content_image/427736.jpg content_image/427738.jpg content_image/427739.jpg content_image/427741.jpg content_image/427735.jpg content_image/427737.jpg content_image/427740.jpg content_image/427746.jpg content_image/427745.jpg content_image/427743.jpg content_image/427747.jpg content_image/427744.jpg content_image/427742.jpg
where f$_{1}$ = 4 . 52, f$_{2}$ = 5 . 63 are obtained from decay width Γ(Σ ∗ → Λ γ ) and model predicted helicity am- plitudes; and g$_{KN}$$_{Λ}$ = − 13 . 24 is estimated from flavor SU(3) symmetry relation as in Ref. [12]. ∗ 

For u-channel Σ exchange, the effective Lagrangian for γ Σ $^{∗}$Σ∗ is 

with 

<img src='content_image/427736.jpg'>

where Q$_{Σ}$ ∗ denotes the electric charge of Σ ∗ in unit of e and κ$_{Σ}$ ∗ denotes the anomalous magnetic moment of Σ $^{∗}$; κ$_{Σ}$ $_{∗}$0 = 0 . 36 and κ$_{Σ}$ ∗− = − 2 . 43 are taken from the quark model prediction [23]. 

For each vertex of these channels, a form factor is at- tached to describe the off-shell properties of the ampli- tudes. For t-channel K meson exchange, we adopt the form factor [12] 

where q$_{t}$ = k − q is the 4-momentum transfer in t-channel. For the s-channel and u-channel processes, we adopt the form factor 

<img src='content_image/427738.jpg'>

where the q$_{ex}$ and M$_{ex}$ are the 4-momentum and the mass of the exchanged hadron, respectively. For s-channel N and Δ exchange and the u-channel processes, we take n = 1 as in Ref. [12]; for s-channel resonances exchange, n → ∞ is taken to obtain the Gaussian form for the form factors [12] 

<img src='content_image/427739.jpg'>

The cutoff parameters Λ$_{M}$ and Λ$_{B}$ were taken to be 0.83 and 1.0 GeV, respectively, in Refs. [9, 12], by fitting to the γp → K $^{+}$Σ ∗ 0 data. The contact term illustrated with Fig. 1(d) serves to 

keep the full amplitude gauge invariant. The contact currents for K Σ ∗ photoproduction are related to the La- grangian of Eq.(2). For the process γp → K $^{+}$Σ ∗ $^{0}$, we adopt the contact current [12, 18] 

where C ν is expressed as 

<img src='content_image/427741.jpg'>

<img src='content_image/427735.jpg'>

<img src='content_image/427737.jpg'>

<img src='content_image/427740.jpg'>

Here the Lorenz index µ and ν couple to that of Σ ∗ and the photon respectively; f$_{t}$ = F 2 M and f$_{s}$ = F 2 $_{B}$( s, M$_{N}$ ) are form factors squared, and t = q 2 t and s = q 2 s are squared momentum transfer for t- and s-channel; h is a parameter to be fitted to experiments, and h = 1 is used in Ref.[12]. From this contact term, we can check that the total amplitude is gauge invariant. For the process γn → K $^{+}$Σ $^{∗−}$, the contact current is [18] 

with 

<img src='content_image/427746.jpg'>

Where f$_{u}$ = F 2 $_{B}$( u, M ∗ $_{Σ}$) is form factor squared, and u = q 2 u is squared momentum transfer for u-channel. For the propagators, we use 1 / ( q 2 t − m 2 $_{K}$) for t-channel K meson exchange. For the propagator of a baryon with mass m and 4-momentum p , we use ̸ p + m p $^{2}$− m 2 for spin-1/2 propagator; 

<img src='content_image/427745.jpg'>

for spin-3/2 propagator; and 

for spin-5/2 propagator, where 

<img src='content_image/427743.jpg'>

with 

For the s-channel resonances with sizeable width Γ, we replace the denominator 1 p $^{2}$− m 2 in the propagators by 1 p $^{2}$− m $^{2}$+ im $_{Γ}$, and replace m in the rest of the propagators by √ p $^{2}$. 

Since five quark components for baryons may exist, there may be a Σ( 1 2 $^{−}$) that has a large probability of five quark structure with mass near 1380 MeV as models pre- dict [13, 16]. Both Σ $^{∗}$( 3 2 $^{+}$) and Σ( 1 2 $^{−}$) decay strongly to 

<img src='content_image/427747.jpg'>

<img src='content_image/427744.jpg'>

<img src='content_image/427742.jpg'>

## B. K Σ( 1 2$^{−}$ ) photoproduction 

