Few-Body SystDOI 10.1007/s00601-014-0883-6

H.-Ch. Kim · H.-Y. Ryu · A. Titov · A. Hosaka

φN photoproduction coupled with the KΛ∗ channel

Received: 25 October 2013 / Accepted: 25 March 2014© Springer-Verlag Wien 2014

Abstract We present in this talk a recent investigation on φ photoproduction, emphasizing the rescatteringeffects of the KΛ∗ channel near the threshold region. We discuss the results of the differential cross sectionand the angular distributions.

1 Introduction

The strangeness content of the nucleon has been one of the most interesting issues. In particular, it is ofgreat importance to understand how strange quarks can be created from the nonstrange nucleon. In this sense,φ photoproduction provides essential information on it. On the other hand, the coupling of the φ mesonto the nucleon is suppressed by the Okubo–Zweig–Iizuka (OZI) rule. Because of this, the pomeron wasregarded as the main contribution to φ photoproduction. However, a recent measurement performed by theLEPS collaboration [1] finds a bump-like structure around the photon energy Eγ ≈ 2.3 GeV. It seems thatthe Pomeron alone cannot account for this bump-like structure and requires that one should consider otherproduction mechanism of φ photoproduction near the threshold energy.

In an attempt to explain this experiment, Ozaki et al. [2] introduced coupled-channel effects with the K -matrix method. They considered the γ N → KΛ∗(1520) and KΛ∗ → φN kernels [3] but the coupled-channeleffects turned out to be not enough to describe the bump-like structure at Eγ ≈ 2.3 GeV. Another idea wassuggested by Ref. [4]: the bump-like structure could arise from a destructive interference due to the N∗(2010)resonance with the large ss̄ content. Recently, we have shown that the KΛ∗ rescattering effects [5] can explain

The present work is supported by Basic Science Research Program through the National Research Foundation of Korea funded bythe Ministry of Education, Science and Technology (Grant Number: 2012001083). It is also supported in part by the Grant-in-Aidfor Scientific Research on Priority Areas titled “Elucidation of New Hadrons with a Variety of Flavors”(E01:21105006).

H.-C. Kim (B)Department of Physics, Inha University, Incheon 402–751, Republic of Korea.E-mail: hchkim@inha.ac.kr

H.-Y. RyuKorea Institute of Science and Technology Information (KISTI) 245, Daejeon 305-806, Republic of Korea.E-mail: hyryu@kisti.re.kr

A. TitovBogoliubov Laboratory of Theoretical Physics, JINR, Dubna 141980, Russia.E-mail: atitov@theor.jinr.ru

A. HosakaResearch Center for Nuclear Physics, Osaka University, Ibaraki 567–0047, Japan.E-mail: hosaka@rcnp.osaka-u.ac.jp

H.-C. Kim et al.

the 2.3-GeV bump-like structure on the contrary to Ref. [2] with the imaginary part of the effects taken intoaccount.

In the present talk, we will briefly report the extension of the previous work [5] by including the real partof the KΛ∗ rescattering effects. The KΛ∗ rescattering channel indeed explains the experimental data of theLEPS collaboration.

2 Effects of the K+Λ(1520) Channel

In Ref. [5], the amplitude of φ photoproduction was constructed by considering the Pomeron-exchange,pseudoscalar meson-exchanges, and seven different rescattering amplitudes. It was found that the KΛ(1520)rescattering amplitude is the dominant one among others in describing φ photoproduction near the threshold.Thus, we will focus on the K +Λ(1520) channel in this talk. The main component of the K +Λ(1520) rescat-tering effects is surely the amplitude of the K +Λ∗ photoproduction [3]. Then, the rescattering equation canbe written as

Mγ N→φN (p, p′; s) = MBornγ N→φN (p, p′; s)

+∫

d3qω+E

(2π)32ωEMγ N→K +Λ∗(p, q; s)

