Role of the triangle mechanism in the $\Lambda_b\rightarrow \Lambda_c\pi^-f_0(980)$ reaction

We investigate the $\Lambda_b\to\Lambda_c\pi^-f_0(980)$ production with a $f_0(980)$ decay into $\pi^+\pi^-$ via the $K^{*0}K^-K^+$ and $K^{*-}K^0\bar{K}^0$ triangle loops. These loops produce a peak around 1.42 GeV in the $\pi^-f_0(980)$ invariant mass distribution, which is the same mechanism as the one considered to explain the $a_1(1420)$ peak. In the $\pi^+\pi^-$ distribution obtained by fixing the $\pi^-f_0(980)$ invariant mass to some values, a clear peak of $f_0(980)$ is seen, and the $\pi^-f_0(980)$ distribution has a peak around $M_{\pi^-f_0}=1.42$ GeV, which is caused by the triangle mechanism of the $K^*\bar KK$ loop. The branching ratio of $\Lambda_b\rightarrow\Lambda_c\pi^-f_0(980)$ with $f_0(980)\rightarrow\pi^+\pi^-$ by the triangle mechanism, obtained by integrating the $\pi^-f_0(980)$ distribution from 1 to 1.6 GeV, is estimated to be the order $10^{-4}$. Future measurements of the $\Lambda_b\to\Lambda_c\pi^-f_0(980)$ branching ratio and the $\pi^-f_0(980)$ invariant mass distribution predicted in this work would give further clues to clarify the nature of the $a_1(1420)$ peak.