Photoproduction of $\gamma N\to K^{+}{\mathrm{\Sigma }}^{*}\left(1385\right)$ in the Reggeized framework

Photoproduction of $K{\mathrm{\Sigma }}^{*}\left(1385\right)$ on the nucleon is investigated within the Regge framework, and the reaction mechanism is analyzed based on the data existing in the channels $\gamma p\to K^{+}{\mathrm{\Sigma }}^{*0}$ and $\gamma n\to K^{+}{\mathrm{\Sigma }}^{*-}$. The Reggeization of the $t$-channel meson exchanges $K\left(494\right)+K^{*}\left(892\right)+K_2^{*}\left(1430\right)$ is employed to construct the photoproduction amplitude. The Rarita-Schwinger formalism is applied for the spin-$3/2^{+}$ strangeness-baryon ${\mathrm{\Sigma }}^{*}$ with a special gauge prescription utilized for the convergence of these reaction processes. Within a set of coupling constants determined from the symmetry argument for $K$ and $K^{*}$ and from the duality and vector dominance for $K_2^{*}$, the data of both processes are reproduced to a good degree. The production mechanism of these processes is featured by the dominance of the contact term over the $K$ exchange. The role of $K_2^{*}$ is found to be more important than that of $K^{*}$.

Figure 1

Feynman diagrams for $\gamma N\to K^{+}{\mathrm{\Sigma }}^{*}$. (a) The exchange of $K$ in the $t$-channel, (b) the proton pole in the $s$-channel, (c) the ${\mathrm{\Sigma }}^{*}$ pole in the $u$-channel, and (d) the contact terms are the basic ingredients for the gauge invariance of the reaction. (a) $K^{*}$ and $K_2^{*}$ exchanged in the $t$-channel are themselves gauge invariant.

Figure 2

The total cross section for $\gamma p\to K^{+}{\mathrm{\Sigma }}^{*0}\left(1385\right)$. Contributions of the contact term and meson exchanges are shown with the dotted, dashed, dashed-dotted, and dashed-dot-dotted curves, respectively. The dominance of the contact term is shown. The CLAS Collaboration data are taken from Ref. [4]. The data of the CBCG and ABBHHM Collaborations are from Refs. [13, 14, 15].

Figure 3

The differential cross sections for $\gamma p\to K^{+}{\mathrm{\Sigma }}^{*0}\left(1385\right)$. The angle dependence of the cross sections are shown in the first three panels (a)–(c) with the data taken from the CLAS Collaboration [4]. The energy dependence is shown in panel (d) with the data from the LEPS Collaboration [6]. The contributions of the contact terms and the respective meson exchanges are displayed in (b) and (d) with the same notations as in Fig. 2.

Figure 4

The total cross section for $\gamma n\to K^{+}{\mathrm{\Sigma }}^{*-}\left(1385\right)$. The contributions of the contact term and meson exchanges are displayed with the same notations as in Fig. 2. The dominance of the contact term is shown. The data are taken from Ref. [16].

Figure 5

The differential cross-sectional ${(s-M^2)}^{2}d\sigma /dt$ for $\gamma n\to K^{+}{\mathrm{\Sigma }}^{*-}\left(1385\right)$ at $E_{\gamma }=3–5\mathrm{GeV}$. The solid and dotted curves are the cross sections at $E_{\gamma }=3\mathrm{GeV}$ with and without $K_2^{*}$, showing the role of the tensor meson. The data are taken from Ref. [16].

Figure 6

The dependence of the differential cross sections for $\gamma n\to K^{+}{\mathrm{\Sigma }}^{*-}\left(1385\right)$ on the energy (upper panels) and angle (lower panels). The model predictions are given by the gray band to cover the range of the angle denoted. The contributions of the contact terms and the respective meson exchanges estimated at $cos\theta =0.85$ are displayed in the upper right and at $E_{\gamma }=2.4\mathrm{GeV}$ in the lower right panels with the same notations as in Fig. 4. The dip structure appears there due to the canonical phase $(1+e^{-i\pi {\alpha }_K})/2$ of the $K$ exchange. The data of the LEPS Collaboration (black squares) are taken from Ref. [7] and those of the CLAS Collaboration (empty circles) are from Ref. [5].

Figure 7

The energy dependence of the beam polarization asymmetries for $\gamma n\to K^{+}{\mathrm{\Sigma }}^{-}\left(1190\right)$ from (a) $\mathrm{\Sigma }=\frac{d{\sigma }_y-d{\sigma }_x}{d{\sigma }_y+d{\sigma }_x}$ and $\gamma n\to K^{+}{\mathrm{\Sigma }}^{*-}\left(1385\right)$ from (b) $\mathrm{\Sigma }=-\frac{d{\sigma }_y-d{\sigma }_x}{d{\sigma }_y+d{\sigma }_x}$. The beam polarization asymmetry in (a) is calculated by the model in Ref. [19]. The model predictions are given by the gray band to cover the range of the angle denoted. The data are taken from Ref. [7].