We study the transverse momentum ( $p_T$ ) differential anisotropic flow and flow fluctuation in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ =5.02 TeV at the LHC. A (3+1)-dimensional CLVisc hydrodynamics framework with fluctuating TRENTO (or AMPT) initial conditions is utilized to simulate the space-time evolution of the quark-gluon plasma (QGP) medium. The effects of shear viscosity and the sub-nucleon structure on anisotropic flow and flow fluctuation are analyzed. Our result shows that shear viscosity tends to suppress both flow coefficients ( ${v_2\{2}\}$ , ${v_2\{4\}}$ , and ${\langle v_2\rangle}$ ) and flow fluctuation ( ${\sigma_{v_2}}$ ) owing to its smearing effect on local density fluctuation. The flow coefficients appear to be insensitive to the sub-nucleon structure, whereas the flow fluctuation ${\sigma_{v_2}}$ tends to be suppressed by the sub-nucleon structure in central collisions but enhanced in peripheral collisions. After taking into account the sub-nucleon structure effect, our numerical result can qualitatively describe the relative flow fluctuations ( ${v_2\{4\}/v_2\{2\}}$ , $F({v_2})$ ) measured by the ALICE Collaboration at the LHC. We further investigate the effects of shear viscosity, sub-nucleon structure, and initial condition model on the flow angle and flow magnitude decorrelations ( ${A_2^f}$ , ${M_2^f}$ ) using the four-particle correlation method. We find that the flow decorrelation effect is typically stronger in central collisions than in peripheral collisions. The flow angle decorrelation is found to be insensitive to the shear viscosity and sub-nucleon structure, whereas the flow magnitude decorrelation shows quite different behaviors when using the TRENTO and AMPT initial condition models. Our study sheds light on the anisotropic flow, transport properties, and initial structure of the QGP created in high-energy nuclear collisions.

China

Germany

Jie Zhu

Canada

Xiang-Yu Wu

Guang-You Qin

Anisotropic flow, flow fluctuation, and flow decorrelation in relativistic heavy-ion collisions: the roles of sub-nucleon structure and shear viscosity * Supported in part by the Natural Science Foundation of China (12225503, 11890710, 11890711, 11935007). Zhu Jie is supported in part by the China Scholarship Council (202306770009). Wu Xiang-Yu is supported in part by the National Science Foundation within the framework of the JETSCAPE collaboration (OAC-2004571) and in part by the Natural Sciences and Engineering Research Council of Canada. Some of the calculations were performed in the Nuclear Science Computing Center at Central China Normal University (NSC$^{3}$), Wuhan, Hubei, China.

The measurements in $$b\rightarrow s$$ penguin-dominated decays are widely recognized as a powerful test for searching for New Physics by studying the deviation from theoretical estimations within the Standard Model. We examine the final-state rescattering effects on the decay $$B_s\rightarrow K^{*0}\bar{K}^{*0}$$ and provide estimations of the branching ratio and longitudinal polarization of $$B_s\rightarrow K^{*0}\bar{K}^{*0}$$ , which is consistent with experimental observations. Our conclusion is that both short- and long-distance interactions contribute significantly in this decay. The small longitudinal polarization in $$B\rightarrow VV$$ modes may not be a signal for New Physics.

Yao Yu

Hai-Bing Fu

Han Zhang

Bai-Cian Ke

A phenomenological estimate of rescattering effects in $$B_s\rightarrow K^{*0}\bar{K}^{*0}$$

Our main objective is to derive the decay rate for the semileptonic decays <math><mi>D</mi><mo>→</mo><mi>V</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub><mo>(</mo><mo>ℓ</mo><mo>=</mo><mi>e</mi><mo>,</mo><mi>μ</mi><mo>)</mo></math>, where <math><mi>V</mi></math> represents a vector particle. In these decays, the vector particle <math><mi>V</mi></math> decays into three pseudoscalar particles. To accomplish this, we evaluate the phase-space factor for the five-body decay with a set of eight independent variables which uniquely define a point in the phase space. We further conduct a detailed investigation of the <math><mi>D</mi><mo>→</mo><mi>ω</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math>, where <math><mi>ω</mi></math> subsequently decays into <math><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math>, within the Standard Model and in a general effective field theory description of the weak interactions at low energies. The outcomes of this study have potential applications in the measurement of <math><mi>D</mi><mo>→</mo><mi>ω</mi></math> form factors. These measurements can be performed using data obtained from BESIII.

