The $\overline{p}p\to \varphi \varphi$ reaction in an effective Lagrangian approach

We investigate the $\overline{p}p\to \varphi \varphi$ reaction within an effective Lagrangian approach. We show that the inclusion of either a scalar meson $f_0$ or a tensor meson $f_2$ in the $s$-channel can lead to a fairly good description of the bump structure of the total cross section around the invariant $\overline{p}p$ mass $W\simeq 2.2$ GeV, which cannot be reproduced with only the “background” contributions from $t$- and $u$-channel $N^{*}\left(1535\right)$ resonance as studied in a previous work. From the fits, we infer the properties of the involved scalar or tensor resonances.

Figure 1

Feynman diagrams for the $\overline{p}p\to \varphi \varphi$ reaction. The contributions from $t$- and $u$-channel $N^{*}\left(1535\right)$ resonance exchange, and $s$-channel $f_0$ or $f_2$ resonance are considered.

Figure 2

Total cross sections for the $\overline{p}p\to \varphi \varphi$ reaction. The experimental data are taken from Ref. [5]. The curves are the contributions from $s$-channel $f_0$ and $f_2,t$- and $u$-channel $N^{*}\left(1535\right)$ resonance, and the total results of fits I and II.

Figure 3

Differential cross sections for $\overline{p}p\to \varphi \varphi$ reaction. The curves are the contributions from $s$-channel scalar meson $f_0$ (dash-dotted) and tensor meson $f_2$ (dotted), $t$- and $u$-channel $N^{*}\left(1535\right)$ resonance (dashed), and the total results of fit I (dash-dot-dotted) and fit II (solid).