# Possible Σ( 1 2$^{−}$ ) under the Σ ∗ (1385) peak in K Σ ∗ photoproduction 

Institute of High Energy Physics, CAS, P.O. Box 918(4), Beijing 100049, China and Theoretical Physics Center for Science Facilities, CAS, Beijing 100049, China 

Puze Gao, Jia-Jun Wu and B.S. Zou 

The LEPS collaboration has recently reported a measurement of the reaction γn → K $^{+}$Σ ∗− (1385) with linearly polarized photon beam at resonance region. The observed beam asymmetry is sizably negative at E$_{γ}$ = 1 . 8 − 2 . 4GeV, in contrast to the presented theoretical prediction. In this paper, we calculate this process in the framework of the effective Lagrangian approach. By including a newly proposed Σ( J P = 1 2$^{−}$ ) state with mass around 1380 MeV, the experimental data for both γn and γp experiments can be well reproduced. It is found that the Σ( 1 2$^{−}$ ) and/or the contact term may play important role and deserve further investigation. 

With the development of accelerator facilities, strangeness production from photon-nucleon scattering has been extensively studied at resonance region [1–9]. These experiments can provide not only more informa- tion on the properties and interactions of the known res- onances, but also clues for the existence of some new res- onances. For K Σ $^{∗}$(1385) photoproduction, high statistic data have been available only recently. The CLAS collab- oration has studied the reaction γ + p → K $^{+}$+Σ ∗ $^{0}$(1385) with unpolarized photon beam at energy E$_{γ}$ = 1 . 5 − 4 GeV [2]. The LEPS collaboration has reported the reaction γ + n → K $^{+}$+ Σ $^{∗−}$(1385), with a linearly polar- ized photon beam at E$_{γ}$ = 1 . 5 − 2 . 4 GeV [9]. The high statistic data and the polarized observables provide more information and challenges for theoretical studies. 

Theoretical investigations on K Σ $^{∗}$(1385) photoproduc- tion include the work by Lutz and Soyeur [10], which mainly studies the t-channel processes, the work by D¨ oring, Oset and Strottman [11], where the role of Δ(1700) is addressed, and the work by Oh, Ko, and Nakayama [12], where the roles of N and Δ resonances in s-channel are stressed and compared with the CLAS data [2]. 

For the approach by Oh, Ko, and Nakayama [12], the total cross section for γ + p → K + + Σ ∗ $^{0}$(1385) is cal- culated in the framework of gauge-invariant effective La- grangians. The results are in reasonable agreement with the CLAS data [2], showing that the s-channel N and Δ resonances above K Σ ∗ threshold may give important contributions to cross sections. Although this theory can well describe the total cross section of K Σ ∗ photoproduc- tion from CLAS as well as from LEPS experiment [9], the theoretical prediction deviates greatly from the data for linear beam asymmetry measured by LEPS with polar- ized photon beam. This is an urgent problem for theo- retical studies. 

From studies of baryon spectroscopy and structures, five quark qqqqq components are proposed to play im- portant roles in some baryons [13, 14]. A few years ago, Jaffe and Wilczek have promoted a diquark-diquark- 

PACS numbers: 14.20.Jn, 25.20.Lj, 13.60.Le, 13.60.Rj 

## I. INTRODUCTION 

antiquark picture for the pentaquark baryons [15]. Zhang et al. then studied the J P = 1 2 − pentaquark baryons based on this picture and predicted a Σ( 1 2 $^{−}$) state with mass around 1360 MeV [16]. A more general pentaquark model [13] without introducing explicitly diquark clusters predicts that Σ( 1 2 $^{−}$) has a mass similar to Λ( 1 2 $^{−}$), which is around 1405 MeV. From these two models, one would ex- pect a Σ( 1 2 $^{−}$) state with mass around 1380 MeV. Recent studies on K $^{−}$p → Λ π $^{+}$π − process have shown some evi- dence for the existence of the Σ( 1 2 $^{−}$) near 1380 MeV [17]. In this work, we study the K Σ $^{∗}$(1385) photoproduction processes with the consideration of the case that a por- tion of K Σ( 1 2 $^{−}$) photoproduction is mixed in. 

This paper is organized as follows. In section II, the theoretical framework is presented for the K Σ ∗ and K Σ( 1 2 $^{−}$) photoproduction from the nucleons. In section III, the numerical results for cross sections and the beam asymmetry are presented and compared with the exper- imental data, with some discussions. In section IV, we give the summery of this work. 

The effective Lagrangian method is an important the- oretical approach in describing the various processes at resonance region. We use the effective Lagrangians of Ref. [12] for K Σ ∗ photoproduction, where the contact term is derived from Ref. [18] to keep the amplitude gauge invariant. In the following equations we use Σ ∗ and Σ denoting the Σ $^{∗}$( 3 2 $^{+}$) at 1385 MeV and the Σ( 1 2 $^{−}$) near 1380 MeV, respectively. 

For the reaction γN → K Σ $^{∗}$( 3 2 $^{+}$), the Feynman dia- grams are shown in Fig. 1, where the incoming momenta are k and p for photon and nucleon, respectively, and the outgoing momenta are q and p ′ for K meson and the 

## II. THEORETICAL FRAMEWORK 

## A. K Σ ∗ ( 3 2 $^{+}$) photoproduction 

