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

TL;DR

This paper calculates magnetic dipole transition rates in the $(car{b})$ meson system using the Bethe-Salpeter framework, aiding experimental identification and understanding of hyperfine splitting.

Contribution

It provides the first detailed theoretical estimates of magnetic dipole transition rates in the $(car{b})$ system within the Bethe-Salpeter approach.

Findings

Calculated decay rates for $B_c^* o B_c o ext{photon}$ and $e^+e^-$ channels.

Analyzed the dependence of transition rates on the mass difference $ riangle M$.

Results support experimental efforts to identify $B_c^*$ mesons.

Abstract

The magnetic dipole transitions between the vector mesons $B_c^*$ and their relevant pseudoscalar mesons $B_c$ ($B_c$, $B_c^*$, $B_c(2S)$, $B_c^*(2S)$, $B_c(3S)$ and $B_c^*(3S)$ etc, the binding states of $(c\bar{b})$ system) of the $B_c$ family are interesting. To see 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 $B_c$ accordingly. Considering the possibility to observe the vector mesons via the transitions at $Z^0$ factory and the potentially usages of the theoretical estimate on the transitions, we fucus our efforts on calculating the magnetic dipole transitions, i.e. precisely to calculate the rates for the transitions such as decays $B_c^*\to B_c\gamma$ and $B_c^*\to B_c e^+e^-$, and particularly work in the Behte-Salpeter framework. In the estimate, as a typical example, we carefully investigate the dependance of the rate $\Gamma(B_c^*\to B_c\gamma)$ on the mass difference $\Delta M=M_{B_c^*}-M_{B_c}$ as well.