Eur. Phys. J. C (2023) 83: 961
https://doi.org/10.1140/epjc/s10052-023-12042-4

Regular Article - Theoretical Physics

Revisiting ${\mathrm{\Xi }}_Q-{\mathrm{\Xi }}_Q^{\prime }$ mixing in QCD sum rules

¹ School of Physical Science and Technology, Inner Mongolia University, 010021, Hohhot, China
² School of Physics, East China University of Science and Technology, 200237, Shanghai, China

^d zhaozx19@imu.edu.cn

Received: 26 June 2023
Accepted: 14 September 2023
Published online: 24 October 2023

Abstract

In this work, we perform a QCD sum rules analysis on ${\mathrm{\Xi }}_Q-{\mathrm{\Xi }}_Q^{\prime }$ mixing. Contributions from up to dimension-6 four-quark operators are considered. However, it turns out that only dimension-4 and dimension-5 operators contribute, which reveals the non-perturbative nature of mixing. In particular, we observe that only the diagrams with the two light quarks participating in gluon exchange contribute to the mixing. Our results indicate that the mixing angle ${\theta }_c={(1.2\sim 2.8)}^{\circ }$ for the $Q=c$ case and ${\theta }_b={(0.28\sim 0.34)}^{\circ }$ for the $Q=b$ case. Our prediction of ${\theta }_c$ is consistent with the most recent Lattice QCD result within error. Such a small mixing angle seems unlikely to resolve the tension between the recent experimental measurement from Belle and Lattice QCD calculation for the semileptonic decay ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{e}^{+}{\nu }_e$.