Isospin violation in the yield of S -wave heavy meson pairs near threshold

We consider the production of overall neutral pairs consisting of heavy D(*) or B(*) mesons and antimesons in processes where such pairs can be created in an S wave, such as e+e-→π0D*D̄(*), e+e-→γD(*)D̄(*), and similar reactions with B(*) mesons. The ratio Rc/n of the yield of pairs of charged mesons to that of neutral mesons near the threshold for the heavy pair is strongly affected by isospin breaking due to the isotopic mass differences and due to the Coulomb interaction between the charged mesons. The actual behavior of isospin breaking in Rc/n is also sensitive to the strong interaction between the heavy mesons, so that experimental measurement of this ratio can be used as a probe of this strong interaction. We calculate Rc/n at and very near the threshold in terms of the isotopic scattering lengths for the meson pairs. In particular, we find that the yield of pairs of charged mesons does not go to zero at exactly the threshold, but rather starts with a finite step, whose height depends on the value of the scattering length in a particular channel.