Yechun Yu

Zhuang Xiong

Jia-Wei Zhang

Xue-Wen Chen

Five-body <math><mi>D</mi><mo>→</mo><mi>V</mi></math> semileptonic decays

We study the <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>3985</mn><mo>)</mo></math> and <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4000</mn><mo>)</mo></math> exotic states in the decays of <math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub></math> baryons through a molecular scenario. In the final state interaction, the <math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><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><mo>⁎</mo><mo>)</mo><mo>−</mo></mrow></msubsup></math> decays are followed by the <math><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><mo>⁎</mo><mo>)</mo><mo>−</mo></mrow></msubsup></math> to <math><msubsup><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mi>p</mi></math> rescatterings via exchange of a <math><msup><mrow><mi>D</mi></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo></mrow></msup></math> meson. We predict a branching fraction of <math><mo>(</mo><msubsup><mrow><mn>3.1</mn></mrow><mrow><mo>−</mo><mn>2.6</mn></mrow><mrow><mo>+</mo><mn>1.4</mn></mrow></msubsup><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></math> for <math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>→</mo><msubsup><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mi>p</mi></math>, which can be measured in the <math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mrow><mi>K</mi></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo><mo>−</mo></mrow></msup><mi>p</mi></math> decay. This study proposes a new approach to test the molecular model, and guides future experimental searches for the <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>3985</mn><mo>)</mo></math> and <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4000</mn><mo>)</mo></math>.

Dong-Ze He

Rui-Yu Zhou

Investigating (3985) and (4000) Exotic States in Decays

An analysis of the <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>η</mi><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup><mi>γ</mi></math> decay by the BESIII collaboration claims the observation of an exotic state <math><msub><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1855</mn><mo>)</mo></math> with <math><msup><mrow><mi>I</mi></mrow><mrow><mi>G</mi></mrow></msup><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mn>1</mn></mrow><mrow><mo>−</mo><mo>+</mo></mrow></msup></math>. To establish its C-parity partner <math><msubsup><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mn>1855</mn><mo>)</mo></math> in the picture of the <math><mi>K</mi><msub><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1400</mn><mo>)</mo></math> molecular state, we propose that <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msubsup><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mn>1855</mn><mo>)</mo><msup><mrow><mi>η</mi></mrow><mrow><mo>(</mo><mo>′</mo><mo>)</mo></mrow></msup></math> receives the main contributions from the final state interaction of <math><mi>K</mi><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math>(<math><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo><mo>−</mo></mrow></msup></math>, <math><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo><mo>+</mo></mrow></msup></math>, <math><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo><mn>0</mn></mrow></msup></math>, and <math><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo><mn>0</mn></mrow></msup></math>). Specifically, K and <math><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math> in <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>K</mi><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math> decays transform as <math><msubsup><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mn>1855</mn><mo>)</mo><msup><mrow><mi>η</mi></mrow><mrow><mo>(</mo><mo>′</mo><mo>)</mo></mrow></msup></math>, by exchanging a <math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1400</mn><mo>)</mo></math>. We predict <math><mi>B</mi><mo>(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msubsup><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mn>1855</mn><mo>)</mo><mi>η</mi><mo>)</mo><mo>=</mo><mo>(</mo><msubsup><mrow><mn>6.3</mn></mrow><mrow><mo>−</mo><mn>3.5</mn></mrow><mrow><mo>+</mo><mn>12.6</mn></mrow></msubsup><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>, and <math><mi>B</mi><mo>(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msubsup><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mn>1855</mn><mo>)</mo><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo><mo>=</mo><mo>(</mo><msubsup><mrow><mn>6.5</mn></mrow><mrow><mo>−</mo><mn>4.6</mn></mrow><mrow><mo>+</mo><mn>6.6</mn></mrow></msubsup><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>, which can be studied in the <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msup><mrow><mi>η</mi></mrow><mrow><mo>(</mo><mo>′</mo><mo>)</mo></mrow></msup></math> decays.

Yi Teng

Qing-Shan Liu

Investigating the Exotic State in the Decays

We derive a parameterization formula for the partial wave analyses of charmed meson semi-leptonic decays while considering the effects of lepton mass. Because the proposed super-tau-charm factory will reach a significantly enhanced luminosity and BESIII is collecting new   $ \psi(3770)\to D\bar{D} $   data, our results will help improve the measurement precision of future partial wave analyses of charmed meson semi-muonic decays.

