The $\\gamma p \\rightarrow K^+ \\pi^0 \\Lambda$ and $\\gamma p \\rightarrow K^+ \\pi \\Sigma $
reactions are studied in the kinematic region where the $\\pi^0 \\Lambda$(1116) and $\\pi\\Sigma$(1192) pairs
originate dominantly from the decay of the $\\Sigma$(1385) and $\\Lambda$(1405) resonances.
We consider laboratory photon energies around 2 GeV, significantly above the threshold
for producing the $K^+\\,\\Sigma$(1385)
and $K^+\\,\\Lambda$(1405)
final states.
We compute for both reactions
the process in which the ingoing photon dissociates
into a real K$^+$ and a virtual K$^-$, the off-shell K$^-$ scattering subsequently
off the proton target to produce the $\\pi^0\\, \\Lambda$ or $\\pi\\, \\Sigma$ pair.
The $K^- p \\rightarrow \\pi^0 \\Lambda$ and $K^- p \\rightarrow \\pi \\Sigma$
amplitudes are calculated in the framework of a chiral coupled-channel
effective field theory of meson-baryon scattering. The structure of the amplitudes
reflects the dominance of the $\\Lambda(1405)$ in the $\\pi \\Sigma$ channel
and of the $\\Sigma(1385)$ in the $\\pi \\Lambda$ channel. The full pion-hyperon
final state interaction is included in these amplitudes.
We extract from the calculated cross section the gauge-invariant double kaon pole
term. We found this term to be large and leading to sizeable cross sections
for both the
$\\gamma p \\rightarrow K^+ \\pi^0 \\Lambda$ and $\\gamma p \\rightarrow K^+ \\pi \\Sigma $
reactions,
in qualitative agreement with the scarce data presently available.
Accurate measurements of these cross sections
should make it possible to extract the contribution of the double kaon pole
and hence to assess the possibility of studying kaon-nucleon dynamics
just below threshold through these reactions. |
