Experimental study of the reactions $\overline{p}p\to {\pi }^{-}{\pi }^{+}$ and $K^{-}{K}^{+}$ between 360 and 760 MeV/c

The folded differential cross sections $\frac{d\sigma }{d\Omega \left({\theta }^{*}\right)}+\frac{d\sigma }{d\Omega \left({\pi -\theta }^{*}\right)}$, where ${\theta }^{*}$ is the center-of-mass angle of the negatively charged outgoing particle, have been measured for the reactions $\overline{p}p\to {\pi }^{-}{\pi }^{+}$ and $K^{-}{K}^{+}$ at 15 incident beam momenta between 360 and 760 MeV/c with much better statistics than previous experiments. The total cross sections for these reactions, ${\sigma }_{{\pi }^{-}{\pi }^{+}}$ and ${\sigma }_{{\kappa }^{-}{\kappa }^{+}}$, have also been obtained by integrating the folded differential cross sections. The folded differential cross sections of both reactions show a similar behavior at all measured beam momenta, characterized by a prominent peak at $\left|cos{\theta }^{*}\right|=1\mathrm{}$. The cross section ${\sigma }_{{\pi }^{-}{\pi }^{+}}$ shows a smooth but rapidly decreasing behavior as the beam momentum increases up to 550 MeV/c, whereas ${\sigma }_{{\kappa }^{-}{\kappa }^{+}}$ shows a smooth and flat momentum dependence. These results are compared with some theoretical calculations based on nonrelativistic quark models. Although the shape of the folded differential cross section of the $\overline{p}p\to {\pi }^{-}{\pi }^{+}$ reaction is rather well reproduced by these models, that of the $\overline{p}p\to K^{-}{K}^{+}$ reaction, and, in particular, the prominent peak at $\left|cos{\theta }^{*}\right|=1\mathrm{}$ cannot be explained at all. The information from other experiments indicates that this discrepancy is most pronounced at the backward angles. Moreover, the momentum dependence of both ${\sigma }_{{\pi }^{-}{\pi }^{+}}$ and ${\sigma }_{{\kappa }^{-}{\kappa }^{+}}$ is not satisfactorily reproduced by these models.