En Wang

Lepton mass correction in partial wave analyses of charmed meson semi-leptonic decays  

We study  $$D_{s}^{+}\rightarrow \rho ^{0(+)}a^{+(0)}_{0}$$  <math> <mrow> <msubsup> <mi>D</mi> <mrow> <mi>s</mi> </mrow> <mo>+</mo> </msubsup> <mo>→</mo> <msup> <mi>ρ</mi> <mrow> <mn>0</mn> <mo>(</mo> <mo>+</mo> <mo>)</mo> </mrow> </msup> <msubsup> <mi>a</mi> <mn>0</mn> <mrow> <mo>+</mo> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> </mrow> </math>  ,  $$D_{s}^{+}\rightarrow \omega a^{+}_{0}$$  <math> <mrow> <msubsup> <mi>D</mi> <mrow> <mi>s</mi> </mrow> <mo>+</mo> </msubsup> <mo>→</mo> <mi>ω</mi> <msubsup> <mi>a</mi> <mn>0</mn> <mo>+</mo> </msubsup> </mrow> </math>  , and the resonant  $$D_{s}^{+}\rightarrow \rho a_0$$  <math> <mrow> <msubsup> <mi>D</mi> <mrow> <mi>s</mi> </mrow> <mo>+</mo> </msubsup> <mo>→</mo> <mi>ρ</mi> <msub> <mi>a</mi> <mn>0</mn> </msub> </mrow> </math>  ,  $$a_{0}\rightarrow \eta \pi (KK)$$  <math> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>→</mo> <mi>η</mi> <mi>π</mi> <mrow> <mo>(</mo> <mi>K</mi> <mi>K</mi> <mo>)</mo> </mrow> </mrow> </math>   decays. In the final state interaction, where  $$D_s^+\rightarrow (\eta ^{(\prime )}\pi ^+,K^+{{\bar{K}}}^0)$$  <math> <mrow> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> <mo>→</mo> <mrow> <mo>(</mo> <msup> <mi>η</mi> <mrow> <mo>(</mo> <mo>′</mo> <mo>)</mo> </mrow> </msup> <msup> <mi>π</mi> <mo>+</mo> </msup> <mo>,</mo> <msup> <mi>K</mi> <mo>+</mo> </msup> <msup> <mrow> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mn>0</mn> </msup> <mo>)</mo> </mrow> </mrow> </math>   are followed by the  $$(\eta ^{(\prime )}\pi ^+,K^+{{\bar{K}}}^0)$$  <math> <mrow> <mo>(</mo> <msup> <mi>η</mi> <mrow> <mo>(</mo> <mo>′</mo> <mo>)</mo> </mrow> </msup> <msup> <mi>π</mi> <mo>+</mo> </msup> <mo>,</mo> <msup> <mi>K</mi> <mo>+</mo> </msup> <msup> <mrow> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mn>0</mn> </msup> <mo>)</mo> </mrow> </math>   to  $$\rho ^{0(+)}a^{+(0)}_{0}$$  <math> <mrow> <msup> <mi>ρ</mi> <mrow> <mn>0</mn> <mo>(</mo> <mo>+</mo> <mo>)</mo> </mrow> </msup> <msubsup> <mi>a</mi> <mn>0</mn> <mrow> <mo>+</mo> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> </mrow> </math>   rescatterings, we predict  $$\mathcal{B}(D_{s}^{+}\rightarrow \rho ^{0(+)}a^{+(0)}_{0})=(3.0\pm 0.3\pm 1.0)\times 10^{-3}$$  <math> <mrow> <mi>B</mi> <mrow> <mo>(</mo> <msubsup> <mi>D</mi> <mrow> <mi>s</mi> </mrow> <mo>+</mo> </msubsup> <mo>→</mo> <msup> <mi>ρ</mi> <mrow> <mn>0</mn> <mo>(</mo> <mo>+</mo> <mo>)</mo> </mrow> </msup> <msubsup> <mi>a</mi> <mn>0</mn> <mrow> <mo>+</mo> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>3.0</mn> <mo>±</mo> <mn>0.3</mn> <mo>±</mo> <mn>1.0</mn> <mo>)</mo> </mrow> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </math>  . Due to the cancellation of the rescattering effects and the suppressed short-distance W annihilation contribution, we expect that  $${{\mathcal {B}}}(D_{s}^{+}\rightarrow \omega a^{+}_{0}) \simeq \mathcal{B}(D_s^+\rightarrow \pi ^+\pi ^0)&lt;3.4\times 10^{-4}$$  <math> <mrow> <mi>B</mi> <mrow> <mo>(</mo> <msubsup> <mi>D</mi> <mrow> <mi>s</mi> </mrow> <mo>+</mo> </msubsup> <mo>→</mo> <mi>ω</mi> <msubsup> <mi>a</mi> <mn>0</mn> <mo>+</mo> </msubsup> <mo>)</mo> </mrow> <mo>≃</mo> <mi>B</mi> <mrow> <mo>(</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> <mo>→</mo> <msup> <mi>π</mi> <mo>+</mo> </msup> <msup> <mi>π</mi> <mn>0</mn> </msup> <mo>)</mo> </mrow> <mo>&lt;</mo> <mn>3.4</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </msup> </mrow> </math>  . In our calculation,  $${{\mathcal {B}}}(D_{s}^{+}\rightarrow \rho ^{0}(a^{+}_{0}\rightarrow )\eta \pi ^{+}) =(1.6^{+0.2}_{-0.3}\pm 0.6)\times 10^{-3}$$  <math> <mrow> <mi>B</mi> <mrow> <mo>(</mo> <msubsup> <mi>D</mi> <mrow> <mi>s</mi> </mrow> <mo>+</mo> </msubsup> <mo>→</mo> <msup> <mi>ρ</mi> <mn>0</mn> </msup> <mrow> <mo>(</mo> <msubsup> <mi>a</mi> <mn>0</mn> <mo>+</mo> </msubsup> <mo>→</mo> <mo>)</mo> </mrow> <mi>η</mi> <msup> <mi>π</mi> <mo>+</mo> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>.</mo> <msubsup> <mn>6</mn> <mrow> <mo>-</mo> <mn>0.3</mn> </mrow> <mrow> <mo>+</mo> <mn>0.2</mn> </mrow> </msubsup> <mo>±</mo> <mn>0.6</mn> <mo>)</mo> </mrow> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </math>   agrees with the data, whereas  $${{\mathcal {B}}}(D_{s}^{+}\rightarrow \rho ^{+}(a^{0}_{0}\rightarrow )K^+K^-)$$  <math> <mrow> <mi>B</mi> <mo>(</mo> <msubsup> <mi>D</mi> <mrow> <mi>s</mi> </mrow> <mo>+</mo> </msubsup> <mo>→</mo> <msup> <mi>ρ</mi> <mo>+</mo> </msup> <mrow> <mo>(</mo> <msubsup> <mi>a</mi> <mn>0</mn> <mn>0</mn> </msubsup> <mo>→</mo> <mo>)</mo> </mrow> <msup> <mi>K</mi> <mo>+</mo> </msup> <msup> <mi>K</mi> <mo>-</mo> </msup> <mo>)</mo> </mrow> </math>   is 10 times smaller than the observation, which requires a careful examination.

