Towards establishing the second $b$-flavored CKM unitarity triangle

Abstract

Some fine differences between the twin $b$-flavored unitarity triangles are calculated by means of a generalized Wolfenstein parametrization of the CKM matrix, and a possibility of experimentally establishing the second triangle is briefly discussed. We find that the apexes of these two triangles, characterized respectively by $(\overline{\rho },\overline{\eta })$ and $(\tilde{\rho },\tilde{\eta })$, are located on the same circular arc in the complex plane. This observation provides us with a new way to test consistency of the CKM picture of CP violation in the quark sector and probe possible new physics. The differences between the apexes (i.e., $\tilde{\rho }-\overline{\rho }$ and $\tilde{\eta }-\overline{\eta }$) are found to be of $\mathcal{O}({\lambda }^2)$ with $\lambda \simeq 0.22$ being the Wolfenstein expansion parameter, and the shapes of these two triangles are found to be insensitive to the two-loop renormalization-group-equation running effects up to the accuracy of $\mathcal{O}\left({\lambda }^4\right)$.

Comments: 6 pages, 2 figures; To appear in the 40th International Conference on High Energy physics (ICHEP2020)