Resolving puzzle in [formula omitted] with [formula omitted] mixing spectrum within the quark model

Abstract

We study the ratio of R=2Γ(Ξc0→Ξ−e+νe)/3Γ(Λc+→Λe+νe), which is found to be R=1(0.8) from the exact (broken) SU(3) flavor symmetry, in sharp contrast to the average value of Rav=0.59±0.10 from the ALICE collaboration and lattice QCD results. We propose to use the mixing of Ξc−Ξc′ to resolve the puzzle. From the mass spectra, we find that the mixing angle is |θc|=0.137(5)π, which suppresses Ξc→Ξe+νe about 20% model-independently, resulting in R≈0.6 with the SU(3) flavor breaking effect. We explicitly demonstrate that R=0.70±0.09 from the bag model, which is also consistent with Rav. To test the mixing mechanism, we recommend the experiments to measure the decays of Ξc→Ξ′(1530)e+νe, whose branching fractions are determined to be (4.4∼8.7)×10−3 and (1.3∼2.6)% for Ξc0 and Ξc+, respectively, but vanish without the mixing. In addition, nonvanishing values of B(Ξc+→Ξ′0(1530)π+) and B(Ξc+→Σ′+(1385)K‾0) will also be evidences of the mixing based on the Körner-Pati-Woo theorem, which are calculated as (3.8∼7.5)×10−3 and (6.6∼13)×10−4, respectively. We emphasize that θc is sizable and should be given serious considerations in future studies on the heavy baryon systems.