Yu-Kuo Hsiao

Study of the  $$D_s^+\rightarrow a_0(980) \rho $$  <math> <mrow> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> <mo>→</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> <mi>ρ</mi> </mrow> </math>   and  $$a_0(980) \omega $$  <math> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> <mi>ω</mi> </mrow> </math>   decays

The anti-triplet charmed baryon decays with the light scalar mesons are rarely measured, whereas the recent observation of the Cabibbo-favored <math><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><mi>Λ</mi><mi>η</mi><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></math> decay hints a possible <math><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><mi>Λ</mi><msub><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow></msub><msup><mrow><mo>(</mo><mn>980</mn><mo>)</mo></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow></msub><msup><mrow><mo>(</mo><mn>980</mn><mo>)</mo></mrow><mrow><mo>+</mo></mrow></msup><mo>→</mo><mi>η</mi><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></math> process. We hence study the <math><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><mi>Λ</mi><msub><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow></msub><msup><mrow><mo>(</mo><mn>980</mn><mo>)</mo></mrow><mrow><mo>+</mo></mrow></msup></math> decay. Particularly, it is found that the final state interaction can give a significant contribution, where <math><msup><mrow><mi>Σ</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><mn>1385</mn><mo>)</mo></math> and η in <math><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><msup><mrow><mi>Σ</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><mn>1385</mn><mo>)</mo><mi>η</mi></math> by exchanging a charged pion are transformed as Λ and <math><msub><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow></msub><msup><mrow><mo>(</mo><mn>980</mn><mo>)</mo></mrow><mrow><mo>+</mo></mrow></msup></math>, respectively. Accordingly, we predict <math><mi>B</mi><mo>(</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><mi>Λ</mi><msub><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow></msub><msup><mrow><mo>(</mo><mn>980</mn><mo>)</mo></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo><mo>=</mo><mo>(</mo><msubsup><mrow><mn>1.7</mn></mrow><mrow><mo>−</mo><mn>1.0</mn></mrow><mrow><mo>+</mo><mn>2.8</mn></mrow></msubsup><mo>±</mo><mn>0.3</mn><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>, accessible to the BESIII, BELLEII and LHCb experiments.

