Triangle singularity in $\tau^- \to \nu_\tau \pi^- f_0(980)$ ($a_0(980)$) decays

TL;DR

This paper investigates a triangle singularity mechanism in tau decays involving scalar mesons, predicting narrow peaks and measurable branching ratios that can clarify the nature of scalar mesons and related experimental peaks.

Contribution

It introduces a novel triangle mechanism explanation for tau decay processes involving $f_0(980)$ and $a_0(980)$, with specific predictions for invariant mass peaks and branching ratios.

Findings

A narrow peak in the $ o u_ au o u_ au o u_ au$ invariant mass distribution.

Predicted branching ratios of about $4 imes 10^{-4}$ for $ au^- o u_ au o o o$ and $7 imes 10^{-5}$ for $ au^- o u_ au o o o$ decays.

The triangle mechanism can explain the $a_1(1420)$ peak observed in other reactions.

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 $\tau^- \to \nu_\tau K^{*0} K^-$ 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 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.