Contribution of N^{*} and \Delta^{*} resonances in K^{*}\Sigma(1190) photoproduction

# Contribution of N∗ and Δ∗ resonances in K∗Σ(1190) photoproduction

## Abstract

In this talk, we report theoretical studies on the photoproduction in the tree-level Born approximation, employing the effective Lagrangian method. We present the energy and angular dependences of the cross sections. It turns out that the and resonance contributions are negligible in the vicinity of the threshold. On the contrary, we observe that the and exchanges in the channel and in the channel dominate the scattering process, reproducing the experimental data qualitatively well.

Photoproduction of , effective Lagrangian, and resonances
12

## I Introduction

The strangeness production from various scattering processes plays an important role in understanding the microscopic mechanism of the strong interaction beyond the chiral limit and extends our knowledge into multi-strangeness particles. In the present talk, we would like to report theoretical studies on the photoproduction off the proton target, i.e. . There have been two experimental data from the CLAS collaboration at Jefferson laboratory Hleiqawi:2007ad () and the TAPS collaboration at CBELSA Nanova:2008kr (). Theoretical studies are also carried out based on the effective Lagrangian method Oh:2006hm () and chiral quark model Zhao:2001jw (). In the present work for the process, we employ the effective Lagrangian method at the tree-level Born approximation, including the and resonance contributions, such as , , , , , , and  Nakamura:2010zzi (). The relevant Feynman diagrams preserving the gauge invariance are given in Fig. 1, in which , , , and indicate the nucleon, , , and , respectively. The strong coupling constants for the ground-state baryons , i.e. , are determined by experimental information Nakamura:2010zzi () as well as the Nijmegen soft-core potential model (NSC97a) Stoks:1999bz (). As for the strong couplings for the baryon resonances , we make use of the following relation:

 Γ(B∗→K∗Σ)=∑l,s|G(l,s)|2, (1)

where the amplitude is computed by the SU(6) quark model Capstick:1998uh (). For simplicity, we consider only the low-lying resonance states, since we are interested in the vicinity of the threshold. The magnetic transition strengths for the resonances, , are estimated from the experimental and theoretical values for the helicity amplitudes and  Nakamura:2010zzi (); Capstick:1992uc (). The scattering amplitude can be written with the phenomenological form factors that satisfy the Ward-Takahashi identity as follows:

 M=[Ms(p)+Mu(Σ)]F2c+Mt(K)F2K+Mt(κ)F2κ+Ms(Δ)F2Δ+Mu(Σ∗)F2Σ∗+Ms(N∗)F2N∗+Ms(Δ∗)F2Δ∗ (2)

and the form factors are defined generically as

 Fc=FpFΣ−Fp−FΣ,FΦ=Λ2Φ−M2ΦΛ2Φ−q2,FB=Λ4BΛ4B+(q2−M2B)2, (3)

where , and stand for the momentum transfer, the cutoff masses for the meson-exchange and baryon-pole diagrams, respectively. For the details of the theoretical framework, readers can refer to Oh:2006hm (); Kim:2011rm ().

## Ii Numerical results

In this section, we discuss the numerical results. In Fig. 2, we show them for the differential cross section as functions of for different photon energies GeV. The solid and dotted curves indicate the cases with and without the resonance contributions, respectively. The experimental data are taken from the CLAS Hleiqawi:2007ad () and TAPS Nanova:2008kr (). As shown in Fig. 2, the two experimental data are qualitatively well reproduced and the resonance contributions are almost negligible. We verify that the and exchanges provide strong contribution in the forward scattering region, whereas the backward scattering regions are dominated by the exchange in the channel.

The numerical results for the total cross sections are given in the left panel of Fig. 3 as functions of . Note that the numerical results are slightly underestimated for GeV in comparison to the data even with the resonance contributions. In the right panel of Fig. 3, we depict each contribution from the -channel resonances. Although and provide sizable contributions near the threshold, they are still far smaller than those from the Born contributions. We note that this tendency of the small effects from the resonances are obviously different from the  Oh:2006hm (); Kim:2011rm () and  Janssen:2001pe () photoproductions. The difference between the and channels can be understood by the much smaller strong couplings for the channel computed by the SU(6) quark model in comparison to those for the channel Capstick:1998uh ().

## Iii Summary

We have investigated the photoproduction using the effective Lagrangian method at the tree-level Born approximation. In addition to the Born terms, we also took into account the resonance contributions in the and channels. The experimental data were reproduced qualitatively well. It also turns out that the resonance contributions are almost negligible in the energy and angular dependences of the cross sections, being different from the and photoproductions. The strange meson ( and ) exchanges in the channel and the contribution in the channel are the most dominant in describing the photoproduction. More detailed works are under progress and appear elsewhere.

## Acknowledgments

This talk was presented at the 20th International IUPAP Conference on Few-Body Problems in Physics, August 2012, Fukuoka, Japan. The authors thank Y. Oh and K. Hicks for fruitful discussions on this subject. The present work is supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (Grant Number: 2012R1A1A2001083).

### Footnotes

1. preprint: INHA-NTG-04/2012
2. preprint: KIAS-P12053

### References

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2. M. Nanova et al. [CBELSA/TAPS Collaboration], Eur. Phys. J. A 35, 333 (2008).
3. Y. Oh and H. Kim, Phys. Rev. C 73, 065202 (2006).
4. Q. Zhao, J. S. Al-Khalili and C. Bennhold, Phys. Rev. C 64, 052201 (2001).
5. K. Nakamura [Particle Data Group], J. Phys. G 37, 075021 (2010).
6. V. G. J. Stoks and T. A. Rijken, Phys. Rev. C 59, 3009 (1999).
7. S. Capstick and W. Roberts, Phys. Rev. D 58, 074011 (1998).
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10. S. Janssen, J. Ryckebusch, W. Van Nespen, D. Debruyne and T. Van Cauteren, Eur. Phys. J. A 11, 105 (2001).
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