Cabibbo-favored Decay in the Final State Interaction

In the <math><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup></math> decay, LHCb has reported the observation of the open-charm exotic states <math><msubsup><mi>X</mi><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow><mn>0</mn></msubsup><mo>≡</mo><msub><mi>X</mi><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>(</mo><mn>2900</mn><msup><mo>)</mo><mn>0</mn></msup></math> with four different quark flavors <math><mo>(</mo><mi>u</mi><mi>d</mi><mover><mi>s</mi><mo>¯</mo></mover><mover><mi>c</mi><mo>¯</mo></mover><mo>)</mo></math>, where the subscripts (0,1) denote the spins. To confirm the discovery, we propose <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Σ</mi><mi>c</mi><mrow><mn>0</mn><mo>(</mo><mo>+</mo><mo>+</mo><mo>)</mo></mrow></msubsup><msubsup><mi>X</mi><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow><mrow><mo>′</mo><mn>0</mn><mo>(</mo><mo>−</mo><mo>−</mo><mo>)</mo></mrow></msubsup></math> in the final state interaction, where <math><msubsup><mi>X</mi><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow><mrow><mo>′</mo><mn>0</mn><mo>(</mo><mo>−</mo><mo>−</mo><mo>)</mo></mrow></msubsup></math> with <math><mi>s</mi><mi>u</mi><mover><mi>d</mi><mo>¯</mo></mover><mover><mi>c</mi><mo>¯</mo></mover></math> (<math><mi>d</mi><mi>s</mi><mover><mi>u</mi><mo>¯</mo></mover><mover><mi>c</mi><mo>¯</mo></mover></math>) are the new <math><msub><mi>X</mi><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow></msub></math>-like exotic states. More specifically, <math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mi>D</mi><mi>s</mi><mo>−</mo></msubsup></math> in <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mi>D</mi><mi>s</mi><mo>−</mo></msubsup></math> are transformed as <math><msubsup><mi>Σ</mi><mi>c</mi><mrow><mn>0</mn><mo>(</mo><mo>+</mo><mo>+</mo><mo>)</mo></mrow></msubsup><msubsup><mi>X</mi><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow><mrow><mo>′</mo><mn>0</mn><mo>(</mo><mo>−</mo><mo>−</mo><mo>)</mo></mrow></msubsup></math>, by exchanging <math><msup><mi>π</mi><mrow><mo>+</mo><mo>(</mo><mo>−</mo><mo>)</mo></mrow></msup></math>. As the order of magnitude estimates, we calculate <math><mrow><mi>B</mi><mo>(</mo><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>→</mo><msubsup><mrow><mi>Σ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mn>0</mn><mo>(</mo><mo>+</mo><mo>+</mo><mo>)</mo></mrow></msubsup><msubsup><mrow><mi>X</mi></mrow><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow><mrow><mo>′</mo><mn>0</mn><mo>(</mo><mo>−</mo><mo>−</mo><mo>)</mo></mrow></msubsup><mo>)</mo><mo>=</mo><mo>(</mo><mn>2.3</mn><mo>±</mo><mn>0.6</mn><mo>,</mo><mn>4.3</mn><mo>±</mo><mn>0.</mn><msubsup><mrow><mn>8</mn></mrow><mrow><mo>−</mo><mn>2.5</mn></mrow><mrow><mo>+</mo><mn>3.3</mn></mrow></msubsup><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math>. In addition, we estimate other <math><mi>b</mi></math>-baryon decays with the <math><msub><mi>X</mi><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow></msub></math>-like states, such as <math><mi>B</mi><mo>(</mo><msubsup><mi>Ξ</mi><mi>b</mi><mrow><mn>0</mn><mo>(</mo><mo>−</mo><mo>)</mo></mrow></msubsup><mo>→</mo><msubsup><mi>Ξ</mi><mi>c</mi><mrow><mn>0</mn><mo>(</mo><mo>+</mo><mo>)</mo></mrow></msubsup><mo>(</mo><mn>2645</mn><mo>)</mo><msubsup><mi>X</mi><mn>0</mn><mrow><mo>′</mo><mn>0</mn><mo>(</mo><mo>−</mo><mo>−</mo><mo>)</mo></mrow></msubsup><mo>,</mo><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Ξ</mi><mi>c</mi><mrow><mo>′</mo><mn>0</mn></mrow></msubsup><msubsup><mi>X</mi><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow><mn>0</mn></msubsup><mo>)</mo><mo>∼</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>. While one needs <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Σ</mi><mi>c</mi><mrow><mn>0</mn><mo>(</mo><mo>+</mo><mo>+</mo><mo>)</mo></mrow></msubsup><msub><mi>M</mi><mi>c</mi></msub><mi>M</mi></math> to observe <math><msubsup><mi>X</mi><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow><mrow><mo>′</mo><mn>0</mn><mo>(</mo><mo>−</mo><mo>−</mo><mo>)</mo></mrow></msubsup><mo>→</mo><msub><mi>M</mi><mi>c</mi></msub><mi>M</mi></math> with <math><msub><mi>M</mi><mi>c</mi></msub><mi>M</mi><mo>=</mo><msubsup><mi>D</mi><mi>s</mi><mo>−</mo></msubsup><msup><mi>π</mi><mo>+</mo></msup></math>, <math><msup><mover><mi>D</mi><mo>¯</mo></mover><mn>0</mn></msup><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup></math> <math><mo>(</mo><msubsup><mi>D</mi><mi>s</mi><mo>−</mo></msubsup><msup><mi>π</mi><mo>−</mo></msup></math>, <math><msup><mi>D</mi><mo>−</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mo>)</mo></math>, <math><mi>B</mi><mo>(</mo><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msubsup><mi>Σ</mi><mi>c</mi><mrow><mn>0</mn><mo>(</mo><mo>+</mo><mo>+</mo><mo>)</mo></mrow></msubsup><msubsup><mi>X</mi><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow><mrow><mo>′</mo><mn>0</mn><mo>(</mo><mo>−</mo><mo>−</mo><mo>)</mo></mrow></msubsup><mo>,</mo><msubsup><mi>X</mi><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow><mrow><mo>′</mo><mn>0</mn><mo>(</mo><mo>−</mo><mo>−</mo><mo>)</mo></mrow></msubsup><mo>→</mo><msub><mi>M</mi><mi>c</mi></msub><mi>M</mi><mo>)</mo><mo>∼</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math> are accessible to the LHCb experiment.

New <math><msub><mi>X</mi><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math>-like exotic states in <math><mi>b</mi></math>-baryon decays

