Abstract
The low energy (below 2 GeV) πη channel interaction amplitude becomes an object of interest mainly because of the search for exotic mesons in just beginning to collect data detector GlueX in JLab. Finding and interpretation of expected weak signals from these states require a comparison with a very accurate amplitude containing standard ( qq ) states i.e. a 0 (980) and a 0 (1450). The main problem in the determination of such amplitude is a total absence of data about the phases and inelasticities in the elastic and inelastic region. In addition, it is necessary to take into account the next two coupled higher channels - KK and πη ′. Presented here amplitude is based on separable potential model (working very well for the scalar-isoscalar ππ interactions) with only 9 free parameters. To determine such 3-coupled channel amplitude, the following information has been taken into account: experimental branching ratios and positions of both a 0 resonances, theoretical couplings, scattering length from ChPT and value of squared radius of the πη form factor. Phase shifts, inelasticities and cross sections in all single and crossed channels are presented.
Highlights
The πη scalar-isovector channel is very interesting there is no data on phase shifts and inelasticities
Πη → πη shows that this meson decays mostly to πη channel
From experimental point of view, the scalar-isovector πη channel is the one of the least known channel of interactions of light mesons one can construct three-coupled channel amplitude using constraints like positions of poles corresponding to the a0(980) and a0(1450) states, scattering length and relative couplings for the πη, KKand πη channels
Summary
The πη scalar-isovector channel is very interesting there is no data on phase shifts and inelasticities. Group of theorists proposed simple model [1] in which the a0(1450) is a seed qqstate which, due to coupling via meson loops (derivate and nonderivative terms added to Lagrangian), generates a0(980). Such dynamically generated a0(980) is not qqstate but rather mesonmeson molecule or 2q2qstate. In another paper [3] unitary relations, chiral constraints and asymptotic QCD behavior have been used to calculate phase shifts for the πη channel and radius of the πη form factor. As outcome the a0(980) appears as a 2q2qstate, calculated are phase shifts and inelasticities in agreement with ChPT
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