Triangle singularity in ${\tau }^{-}\to {\nu }_{\tau }{\pi }^{-}{f}_0(980)$ ($a_0(980)$) decays

Abstract

We study the triangle mechanism for the decay ${\tau }^{-}\to {\nu }_{\tau }{\pi }^{-}{f}_0(980)$, with the $f_0(980)$ decaying into ${\pi }^{+}{\pi }^{-}$. This process is initiated by ${\tau }^{-}\to {\nu }_{\tau }{K}^{\ast 0}{K}^{-}$ followed by the $K^{\ast 0}$ decay into ${\pi }^{-}{K}^{+}$, then the $K^{-}{K}^{+}$ produce the $f_0(980)$ through a triangle loop containing $K^{\ast }{K}^{+}{K}^{-}$ which develops a singularity around $1420$~MeV in the $\pi f_0(980)$ invariant mass. We find a narrow peak in the ${\pi }^{+}{\pi }^{-}$ invariant mass distribution, which originates from the $f_0(980)$ amplitude. Similarly, we also study the triangle mechanism for the decay $\tau \to \nu {\pi }^{-}{a}_0(980)$, with the $a_0(980)$ decaying into ${\pi }^0\eta$. The final branching ratios for ${\pi }^{-}{f}_0(980)$ and ${\pi }^{-}{a}_0(980)$ are of the order of $4\times 10^{-4}$ and $7\times 10^{-5}$, respectively, which are within present measurable range. Experimental verification of these predictions will shed light on the nature of the scalar mesons and on the origin for the "$a_1(1420)$" peak observed in other reactions.

Comments: 7 figures, 20 pages