We study the  $$D_s^+\rightarrow \pi ^+(a_0(980)^0\rightarrow )\pi ^0\eta $$  <math> <mrow> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> <mo>→</mo> <msup> <mi>π</mi> <mo>+</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msup> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> <mn>0</mn> </msup> <mo>→</mo> <mo>)</mo> </mrow> <msup> <mi>π</mi> <mn>0</mn> </msup> <mi>η</mi> </mrow> </math>  ,  $$\pi ^0(a_0(980)^+\rightarrow )\pi ^+\eta $$  <math> <mrow> <msup> <mi>π</mi> <mn>0</mn> </msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msup> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> <mo>+</mo> </msup> <mo>→</mo> <mo>)</mo> </mrow> <msup> <mi>π</mi> <mo>+</mo> </msup> <mi>η</mi> </mrow> </math>   decays, which have been recently measured by the BESIII collaboration. We propose that  $$D_s^+\rightarrow \pi ^{+(0)}(a_0(980)^{0(+)}\rightarrow )\pi ^{0(+)}\eta $$  <math> <mrow> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> <mo>→</mo> <msup> <mi>π</mi> <mrow> <mo>+</mo> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msup> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> <mrow> <mn>0</mn> <mo>(</mo> <mo>+</mo> <mo>)</mo> </mrow> </msup> <mo>→</mo> <mo>)</mo> </mrow> <msup> <mi>π</mi> <mrow> <mn>0</mn> <mo>(</mo> <mo>+</mo> <mo>)</mo> </mrow> </msup> <mi>η</mi> </mrow> </math>   receives the contributions from the triangle rescattering processes, where  $$M^0$$  <math> <msup> <mi>M</mi> <mn>0</mn> </msup> </math>   and  $$\rho ^+$$  <math> <msup> <mi>ρ</mi> <mo>+</mo> </msup> </math>   in  $$D_s^+\rightarrow M^0 \rho ^+$$  <math> <mrow> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> <mo>→</mo> <msup> <mi>M</mi> <mn>0</mn> </msup> <msup> <mi>ρ</mi> <mo>+</mo> </msup> </mrow> </math>  , by exchanging  $$\pi ^{0(+)}$$  <math> <msup> <mi>π</mi> <mrow> <mn>0</mn> <mo>(</mo> <mo>+</mo> <mo>)</mo> </mrow> </msup> </math>  , are formed as  $$a_0(980)^{0(+)}$$  <math> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <msup> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> <mrow> <mn>0</mn> <mo>(</mo> <mo>+</mo> <mo>)</mo> </mrow> </msup> </mrow> </math>   and  $$\pi ^{+(0)}$$  <math> <msup> <mi>π</mi> <mrow> <mo>+</mo> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msup> </math>  , respectively, with  $$M^0=(\eta ,\eta ')$$  <math> <mrow> <msup> <mi>M</mi> <mn>0</mn> </msup> <mo>=</mo> <mrow> <mo>(</mo> <mi>η</mi> <mo>,</mo> <msup> <mi>η</mi> <mo>′</mo> </msup> <mo>)</mo> </mrow> </mrow> </math>  . Accordingly, we calculate that  $$\mathcal{B}(D_s^+\rightarrow a_0(980)^{0(+)}\pi ^{+(0)})= (1.7\pm 0.2\pm 0.1)\times 10^{-2}$$  <math> <mrow> <mi>B</mi> <mrow> <mo>(</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> <mo>→</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msup> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> <mrow> <mn>0</mn> <mo>(</mo> <mo>+</mo> <mo>)</mo> </mrow> </msup> <msup> <mi>π</mi> <mrow> <mo>+</mo> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>1.7</mn> <mo>±</mo> <mn>0.2</mn> <mo>±</mo> <mn>0.1</mn> <mo>)</mo> </mrow> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> </math>   and  $$\mathcal{B}(D_s^+\rightarrow \pi ^{+(0)}(a_0(980)^{0(+)}\rightarrow )\pi ^{0(+)}\eta ) =(1.4\pm 0.1\pm 0.1)\times 10^{-2}$$  <math> <mrow> <mi>B</mi> <mrow> <mo>(</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> <mo>→</mo> <msup> <mi>π</mi> <mrow> <mo>+</mo> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <msup> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> <mrow> <mn>0</mn> <mo>(</mo> <mo>+</mo> <mo>)</mo> </mrow> </msup> <mo>→</mo> <mo>)</mo> </mrow> <msup> <mi>π</mi> <mrow> <mn>0</mn> <mo>(</mo> <mo>+</mo> <mo>)</mo> </mrow> </msup> <mi>η</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>1.4</mn> <mo>±</mo> <mn>0.1</mn> <mo>±</mo> <mn>0.1</mn> <mo>)</mo> </mrow> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> </math>  , being consistent with the data.

Resonant  $$a_0(980)$$  <math> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> </mrow> </math>   state in triangle rescattering  $$D_s^+\rightarrow \pi ^+\pi ^0\eta $$  <math> <mrow> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> <mo>→</mo> <msup> <mi>π</mi> <mo>+</mo> </msup> <msup> <mi>π</mi> <mn>0</mn> </msup> <mi>η</mi> </mrow> </math>   decays