A note on the tensor and vector exchange contributions to $K \bar K \to K \bar K, D \bar D \to D \bar D$ and $\pi^+ \pi^-\to \pi^+ \pi^-$ reactions

Abstract

In this note we study the tensor and vector exchange contributions to the elastic reactions involving the pseudoscalars mesons $\pi^+ \pi^-$, $K^{+}K^{-}$ and $D^{+}D^{-}$. In the case of the tensor-exchange contributions we assume that an intermediate tensor $f_2(1270)$ is dynamically generated from the interaction of two virtual $\rho$ mesons, with the use of a pole approximation. The calculation of the two-loop amplitude is facilitated since the triangle loops can be factorized and computed separately. The results show very small contributions coming from the tensor-exchange mechanisms when compared with those from the vector-exchange processes.Comment: 8 pages, 5 figure