1

s−(ω + E)2+iεMK +Λ∗→φN (q, p′; s),

(1)

which is a Blankenbecler–Sugar (BbS) equation [6]. The amplitude MBornγ N→φN contains the diagrams of

pomeron- and meson-exchanges. The second part of Eq.(1) in the right-hand side denotes the rescatteringamplitude of the KΛ∗ channel. Both Mγ N→K +Λ∗(p, k; s) and MK +Λ∗→φN (k, p′; s) are the off-mass-shellextended amplitudes for the γ p → K +Λ∗ and K +Λ∗ → φp, respectively. ω and E correspond to the off-mass-shell energies of the K + and the Λ∗ in the intermediate states. s is a Mandelstam variable, i.e. the squareof the total energy s = (Eγ + E p)

2. We will demonstrate in the next section that the effects of the KΛ∗rescattering explain quantitatively the differential cross sections and the decay angular distributions.

3 Results

We now present the results for the rescattering effects of the KΛ∗ coupled channel on φ photoproduction.Figure 1 draws the results of the total cross section for K +Λ(1520) photoproduction, based on Ref. [3]. How-ever, we want to mention that we introduce the three dimensional form factors instead of the four dimensionalone used in Ref. [3]. In order to solve Eq. (1), we prefer to use the three dimensional one as was in the case ofusual models for the nucleon-nucleon interaction. Because of this, the total cross section of the γ p → K +Λ∗reaction seems to be underestimated in the lower photon energy (Eγ ) region. However, one has to deal with

2 3 4 5

Eγ [GeV]

0

0.2

0.4

0.6

0.8

1

σ [μ

b]

Fig. 1 Total cross section for the γ p → K +Λ(1520) process. The experimental data taken from Ref. [7]

The KΛ∗ Channel

1 2 3 4 5 6

Eγ [GeV]

10-1

100

dσ/d

t [μb

/GeV

2 ] (θ

=0)

Total[P] Pomeron[Λ

Re] KΛ(1520)

[ΛIm

] KΛ(1520)

[T] t-channel π+ηBonn (1974)DESY (1978)LEPS (2005)SAPHIR (2003)SLAC (1973)

T

ΛRe

P

ΛIm

Fig. 2 (Color on-line) Differential cross section as a function of the photon energy Eγ in a log scale. The thick solid curve depictsthe result with all contributions included. The solid curves with the symbols P , ΛRe, ΛIm, and T denote the Pomeron contribution,the real part of KΛ∗ rescattering effects, the imaginary part of that and the t-channel contribution of π- and η-exchanges

KΛ∗ photoproduction on the same footing together with the γ p → φp reaction within a full-couple channelformalism. Then the φN rescattering effects will definitely contribute to the KΛ∗ reaction. We will report thecorresponding investigation elsewhere.

In Fig. 2, we show each contribution to the differential cross section dσ/dt for φ photoproduction in logscale. The dashed curve with P represents the pomeron-exchange contribution. The pomeron governs typicallythe general Eγ dependence, in particular, in the high energy region, while the t-channel effects designated byT contribute to the differential cross section almost equally along Eγ . The detailed formalism for the pomeron-exchange can be found in the previous work [5] in the context of φp photoproduction. As shown in Fig. 2, thereal and the imaginary part of the KΛ(1520) rescattering effects are depicted, respectively, being denoted byΛRe and ΛIm. The behavior of the real part is quite distinguished from that of the imaginary one. Actually,the real part plays a dominant role in describing the experimental data near the threshold region. We want toemphasize that the form factors employed in the present work is much more consistent than the previous work.As a result, the imaginary part turns out to be less important as shown in Fig. 2. Thus, the interference of allthese three contributions make it possible to describe the bump-like structure around Eγ = 2.3 GeV.

