FIG. 1: Feynman diagrams for γ + N → K + Σ ∗ ( 3 2 $^{+}$). (a) t-channel; (b) s-channel; (c) u-channel; (d) contact term. 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 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 where Q$_{N}$ is the electric charge (in unite of e ), and κ$_{N}$ denotes the magnetic moment of the nucleon. For the s-channel spin- 3 2 and spin- 5 2 resonances ex- change, the effective Lagrangians for the interactions are The reaction γp → K $^{+}$Σ ∗ 0 contains the u-channel Λ(1116) exchange. The effective Lagrangians are 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. For Δ and Δ resonances of isospin-3/2, the effective La- grangians have the isospin structure 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 2 and L RK Σ ∗ ( 3 2$^{±}$ ) = − h$_{1}$ m$_{K}$ ∂ $^{α}$K Σ ∗ $^{µ}$Γ ( ± ) α R$_{µ}$ + ih$_{2}$ ( m$_{K}$ ) $_{2}$∂ $^{µ}$∂$^{α}$K Σ ∗ $_{α}$Γ ( ± $^{)}$R$_{µ}$ + H . c ., (7) L RK Σ ∗ ( 5 2$^{±}$ ) = ih$_{1}$ m 2 K ∂ $^{µ}$∂$^{β}$K Σ ∗ $^{α}$Γ ( ∓ ) µ R$_{αβ}$ − h$_{2}$ ( m$_{K}$ ) $_{3}$∂ $^{µ}$∂$^{α}$∂$^{β}$K Σ ∗ $_{µ}$Γ ( ∓ $^{)}$R$_{αβ}$ + H . c ., (8) Γ ( ± ) µ = ( γ$_{µ}$γ$_{5}$ γ$_{µ}$ ) , Γ ( ± ) = ( γ$_{5}$ 1 ) . (9) K Σ ∗ · T ( 1 2 , 3 2 )Δ = √$_{3}$$_{K}$ $^{−}$Σ ∗ $^{+}$Δ ++ − √$_{2}$$_{K}$ $^{−}$Σ ∗ $^{0}$Δ + − K $^{−}$Σ$^{∗−}$Δ 0 + K $^{0}$Σ ∗ $^{+}$Δ + − √$_{2}$$_{K}$ $^{0}$Σ ∗ $^{0}$Δ 0 √$_{3}$$_{K}$ $^{0}$Σ $^{∗−}$Δ$^{−}$. (10) L γ ΛΣ ∗ = − ief$_{1}$ 2 M$_{Λ}$ Λ γ$_{ν}$γ$_{5}$F $^{µν}$Σ ∗ µ − ef$_{2}$ (2 M$_{Λ}$ ) $_{2}$∂$_{ν}$ Λ γ$_{5}$F $^{µν}$Σ ∗ µ + H . c ., (11) L KN Λ = g$_{KN}$$_{Λ}$ M$_{N}$ + M$_{Λ}$ Nγ $^{µ}$γ$_{5}$ Λ ∂$_{µ}$K + H . c ., (12) L $_{γNR}$( 3 2$^{±}$ ) = − ief$_{1}$ 2 M$_{N}$ N Γ ( ± ) ν F $^{µν}$R$_{µ}$ − ef$_{2}$ (2 M$_{N}$ ) $_{2}$∂$_{ν}$ N Γ ( ± $^{)}$F $^{µν}$R$_{µ}$ + H . c ., (5) L $_{γNR}$( 5 2$^{±}$ ) = ef$_{1}$ (2 M$_{N}$ ) $_{2}$N Γ ( ∓ ) ν ∂ $^{α}$F $^{µν}$R$_{µα}$ − ief$_{2}$ (2 M$_{N}$ ) $_{3}$∂$_{ν}$ N Γ ( ∓ $^{)}$∂ $^{α}$F $^{µν}$R$_{µα}$ + H . c ., (6) L γNN = − eN ( γ $^{µ}$A$_{µ}$ Q$_{N}$ − κ$_{N}$ 2 M$_{N}$ σ $^{µν}$∂$_{ν}$ A$_{µ}$ ) N , (4) K = ( K $^{−}$, K $^{0}$) , Σ · τ = ( Σ 0 √$_{2Σ}$ + √$_{2Σ}$ − − Σ 0 ) , N = ( p n ) , (3) L γKK = ieA$_{µ}$ ( K $^{−}$∂ $^{µ}$K + − ∂ $^{µ}$K $^{−}$K $^{+}$) , (1) L KN Σ ∗ = f$_{KN}$$_{Σ}$ ∗ m$_{K}$ ∂$_{µ}$K Σ ∗ µ · τN + H.c. , (2)