The magnetic dipole transitions in the (c) binding system

The magnetic dipole transitions between the vector mesons B * c and their relevant pseudoscalar mesons B c ( B c , B * c , B c (2 S ), B * c (2 S ), B c (3 S ), B * c (3 S ) etc., the binding states of ( c ) 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 ) 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 .