Mr
Xin Li
(School of Physics and Astronomy, University of Minnesota)
Recent experimental data have revealed existence of a considerable number of peaks near the thresholds for pairs of mesons containing heavy $c$ or $b$ quarks. Such are $Z_b(10610)$, $Z_b(10650)$, $Z_c(3900)$, $Z_c(3885)$, $Z_c(4020)$ and $Z_c(4025)$. The nature of those peaks are not all clear. Some of them result from the strong-interaction dynamics in the $S$-wave of a heavy meson-antimeson pair. We consider production of overall neutral pairs consisting of heavy charmed or bottom meson and antimeson in the processes, where the pair can be created in an $S$-wave, such as the production of the pairs with a photon or a neutral Pion emitted in $e^+e^-$ collision. The ratio $R^{c/n}$ of the yield of pairs of charged mesons to that of neutral mesons near the threshold for the heavy pair is strongly affected by the isospin breaking due to the isotopic mass differences and due to the Coulomb interaction between the charged mesons. The actual behavior of the isospin breaking in $R^{c/n}$ 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 $R^{c/n}$ 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.
Summary
We have considered the interplay between the isospin violating mass differences, the Coulomb interaction and the strong scattering in the threshold behavior of the charged-to-neutral yield ratio $R^{c/n}$ for the $S$-wave production of overall neutral pairs of heavy charmed or bottom mesons. The expressions which take into account all orders in the mass differences and in the Coulomb interaction are derived in the limit where the strong scattering of heavy mesons can be described by the scattering lengths in the isoscalar and isovector channels, which description is appropriate for the near-threshold behavior in the $S$ wave. In particular we find that the onset of the yield of pairs of charged mesons starts with a finite step at the threshold. The height of the step is sensitive to a strong scattering length, and its measurement can be used as a probe of strong interaction between the heavy mesons.
Prof.
Mikhail Voloshin
(School of Physics and Astronomy, University of Minnesota, USA; William I. Fine Theoretical Physics Institute, University of Minnesota, USA; Institute of Theoretical and Experimental Physics, Moscow, Russia.)
Mr
Xin Li
(School of Physics and Astronomy, University of Minnesota)
