Search for $B_c(ns)$ via the $B_c(ns)\to B_c(ms){\pi }^{+}{\pi }^{-}$ transition at LHCb and $Z_0$ factory

Abstract

It is interesting to study the characteristics of the whole family of $B_c$ which contains two different heavy flavors. LHC and the proposed $Z^0$ factory provide an opportunity because a large database on the $B_c$ family will be achieved. $B_c$ and its excited states can be identified via their decay modes. As suggested by experimentalists, $B_c^{\ast }(ns)\to B_c+\gamma$ is not easy to be clearly measured, instead, the trajectories of ${\pi }^{+}$ and ${\pi }^{-}$ occurring in the decay of $B_c(ns)\to B_c(ms)+{\pi }^{+}{\pi }^{-}$ ($n>m$) can be unambiguously identified, thus the measurement seems easier and more reliable, therefore this mode is more favorable at early running stage of LHCb and the proposed $Z^0$ factory. In this work, we calculate the rate of $B_c(ns)\to B_c(ms)+{\pi }^{+}{\pi }^{-}$ in terms of the QCD multipole-expansion and the numerical results indicate that the experimental measurements with the luminosity of LHC and $Z^0$ factory are feasible.

12 pages, 1 figures and 4 tables, acceptted by SCIENCE CHINA Physics, Mechanics & Astronomy (Science in China Series G)

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• The Electromagnetic Decays of $B_c^{\pm }(2S)$
• Electromagnetic transitions of $(b\bar{c})$ bound system
• The magnetic dipole transitions in the $(c\bar{b})$ binding system
• Re-study on the contribution of scalar potential and spectra of $c\bar{c}$, $b\bar{b}$ and $b\bar{c}(\bar{b}c)$ families
• Phenomenological study on the significance of the scalar potential and Lamb shift