Roles of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>980</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1670</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1385</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">→</mml:mo><mml:mi>η</mml:mi><mml:mi mathvariant="normal">Λ</mml:mi><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math> decay
Guanying Wang, Neng-Chang Wei, H. L. Yang, En Wang, Li‐Sheng Geng, Ju-Jun Xie
Abstract
Recently, the Belle Collaboration has measured the ${\mathrm{\ensuremath{\Lambda}}}_{c}^{+}\ensuremath{\rightarrow}\ensuremath{\eta}\mathrm{\ensuremath{\Lambda}}{\ensuremath{\pi}}^{+}$ decay and reported the $\ensuremath{\eta}\mathrm{\ensuremath{\Lambda}}$ and $\mathrm{\ensuremath{\Lambda}}{\ensuremath{\pi}}^{+}$ invariant mass distributions, which show the clear signals of the resonances $\mathrm{\ensuremath{\Lambda}}(1670)$ and $\mathrm{\ensuremath{\Sigma}}(1385)$, respectively. Based on our previous works [Eur. Phys. J. C 76, 496 (2016) and Phys. Rev. D 95, 074024 (2017)], we reanalyze this process by considering the $S$-wave $\ensuremath{\eta}\mathrm{\ensuremath{\Lambda}}$ and $\ensuremath{\eta}{\ensuremath{\pi}}^{+}$ final state interactions within the chiral unitary approach, which dynamically generate the $\mathrm{\ensuremath{\Lambda}}(1670)$ and ${a}_{0}(980)$, respectively. Our results are in agreement with the Belle measurements of the $\ensuremath{\eta}\mathrm{\ensuremath{\Lambda}}$ and ${\ensuremath{\pi}}^{+}\mathrm{\ensuremath{\Lambda}}$ invariant mass distributions. In addition, the ${\ensuremath{\pi}}^{+}\ensuremath{\eta}$ invariant mass distribution is also calculated and a cusp structure of ${a}_{0}(980)$ is clearly shown around the $K\overline{K}$ mass threshold.