Triangle singularity enhancing isospin violation in $D_s^ + o {pi ^ + }{pi ^0}{f_0}(980)$ and $overline B _s^0 o J/psi {pi ^0}{f_0}(980)$ decays

摘要

We investigate isospin violation in the $overline B _s^0 o J/psi {pi ^0}{a_0}(980)({f_0}(980))$ and $D_s^ + o {pi ^ + }{pi ^0}{a_0}(980)({f_0}(980))$ reactions, which proceed via a triangle mechanism. We show that the mechanism develops a singularity around the π ~(0) f _(0)(980) or π ~(0)a_(0)(980) invariant mass of 1420 MeV where the π ~(0) f _(0)and π ~(0)a_(0)decay modes are magnified and also the ratio of π ~(0)f_(0)to π ~(0)a_(0)production, stressing the role of the triangle singularities as a factor to enhance isospin violation. 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 lying scalar mesons.