Abnormal isospin violation and a0−f0 mixing in the Ds+→π+π0a0(980)(f0(980)) reactions

We have chosen the reactions Ds+→π+π0a0(980)(f0(980)) investigating the isospin violating channel Ds+→π+π0f0(980). The reaction was chosen because by varying the π0a0(980)(f0(980)) invariant mass one goes through the peak of a triangle singularity emerging from Ds+→π+K¯*K, followed by K¯*→K¯π0 and the further merging of KK¯ to produce the a0(980) or f0(980). We found that the amount of isospin violation had its peak precisely at the value of the π0a0(980)(f0(980)) invariant mass where the singularity has its maximum, stressing the role of the triangle singularities as a factor to enhance the mixing of the f0(980) and a0(980) resonances. We calculate absolute rates for the reactions and show that they are within present measurable range. The measurement of these reactions would bring further information into the role of triangle singularities in isospin violation and the a0−f0 mixing, in particular, and shed further light into the nature of the low energy scalar mesons.