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listed. In scheme I, we keep h = 1 fixed for the contact term to be identical to the γp → K $^{+}$Σ ∗ 0 process, and then include the contribution of K Σ( 1 2 $^{−}$) photoproduc- tion for the process. The coupling constant of Σ( 1 2 $^{−}$) to KN and the corresponding cut-off parameter are tuned to describe the experimental data. In scheme II, we do not consider Σ( 1 2 $^{−}$) production, and tune parameter h of the contact term to describe the data. 

In Fig. 2 we show the result of the linear beam asym- metry for γn → K $^{+}$Σ $^{−}$( 1 2 $^{−}$) with cos θ$_{c}$$_{.}$$_{m}$$_{.}$ ≥ 0 . 6, i.e. , the cross sections in Eq. (31) are integrated results for cos θ$_{c}$$_{.}$$_{m}$$_{.}$ = 0 . 6 − 1. The process has a large negative beam asymmetry that approaches − 1. This result comes from the fact that K $^{+}$Σ $^{−}$( 1 2 $^{−}$) is produced mainly from the t-channel kaon exchange process. For the t-channel kaon exchange process, the photon spin is necessary to be vertical to the reaction plane due to angular momentum conservation, and such photon corresponds to the beam (electromagnetic field) with polarization parallel to the reaction plane, i.e. , σ$_{⊥}$ = 0. Thus the K $^{+}$Σ $^{−}$( 1 2 $^{−}$) pro- duction contributes negatively to the beam asymmetry. If a portion of the detected Λ π stems from Σ( 1 2 $^{−}$), the measured beam asymmetry can be pulled to the negative side, and the observed negative beam asymmetry may be explained. 

In Fig. 3, the differential cross sections for the process γn → K $^{+}$Σ ∗− with respect to cos θ$_{c}$$_{.}$$_{m}$$_{.}$ are shown and compared with the LEPS data [9]. The solid lines are the results of scheme I, and the dashed lines are the results 

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of scheme II. The contributions from Σ( 1 2 $^{−}$) production in scheme I are also shown by the dash-dotted lines. 

In Fig. 4 and Fig. 5, the results for the linear beam asymmetry and integrated cross sections of the reaction γn → K $^{+}$Σ ∗− are shown and compared with the LEPS data [9], respectively. The cross sections are intergrated results in phase space cos θ$_{c}$$_{.}$$_{m}$$_{.}$ = 0 . 6 − 1 . 0. The solid lines are the results of scheme I, i.e. , including both Σ $^{∗}$( 3 2 $^{+}$) production with h = 1 and the contribution from Σ( 1 2 $^{−}$). The dashed lines are the results of scheme II, i.e. , for Σ $^{∗}$( 3 2 $^{+}$) production alone with h = 1 . 11. The dotted lines are the results with the h = 1 and without the contribution from Σ( 1 2 $^{−}$). The contribution from Σ( 1 2 $^{−}$) production to the cross section alone is shown by the dash-dotted line in Fig. 5. 

From Fig.3-5, one can see that both schemes can well describe the LEPS data. For scheme I, since the Σ( 1 2 $^{−}$) alone gives a large negative beam asymmetry approach- ing − 1 as shown in Fig. 2, a portion of Σ( 1 2 $^{−}$) in this pro- cess helps to explain the observed negative beam asym- metry. At the same time, we find that tuning the pa- 

