Study on the mixing of Ξc and Ξc′ by the transition Ξb→Ξc(′)

Abstract

Recently, the LHCb Collaboration has observed the decays Ξb0→Ξc+Ds− and Ξb−→Ξc0Ds−. They measured the relative branching fractions times the ratio of beauty-baryon production cross sections R(Ξb0Λb)≡σ(Ξb0)σ(Λb0)×B(Ξb0→Ξc+Ds−)B(Λb0→Λc+Ds−) and R(Ξb−Λb)≡σ(Ξb−)σ(Λb0)×B(Ξb−→Ξc0Ds−)B(Λb0→Λc+Ds−). Once the ratio σ(Ξb0)σ(Λb0) or σ(Ξb−)σ(Λb0) is known, one can determine the relative branching fractions which can be used to exam the mixing of Ξc and Ξc′. In previous literature, Ξc and Ξc′ were assumed to belong to SU(3)F antitriple and sextet, respectively. However, recent experimental measurements, such as the ratio Γ(Ξcc→Ξcπ+)/Γ(Ξcc→Ξc′π+), indicate the spin-flavor structures of Ξc and Ξc′ are a mixture of Ξc3¯ and Ξc6. The exact value of mixing angle θ is still under debate. In theoretical models, the mixing angle was fitted to be about 16.27°±2.30° or 85.54°±2.30° based on decay channels Ξcc→Ξc(′). While in lattice calculation, a small angle (1.2°±0.1°) is preferred. To address such discrepancy and test the mixing of Ξc and Ξc′, here we propose the analysis of semileptonic and nonleptonic decays of Ξb→Ξc and Ξb→Ξc′. We calculate the decay rate of Ξb→Ξc and Ξb→Ξc′ based on the light-front quark model and study the effect of the mixing angle on the ratios of weak decays Ξb→Ξc and Ξb→Ξc′. In particular, we find the transition Ξb→Ξc′ can be an ideal channel to verify the mixing and extract the mixing angle because in theory, the decay rate would be extremely tiny without mixing. Our calculation suggests a measurement of Ξb→Ξc′ can be feasible in the near future, which will help to test flavor mixing angle θ and elucidate the mechanism of decay of heavy baryons. Published by the American Physical Society 2024