Revisiting the transition $\Xi^{+}_{cc}\to\Xi^{(')+}_c$ to understand the data from LHCb

TL;DR

This paper revisits the decay transition of doubly charmed baryons to reconcile theoretical predictions with recent LHCb data by proposing a mixing mechanism of the $us$ diquark's spin-flavor structure, which aligns theory with experiment.

Contribution

The study introduces a mixing model of scalar and vector $us$ diquark states in $ ext{Xi}_c^+$ to explain the observed decay rate ratios, improving agreement with experimental data.

Findings

Mixing angle around 16.3° or 85.5° aligns theory with data.

Previous models underestimated the decay ratio by about half.

More precise measurements are needed to test the mixing hypothesis.

Abstract

The LHCb collaboration newly measured the decay rate of doubly charmed baryon $\Xi^{++}_{cc}\to\Xi^{'+}\pi^+$ and a ratio of its branching fraction with respect to that of the decay $\Xi^{++}_{cc}\to\Xi^{+}\pi^+$ is reported as $1.41\pm 0.17\pm 0.10$. 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 $\Xi^{+}_{c}$ is assumed to be a scalar whereas in $\Xi^{'+}_{c}$ is a vector i.e. the spin-flavor structure of $\Xi^{+}_{c}$ is $[us]_0 c$ and that of $\Xi^{'+}_{c}$ is $[us]_1 c$, we studied the case of $\Xi^{++}_{cc}\to\Xi^{(')+}$ with the light front quark model. Numerically we obtained $\Gamma(\Xi^{++}_{cc}\to\Xi^{'+}\pi^+)/\Gamma(\Xi^{++}_{cc}\to\Xi^{+}\pi^+)=0.56\pm0.18$ which is about half of the data. While abandoning the presupposition, we suppose the spin-flavor structure of $us$ in $\Xi^{+}_{c}$ may be a mixture of scalar and vector, namely the spin-flavor function of $\Xi^{+}_{c}$ could be ${\rm cos}\theta\, [us]_{0}[c]+{\rm sin}\theta\, [us]_{1}[c]$. An alternative combination $-{\rm sin}\theta\,[us]_{0}[c]+{\rm cos}\theta\, [us]_{1}[c]$ would correspond to $\Xi^{'+}_{c}$. Introducing the mixing mechanism the ratio $\Gamma(\Xi^{++}_{cc}\to\Xi^{'+}\pi^+)/\Gamma(\Xi^{++}_{cc}\to\Xi^{+}\pi^+)$ depends on the mixing angle $\theta$. With the mixing scenario, the theoretical prediction on the ratio between the transition rate of $\Xi^{+}_{cc}\to\Xi^{'+}_c$ and that of $\Xi^{+}_{cc}\to\Xi^{+}_c$ can coincide with the data as long as $\theta=16.27^\circ\pm2.30^\circ$ or $85.54^\circ\pm2.30^\circ$ is set. Definitely, more precise measurements on other decay portals of $\Xi^{+}_{cc}$ are badly needed for testing the mixing mechanism and further determining the mixing angle.