content_image/427666.jpg content_image/427663.jpg content_image/427662.jpg content_image/427660.jpg content_image/427661.jpg content_image/427664.jpg content_image/427665.jpg content_image/427654.jpg content_image/427655.jpg content_image/427657.jpg content_image/427659.jpg content_image/427656.jpg content_image/427658.jpg
<img src='content_image/427666.jpg'>

Σ $^{∗}$, respectively. From the investigation of Ref. [12], the main contributions come from the t-channel K meson ex- change, the s-channel N and Δ as well as their resonances exchange, the u-channel Λ (for neutral propagator only) and Σ $^{∗}$( 3 2 $^{+}$) exchange and the contact term. 

For the t-channel K meson exchange, the relevant ef- fective Lagrangians are 

with the isospin structure of K Σ $^{∗}$N coupling 

<img src='content_image/427663.jpg'>

where f$_{KN}$$_{Σ}$ ∗ is the coupling constant and is taken as f$_{KN}$$_{Σ}$ ∗ = − 3 . 22 from the SU(3) flavor symmetry relation as in Ref. [12]; m$_{K}$ is the mass for K meson. 

For the s-channel nucleon exchange, the effective La- grangians for the interactions contain Eq. (2) as well as 

<img src='content_image/427662.jpg'>

where Q$_{N}$ is the electric charge (in unite of e ), and κ$_{N}$ denotes the magnetic moment of the nucleon. 3 5 

For the s-channel spin- 2 and spin- 2 resonances ex- change, the effective Lagrangians for the interactions are 

<img src='content_image/427660.jpg'>

<img src='content_image/427661.jpg'>

<img src='content_image/427664.jpg'>

<img src='content_image/427665.jpg'>

<img src='content_image/427654.jpg'>

<img src='content_image/427655.jpg'>

where F µν = ∂ $^{µ}$Aν − ∂ $^{ν}$A$^{µ}$; R$_{µ}$ and R$_{µα}$ denote the spin- 3 2 and spin- 5 2 fields, respectively, and 

For Δ and Δ resonances of isospin-3/2, the effective La- grangians have the isospin structure 

<img src='content_image/427657.jpg'>

We consider 3 PDG resonances in s-channel, namely, N 3 2$^{−}$ (2080), Δ 3 2$^{−}$ (1940) and Δ 5 2 + (2000), which are the most prominent ones as stated in Ref. [12]. The cou- pling constants f$_{1}$ and f$_{2}$ can be calculated from the helicity amplitudes in PDG [19] or model predictions with Eq.(B3) of Ref. [12]. For γN Δ coupling, we have f$_{1}$ = 4 . 04 and f$_{2}$ = 3 . 87. From the predicted helicity am- plitudes in Ref. [20], one gets f$_{1}$ = − 1 . 25 and f$_{2}$ = 1 . 21 for γpN $^{∗}$(2080) coupling; f$_{1}$ = 0 . 381 and f$_{2}$ = − 0 . 256 for γnN $^{∗}$(2080) coupling; f$_{1}$ = 0 . 39 and f$_{2}$ = 0 . 57 for γN Δ(1940) coupling, and f$_{1}$ = − 0 . 68, f$_{2}$ = − 0 . 062 for γN Δ(2000) coupling. For Δ K Σ ∗ coupling, h$_{1}$ = 2 . 0 and h$_{2}$ = 0 are used from h$_{1}$ = − f$_{K}$$_{ΔΣ}$ ∗ $_{/}$√$_{3 with}$ f$_{K}$$_{ΔΣ}$ ∗ = − 3 . 46 [21]. For the resonances coupling to K Σ $^{∗}$, the coupling constants h$_{1}$ and h$_{2}$ can be calculated from Eq.(B11)-(B18) of Ref. [12] from the model pre- dicted amplitudes G ( l ) [22]. In our concrete calculation, h$_{1}$ = 0 . 24 and h$_{2}$ = − 0 . 54 for N $^{∗}$(2080) K Σ ∗ coupling, h$_{1}$ = − 0 . 68 and h$_{2}$ = 1 . 0 for Δ(1940) K Σ ∗ coupling, and h$_{1}$ = 1 . 1 and h$_{2}$ = 0 . 21 for Δ(2000) K Σ ∗ coupling are taken. ∗ 0 

The reaction γp → K $^{+}$Σ contains the u-channel Λ(1116) exchange. The effective Lagrangians are 

<img src='content_image/427659.jpg'>

<img src='content_image/427656.jpg'>

<img src='content_image/427658.jpg'>

