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We have chosen the reactions $D_s^+ \to \pi^+ \pi^0 a_0(980) (f_0(980))$investigating the isospin violating channel $D_s^+ \to \pi^+ \pi^0 f_0(980)$.The reaction was chosen because by varying the $\pi^0 a_0(980) (f_0(980))$invariant mass one goes through the peak of a triangle singularity emergingfrom $D_s^+ \to \pi^+\bar K^* K$, followed by $\bar K^* \to \bar K \pi^0$ andthe further merging of $K \bar K$ to produce the $a_0(980)$ or $f_0(980)$. Wefound that the amount of isospin violation had its peak precisely at the valueof the $\pi^0 a_0(980) (f_0(980))$ invariant mass where the singularity has itsmaximum, stressing the role of the triangle singularities as a factor toenhance the mixing of the $f_0(980)$ and $a_0(980)$ resonances. We calculateabsolute rates for the reactions and show that they are within presentmeasurable range. The measurement of these reactions would bring furtherinformation into the role of triangle singularities in isospin violation andthe $a_0 -f_0$ mixing in particular and shed further light into the nature ofthe low energy scalar mesons.

Abnormal isospin violation and $a_0 -f_0$ mixing in the $D_s^+ \to \pi^+ \pi^0 a_0(980) (f_0(980))$ reactions