Revisiting the transition <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">Ξ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mo>+</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">→</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">Ξ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mo>′</mml:mo><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math> to understand the data from LHCb

Abstract

The LHCb collaboration newly measured the decay rate of doubly charmed baryon ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}^{\ensuremath{'}+}{\ensuremath{\pi}}^{+}$, and a ratio of its branching fraction with respect to that of the decay ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}^{+}{\ensuremath{\pi}}^{+}$ is reported as $1.41\ifmmode\pm\else\textpm\fi{}0.17\ifmmode\pm\else\textpm\fi{}0.10$. This result conflicts with the theoretical predictions made by several groups. In our previous work, following the prescription given in early literature where the $us$ diquark in ${\mathrm{\ensuremath{\Xi}}}_{c}^{+}$ is assumed to be a scalar, whereas in ${\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}+}$ it is a vector, i.e., the spin-flavor structure of ${\mathrm{\ensuremath{\Xi}}}_{c}^{+}$ is $[us{]}_{0}c$ and that of ${\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}+}$ is $[us{]}_{1}c$, we studied the case of ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}^{(\ensuremath{'})+}$ with the light-front quark model. Numerically we obtained $\mathrm{\ensuremath{\Gamma}}({\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}^{\ensuremath{'}+}{\ensuremath{\pi}}^{+})/\mathrm{\ensuremath{\Gamma}}({\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}^{+}{\ensuremath{\pi}}^{+})=0.56\ifmmode\pm\else\textpm\fi{}0.18$, which is about half of the data. While abandoning the presupposition, we suppose the spin-flavor structure of $[us]c$ in ${\mathrm{\ensuremath{\Xi}}}_{c}^{+}$ may be a mixture of $[us{]}_{0}c$ and $[us{]}_{1}c$, namely the spin-flavor function of ${\mathrm{\ensuremath{\Xi}}}_{c}^{+}$ could be $\mathrm{cos}\ensuremath{\theta}[us{]}_{0}[c]+\mathrm{sin}\ensuremath{\theta}[us{]}_{1}[c]$. An alternative combination $\ensuremath{-}\mathrm{sin}\ensuremath{\theta}[us{]}_{0}[c]+\mathrm{cos}\ensuremath{\theta}[us{]}_{1}[c]$ would correspond to ${\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}+}$. Introducing the mixing mechanism, the ratio $\mathrm{\ensuremath{\Gamma}}({\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}^{\ensuremath{'}+}{\ensuremath{\pi}}^{+})/\mathrm{\ensuremath{\Gamma}}({\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}^{+}{\ensuremath{\pi}}^{+})$ depends on the mixing angle $\ensuremath{\theta}$. With the mixing scenario, the theoretical prediction on the ratio between the transition rate of ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}+}$ and that of ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{+}$ can coincide with the data as long as $\ensuremath{\theta}=16.27\ifmmode^\circ\else\textdegree\fi{}\ifmmode\pm\else\textpm\fi{}2.30\ifmmode^\circ\else\textdegree\fi{}$ or $85.54\ifmmode^\circ\else\textdegree\fi{}\ifmmode\pm\else\textpm\fi{}2.30\ifmmode^\circ\else\textdegree\fi{}$ is set. Definitely, more precise measurements on other decay portals of ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}$ are badly needed for testing the mixing mechanism and further determining the mixing angle.

Topics & Concepts