <mn>0</mn> </msup> <msup> <mi>Σ</mi> <mo>+</mo> </msup> <mo>,</mo> <msup> <mi>K</mi> <mo>+</mo> </msup> <msup> <mi>Σ</mi> <mn>0</mn> </msup> <mo>,</mo> <msup> <mi>K</mi> <mo>+</mo> </msup> <mi>Λ</mi> </mrow> </math>   and  $$\eta p$$  <math> <mrow> <mi>η</mi> <mi>p</mi> </mrow> </math>  , assuming the  $$N^*(1535)$$  <math> <mrow> <msup> <mi>N</mi> <mo>∗</mo> </msup> <mrow> <mo>(</mo> <mn>1535</mn> <mo>)</mo> </mrow> </mrow> </math>   state as a molecular state of these channels, or an original genuine state, made for instance from three quarks. Looking at very different scenarios, what we conclude is that the predictions of these two pictures are drastically different, to the point that we advise the measurement of these magnitudes, accessible for instance by measuring correlation functions, in order to gain much valuable information concerning the nature of this state.

Contrasting observables related to the  $$N^*(1535)$$  <math> <mrow> <msup> <mi>N</mi> <mo>∗</mo> </msup> <mrow> <mo>(</mo> <mn>1535</mn> <mo>)</mo> </mrow> </mrow> </math>   from the molecular or a genuine structure