The magnetic dipole transitions in the (c $\bar b$) binding system

Abstract

The magnetic dipole transitions between the vector mesons B* _c and their relevant pseudoscalar mesons B _c (B _c , B* _c , B _c (2S), B* _c (2S), B _c (3S), B* _c (3S) etc., the binding states of (c $\bar b$) system) of the B _c family are interesting. The ‘hyperfine’ splitting due to spin-spin interaction is an important topic for understanding the spin-spin interaction and the spectrum of the the (c $\bar b$) binding system. The knowledge about the magnetic dipole transitions is also very useful for identifying the vector boson B* _c mesons experimentally, whose masses are just slightly above the masses of their relevant pseudoscalar mesons B _c . Considering the possibility to observe the vector mesons via the transitions at Z ⁰ factory and the potential use of the theoretical estimate on the transitions, we fucus our efforts on calculating the magnetic dipole transitions, i.e. a precise calculation of the rates for the transitions such as decays B* _c → B _c γ and B* _c → B _c e ⁺ e ⁻, and particularly work in the Bethe-Salpeter framework. As a typical example, we carefully investigate the dependence of the rate Γ(B* _c → B _c γ) on the mass difference $\Delta M = M_{B_c^* } - M_{B_c }$.