Abstract
We calculated the coupled channel photoproduction amplitudes of the scalar isovector resononace $a_0(980)$, which include the $\pi\eta$, $K^+K^-$ and $K^0\overline{K^0}$ intermediate states. Based on them we obtained the mass distribution in the $\pi\eta$ channel at photon energy $E_\gamma$=7 GeV, corresponding to energy accissible in new JLab experiments CLAS12 and GlueX. We also analyzed the shape of mass distribution as a function of the phase of the background amplitude.
Highlights
As dominating decay channels of the a0(980) are πη and KK, the construction of the amplitudes of the resonant πη photoproduction is inevitably the coupled channel problem
Based on them we obtained the mass distribution in the πη channel at photon energy Eγ=7 GeV, corresponding to energy accissible in new JLab experiments CLAS12 and GlueX
The model described in this paper assumes that the isovector a0(980) resonance observed in the πη channel results from the πη and KK interactions in the final state [1]
Summary
As dominating decay channels of the a0(980) are πη and KK, the construction of the amplitudes of the resonant πη photoproduction is inevitably the coupled channel problem. The model described in this paper assumes that the isovector a0(980) resonance observed in the πη channel results from the πη and KK interactions in the final state [1]. The final state interactions are described in terms of the coupled channel and unitary amplitudes. The general form of the πη photoproduction amplitude, which takes into account the final state interactions is λ |Aπη|λγλ. Where Vπη (Vmm ) is the Born amplitude of the πη (mm ) pair photoproduction, tπη;mm is the coupled channel scattering amplitude, λ, λ and λγ are respectively the helicities of the initial and final proton, and photon helicity. Further we use numerical channel indices for the elements of the final state scattering amplitude and denote tπη as T11 and tπη;KK as T12 respectively
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