Near threshold kaon-kaon interaction in the reactions ${e^ + }{e^ - } \to {K^ + }{K^ - }\gamma$ and ${e^ + }{e^ - } \to {K^0}{\bar K^0}\gamma$

L Leśniak,M Silarski,F Sobczuk,F Morawski

doi:10.1051/epjconf/201919903002

Abstract

Strong interactions between pairs of the K+ K- and K0 K0bar mesons can be studied in radiative decays of phi(1020) mesons. We present a theoretical model of the reactions e+ e- --> phi --> K+ K- gamma and e+ e- --> phi --> K0 K0bar gamma. The K+ K- and K0 K0bar effective mass dependence of the differential cross sections is derived. The total cross sections and the branching fractions for the two radiative phi decays are calculated.

Highlights

Strong interactions between pairs of the K+K− and K0K0 mesons can be studied in radiative decays of φ(1020) mesons
The φ(1020) meson decays into π+π−γ, π0π0γ and π0ηγ have been measured, for the φ transition into K0K0γ only the upper limit of the branching fraction has been obtained in Ref. [1] but there are no data for the φ → K+K−γ process
In this paper we outline a general theoretical model of the e+e− reactions leading to final states with two pseudoscalar mesons and a photon

Summary

Description of the theoretical model

The kaon-kaon strong interaction near threshold is largely unknown. the parameters of the scalar resonances f0(980) and a0(980) are still imprecise. At the beginning we derive the amplitude A(m) for the e+e− → K+K−γ process. It is a sum of the four amplitudes corresponding to diagrams (a), (b), (c) and (d) in Fig. 1: e+. The four-momenta of kaons in the K+K− center-of-mass frame are: k1 = (m/2, −kf) and k2 = (m/2, kf), where k f = m2/4 − m2K is the kaon momentum in the final-state. Under a dominance of the pole at m = 2Ek ≡ 2 k2 + m2K, the amplitude A(m) can be written in the following form: A(m) = J · ∗ TK+K− (m) [I(m) − I(mφ)],. In the model of Close, Isgur and Kumano [2] the momentum distribution of the interacting kaons has been expressed by the function μ4 φ(k) = (k2 + μ2)2 ,. In order to get an integral convergence at large k in Eq (9) we use an additional cut-off parameter kmax=1 GeV

Numerical results

Conclusions