The angular distributions of the φ → K +K − decay in the φ rest frame allow one to get access to thehelicity amplitudes experimentally [8,9]. They were measured by the LEPS collaboration at forward angles(−0.2 < t + |t |min) in two different energy regions: 1.97 < Eγ < 2.17 GeV and 2.17 < Eγ < 2.37 GeV [1].Here, |t |min denotes the minimum four-momentum transfer from the incident photon to the φ meson. In thistalk, we focus on the one-dimensional decay angular distribution 2πW (φ −), since it illuminates the effectsof the KΛ∗ coupled channel. The 2πW is defined as

2πW (φ − ) = 1 + 2Pγ ρ11−1 cos 2(φ − ), (2)

where φ is the polar and azimuthal angles of the decay particle K + in the φ rest frame. stands for the azimuthalangle of the photon polarization in the center-of-mass frame. Pγ denotes the degree of the polarization of thephoton beam. The definition of ρ1

1−1 can be found in Ref. [5]. In Fig. 3, we compare the results of the2πW (φ − ) with the experimental data. Note that since the photon energy Eγ = 2.07 GeV is small, thepomeron does not come into play. Interestingly, the KΛ∗ rescattering effects turn out to be crucial in describing2πW (φ − ). The t-channel contribution interferes destructively with the KΛ∗ effects.

4 Summary and Outlook

In the present talk, we briefly reviewed a recent investigation on the KΛ∗ coupled-channel effects in additionto the conventional approach of Pomeron-, π-, and η-exchanges. We found that the KΛ(1520) rescatteringeffects, in particular, the corresponding real part, play a crucial role in describing the bump-like structure nearEγ ≈ 2.3 GeV of the LEPS experiment. The angular distribution of the φ also was well explained by the

H.-C. Kim et al.

0.5

1

1.5LEPSTotalKΛ(1520)π+η

φ−Φ

2πW

Eγ=2.07 GeV Eγ=2.27 GeV

πφ−Φ

Fig. 3 (Color on-line) The decay angular distributions for −0.2 < t + |t |min. The experimental data are taken from Ref. [1]

inclusion of the KΛ(1520) coupled channel. The effects of the KΛ∗ channel on other observables will bepresent elsewhere.

References

1. Mibe, T. et al.: [LEPS Collaboration]: Diffractive phi-meson photoproduction on proton near threshold. Phys. Rev.Lett. 95, 182001 (2005)

2. Ozaki, S., Hosaka, A., Nagahiro, H., Scholten, O.: A coupled-channel analysis for φ-photoproduction with Λ(1520). Phys.Rev. C 80, 035201 (2009) [Erratum-ibid. C 81, 059901 (2010)]

3. Nam, S.-i., Hosaka, A., Kim, H.-Ch.: Λ(1520,3/2-) photoproduction reaction via γ N → KΛ(1520). Phys. Rev.D 71, 114012 (2005)

4. Kiswandhi, A., Xie J., J., Yang, S.N.: Is the nonmonotonic behavior in the cross section of phi photoproduction near thresholda signature of a resonance?. Phys. Lett. B 691, 214 (2010)

5. Ryu, H.-Y., Titov, A.I., Hosaka, A., Kim, H.-Ch.: φ photoprodution with coupled-channel effects. Prog. Theor. Exp.Phys. 2014, 023D03 (2014)

6. Blankenbecler, R., Sugar, R.: Linear integral equations for relativistic multichannel scattering. Phys. Rev. 142, 1051 (1966)7. Adelseck, R.A., Bennhold, C., Wright, L.E.: Kaon photoproduction operator for use in nuclear physics. Phys. Rev.

C 32, 1681 (1985)8. Gottfried, K., Jackson, J.D.: On the connection between production mechanism and decay of resonances at high-

energies. Nuovo Cim. 33, 309 (1964)9. Schilling, K., Seyboth, P., Wolf, G.E.: On the analysis of vector meson production by polarized photons. Nucl. Phys. B 15,

397 (1970) [Erratum-ibid. B 18, 332 (1970)].