Abnormal isospin violation and a_0 - f_0 mixing in the D_s~+ → π~+ π~0a_0(980)(f_0(980)) reactions

摘要

We have chosen the reactions D_s~+→ π~+π~0a_0(980)(f_0(980)) investigating the isospin violating channel D_s~+→ π~+π~0f~0(980). The reaction was chosen because by varying the π~0a_0(980)(f_0(980)) invariant mass one goes through the peak of a triangle singularity emerging from D_s~+→ π~+K~*K, followed by K~*→ K π~0 and the further merging of KK to produce the a_0(980) or f_0(980). We found that the amount of isospin violation had its peak precisely at the value of the π~a_0(980)(f_0(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 f_0(980) and a_0(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 a_0 - f_0 mixing, in particular, and shed further light into the nature of the low energy scalar mesons.