Resonances <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>4140</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>4160</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:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4459</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> in the decay of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>ψ</mml:mi><mml:mi mathvariant="normal">Λ</mml:mi><mml:mi>ϕ</mml:mi></mml:mrow></mml:math>
Wenying Liu, W. Hao, Guanying Wang, Yanyan Wang, En Wang, Demin Li
Abstract
We study the decay of ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}J/\ensuremath{\psi}\mathrm{\ensuremath{\Lambda}}\ensuremath{\phi}$ by taking into account the intermediate resonances $X(4140)$, $X(4160)$, and ${P}_{cs}(4459)$. In addition to the peak of the $X(4140)$, we also find a bump structure around 4160 MeV followed by a cusp structure around ${D}_{s}^{*}{\overline{D}}_{s}^{*}$ threshold in the $J/\ensuremath{\psi}\ensuremath{\phi}$ invariant mass distribution of the ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}J/\ensuremath{\psi}\mathrm{\ensuremath{\Lambda}}\ensuremath{\phi}$ process, which can be associated to the ${D}_{s}^{*}{\overline{D}}_{s}^{*}$ molecular state $X(4160)$. We also show that this reaction can also be used to confirm the existence of the hidden-charm pentaquark ${P}_{cs}(4459)$ with strangeness. We predict an enhancement structure close to the threshold in the ${D}_{s}^{*}{\overline{D}}_{s}^{*}$ invariant mass distribution of the ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{D}_{s}^{*}{\overline{D}}_{s}^{*}\mathrm{\ensuremath{\Lambda}}$ process, which is the reflection of the $X(4160)$ and should not be misidentified with a new resonance. We strongly suggest experimentalists to further measure these processes, which can be useful to clarify the nature of $X(4140)$ and $X(4160)$ resonances, and to confirm the existence of the ${P}_{cs}(4459)$.