Study of Baryon Resonances in the Photoproduction \gamma p\rightarrow K^{*}\Sigma(1190)

# Study of Baryon Resonances in the Photoproduction γp→K∗Σ(1190)

Sang-Ho Kim    Atsushi Hosaka    Seung-il Nam and Hyun-Chul Kim
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July 15, 2013 \abstIn this talk, we report the theoretical studies of baryon resonances for the and reaction processes by making use of the effective Lagrangian method in the tree-level Born approximation. The numerical results for the total and differential cross sections are shown with the presently available data. It turns out that the contributions from the and resonances are almost negligible near the threshold energy. On the other hand, the effects of the exchange in the channel and in the channel are considerably larger than other ones in the scattering process, being in good agreement with the experimental data \kword photoproduction, effective Lagrangian, and resonances

## 1 Introduction

Various efforts to understand the baryon resonances and to find missing resonances have been made for decades via the hadron produtcion processes. Photoproduction is one of them, and, especially, it tuns out that the strange meson-baryon production off the nucleon target is very useful. In the present talk, we would like to investigate the reaction process of photoproduction off the proton target. Recently, CBELSA/TAPS collaboration at Electron Stretcher and Accelerator (ELSA) [1], the CLAS collaboration at Thomas Jefferson National Accelerator Facility (Jefferson Lab) [2, 3], and LEPS collaboration at Super Photon Ring-8 GeV (Spring-8) [4] have provided the experimental data for this reaction channel. The related theoretical studies also exist in both models using the chiral quark model [5] and effective Lagrangian method [6]. The theoretical prediction from Ref. [5] turned out to be hard to reproduce the recent experimental data. In Ref. [6], the effective Lagrangian method was employed at the tree-level Born approximation, considering the and exchanges in the channel, - and -pole contributions in the channel, and hyperons () in the channel. The motivation of our present work is to include all the possible and resonances, in a full relativistic manner, such as , , , , , , and .

## 2 Formalism

We employ the effective Lagrangian method in the tree-level Born approximation. The relevant diagrams are shown in Fig.1, and the effective Lagrangians for the interaction vertices are defined in Ref. [7]. The coupling constants are obtained by using experimental data [8] and the SU(6) relativistic quark model [9, 10]. As for the resonances, we use the following relation:

 Γ(R→Nγ)=k2γπ2MN(2j+1)MR[|A1/2|2+|A3/2|2],Γ(R→K∗Σ)=∑l,s|G(l,s)|2, (1)

for the photo- and strong-coupling constants, respectively. Here, and represent the helicity amplitudes, computed by using the experimental or theoretical values [9, 8], from which the transition magnetic moments are given [7]. In addition, the scattering amplitudes are estimated by the SU(6) quark model [10], based on which the strong coupling constants are calculated [7]. For simplicity, we consider only the resonance states MeV, since we are interested in the vicinity of the threshold. The scattering amplitudes can be written with the phenomenological form factors that satisfy the Ward-Takahashi identity as follows:

 M(γp→K∗0Σ+) = [Melecs(N)+Mu(Σ)]F2com+Mmags(N)F2N+Mt(K)F2K+Mt(κ)F2κ (3) +Ms(Δ)F2Δ+Mu(Σ∗)F2Σ∗+Ms(R)F2R, M(γp→K∗+Σ0) = [Mt(K∗)+Melecs(N)+Mc]F2com+Mmags(N)F2N+Mt(K)F2K+Mt(κ)F2κ (5) +Ms(Δ)F2Δ+Mu(Λ)F2Λ+Mu(Σ)F2Σ+Mu(Σ∗)F2Σ∗+Ms(R)F2R.

Here, the form factors are defined generically as

 Fcom=FN(K∗)FΣ(N)−FN(K∗)−FΣ(N),FΦ=Λ2Φ−M2ΦΛ2Φ−p2,FB=Λ4BΛ4B+(p2−M2B)2, (6)

where , , and stand for the momentum transfer, the cutoff masses for the meson-exchange and baryon-pole diagrams, respectively. The corresponding cutoff masses are determined phenomenologically to reproduce the experimental data:

## 3 Numerical Results

### 3.1 Total Cross Section

The contributions of each of channels are shown separately in Fig. 2. In the left panel of Fig 2, it turns out that the -exchange and -pole contributions are crucial, and in the right panel, it can be understood that -pole one almost dominates the reaction process. From those figures, we find that the numerical results are in good agreement with the CLAS data, and the effect of and resonance contributions turns out to be almost negligible.

### 3.2 Differential Cross Section

Here we show the numerical results for the differential cross sections as functions of for different photon energies and GeV for and production, respectively. As shown in Figs. 3 and 4, we can see that the -channel exchanges ( and ) play an important role in the forward angle scattering region, wheres the backward scattering regions are dominated by the -channel contributions ().

## 4 Summary

We investigated the reaction processes of and , emphasizing on the roles of baryon resonances. We found that the resonance contributions gave only negligible effects. On the other hand, -exchange and -pole contributions turned out to be crucial for both of reaction processes. This observation is quite different from the photoproduction [11]. More details can be found in Ref. [7].

## References

• [1] I. Nanova et al. [CBELSA/TAPS Collaboration], Eur. Phys. J. A 35, 333 (2008).
• [2] I. Hleiqawi et al. [CLAS Collaboration], Phys. Rev. C 75, 042201 (2007); 76, 039905(E) (2007).
• [3] W. Tang et al. [CLAS Collaboration], Phys. Rev. C 87, 065204 (2013).
• [4] S. H. Hwang et al. [LEPS Collaboration], Phys. Rev. Lett. 108, 092001 (2012).
• [5] Q. Zhao, J. S. Al-Khalili, C. Bennhold, Phys. Rev. C 64, 052201 (2001).
• [6] Y. Oh and H. Kim, Phys. Rev. C 74, 015208 (2006).
• [7] S. H. Kim, S. i. Nam, A. Hosaka, H. -Ch. Kim, hep-ph/1211.6285 (2012).
• [8] K. Nakamura [Particle Data Group], J. Phys. G 37, 075021 (2010).
• [9] S. Capstick, Phys. Rev. D 46, 2864 (1992).
• [10] S. Capstick, W. Roberts, Phys. Rev. D 58, 074011 (1998).
• [11] S. H. Kim, S. i. Nam, Y. Oh and H.-Ch. Kim, Phys. Rev. D 84, 114023 (2011).
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