Role of a triangle singularity in the $\gamma p\to K^{+}\mathrm{\Lambda }\left(1405\right)$ reaction

We show the effects of a triangle singularity mechanism for the $\gamma p\to K^{+}\mathrm{\Lambda }\left(1405\right)$ reaction. The mechanism has a $N^{*}$ resonance around 2030 MeV, which decays into $K^{*}\mathrm{\Sigma }$. The $K^{*}$ decays to $K^{+}\pi$, and the $\pi \mathrm{\Sigma }$ merge to form the $\mathrm{\Lambda }\left(1405\right)$. This mechanism produces a peak around $\sqrt{s}=2110$ MeV, and has its largest contribution around $\cos \theta =0$. The addition of this mechanism to other conventional ones leads to a good reproduction of $d\sigma /d\cos \theta$ and the integrated cross section around this energy, providing a solution to a problem encountered in previous theoretical models.

Figure 1

Mechanism for the $\gamma p\to K^{+}\mathrm{\Lambda }\left(1405\right)$ reaction involving the formation of $N^{*}\left(2030\right)$ and its decay to $K^{*}\mathrm{\Sigma }$.

Figure 2

Diagram for $\gamma -V$ conversion.

Figure 3

Two charge configurations to be considered.

Figure 4

Diagram of $K$ exchange.

Figure 5

(a) Contact term for the $\gamma p\to K^{+}{K}^{-}p$ reaction. (b) Diagram leading to the formation of the $K^{+}{\mathrm{\Lambda }}^{*}$ in the final state.

Figure 6

Diagram for $K^{*}$ exchange.

Figure 7

Results for $\sigma$ obtained with the triangle diagram amplitude $t_T$. Solid line for $t_T$ of the text. Dashed line, two form factors of the type ${\mathrm{\Lambda }}^2/({\mathrm{\Lambda }}^2+{\vec{q}}^2)$ have been implemented in addition, with $\mathrm{\Lambda }=0.8$ GeV.

Figure 8

The results of the fit to the differential cross section data ($\sqrt{s}=2000,2100,2200$ MeV [19]) for the $\gamma p\to K^{+}\mathrm{\Lambda }\left(1405\right)$ reaction. TS, triangle singularity; $K^{*},K^{*}$ exchange; $K,K$ exchange; C, contact term; solid line, total.

Figure 9

The predicted integral cross section for the $\gamma p\to K^{+}\mathrm{\Lambda }\left(1405\right)$ reaction.

Figure 10

Same as Fig. 8, but with the form factor in $K$ and $K^{*}$ exchanges.

Figure 11

Same as Fig. 9, but with the form factor in $K$ and $K^{*}$ exchanges.