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

TL;DR

This paper proposes studying the $B_c$ meson family through the decay mode $B_c(ns) o B_c(ms) + \pi^+\pi^-$ at LHCb and $Z^0$ factories, demonstrating the feasibility of experimental measurement based on QCD calculations.

Contribution

It provides a theoretical calculation of the decay rates for $B_c$ transitions via dipion emission, highlighting a practical method for identifying $B_c$ states in experiments.

Findings

Decay rates are within measurable range at LHC and $Z^0$ factory luminosities.

Trajectory analysis of pions offers a reliable identification method.

Feasibility of experimental detection is supported by numerical results.

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, $B_c^*(ns)\to B_c+\gamma$ 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.