$\varphi (2170)$ production in the process $\gamma p\to \eta \varphi p$

We have studied the $\gamma p\to \eta \varphi p$ reaction within the effective Lagrangian approach by considering the contribution of the intermediate state $\varphi (2170)$ production, and the background contributions of $t$-channel ${\pi }^0$ and $\eta$ mesons exchanges with the intermediate states $N$ and $N(1535)$. Our calculations show that there may be a peak, at least a bump structure around 2180 MeV associated to the resonance $\varphi (2170)$ in the $\eta \varphi$ mass distribution. We suggest to search for the resonance $\varphi (2170)$ in this reaction, which would be helpful to shed light on its nature.

Figure 1

Feynman diagrams for the $\gamma p\to \eta \varphi p$ reaction. (a) the contribution of the $t$-channel ${\pi }^0$ and $\eta$ exchanges with the intermediate states $N$ and $N^{*}$. (b) the contribution of the intermediate states $\varphi (2170)$ production.

Figure 2

The $\eta \varphi$ mass distribution of the $\gamma p\to \eta \varphi p$ reaction with $E_{\gamma }=8\mathrm{GeV}$. The curves labeled as “B” and “${\varphi }^{*}$” stand for the contributions of the background and the intermediate $\varphi (2170)$ production, respectively. The curve labeled as “T” corresponds to the total contributions.

Figure 3

The $\eta \varphi$ mass distribution of the $\gamma p\to \eta \varphi p$ reaction with $E_{\gamma }=8\mathrm{GeV}$ in the presence of $\mathrm{\Gamma }(\varphi (2170)\to \eta \varphi )\simeq 6.6\mathrm{MeV}$. The curves labeled as “T-1.0” (‘T-1.3’) and “${\varphi }^{*}-1.0$” (“${\varphi }^{*}-1.3$”) correspond to the contributions of the full model and the intermediate $\varphi (2170)$ with the ${\mathrm{\Lambda }}_{{\varphi }^{*}}=1.0(1.3)\mathrm{GeV}$, respectively.

Figure 4

Total cross section of the $\gamma p\to \varphi \eta p$ reaction.