Role of the triangle mechanism in the ${\Lambda }_b\to {\Lambda }_c{\pi }^{-}{f}_0(980)$ reaction

Abstract

We investigate the ${\Lambda }_b\to {\Lambda }_c{\pi }^{-}{f}_0(980)$ production with a $f_0(980)$ decay into ${\pi }^{+}{\pi }^{-}$ via the $K^{\ast 0}{K}^{-}{K}^{+}$ and $K^{\ast -}{K}^0{\bar{K}}^0$ 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 $K^{\ast }\bar{K}K$ loop. The branching ratio of ${\Lambda }_b\to {\Lambda }_c{\pi }^{-}{f}_0(980)$ with $f_0(980)\to {\pi }^{+}{\pi }^{-}$ 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.

arXiv comment20 pages, 9 figures

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• The role of triangle singularity in the decay process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$
• Box Singularity Conditions in Box Diagrams of Decay Processes
• Proposal to detect a moving triangle singularity in $\psi (2S)\to {\pi }^{+}{\pi }^{-}{K}^{+}{K}^{-}$ process