Triangle singularity in $τ^- \to ν_τπ^- f_0(980)$ ($a_0(980)$) decays

Abstract

We study the triangle mechanism for the decay $τ^- \to ν_τπ^- f_0(980)$, with the $f_0(980)$ decaying into $π^+ π^- $. This process is initiated by $τ^- \to ν_τK^{*0} K^-$ followed by the $K^{*0}$ decay into $π^- K^+$, 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 $πf_0(980)$ invariant mass. We find a narrow peak in the $π^+ π^-$ invariant mass distribution, which originates from the $f_0(980)$ amplitude. Similarly, we also study the triangle mechanism for the decay $τ\to νπ^- a_0(980)$, with the $a_0(980)$ decaying into $π^0 η$. The final branching ratios for $π^- f_0(980)$ and $π^- a_0(980)$ 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.

7 figures, 20 pages