We study the triangle mechanism for the decay ${\tau }^{-}\to {\nu }_{\tau }{\pi }^{-}{f}_0(980)$, with the $f_0(980)$ decaying into ${\pi }^{+}{\pi }^{-}$. The mechanism for this process is initiated by ${\tau }^{-}\to {\nu }_{\tau }{K}^{*0}{K}^{-}$ followed by the $K^{*0}$ decay into ${\pi }^{-}{K}^{+}$, then the $K^{-}{K}^{+}$ produce the $f_0(980)$ through a triangle loop containing $K^{*}{K}^{+}{K}^{-}$ 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 formalism leads to final branching ratios for ${\pi }^{-}{f}_0(980)$ and ${\pi }^{-}{a}_0(980)$ 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 of the “$a_1(1420)$” peak observed in other reactions.

• Received 3 October 2018
• Revised 19 November 2018

DOI:https://doi.org/10.1103/PhysRevD.99.016021

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Published by the American Physical Society