Photon induced $K\Lambda $ production on the proton at $E_{\gamma} < 3$ GeV
The associated photoproduction of $K\Lambda$ from the proton for $E_{\gamma} < 3$ GeV is studied using an isobar model in which the non-resonant contributions corresponding to $s$, $t$, $u$ channel diagrams are obtained from a non-linear sigma model with chiral SU(3) symmetry. The model also predicts a contact term and its coupling strength in a natural way to preserve gauge symmetry. The parameters used are the pion decay constant $f_{\pi}$, vector and axial vector current couplings of the baryon octet in terms of the symmetric and antisymmetric couplings $D$ and $F$. In the non-resonant sector, the model is almost parameter free except a common cut-off parameter $\Lambda_{B}$, to describe the hadronic form factors at the strong kaon-nucleon-hyperon($KN\Lambda$) vertices. In the resonance sector, contribution from the various nucleon resonances($R$) in the $s$ channel, hyperon resonances($Y^{*}$) in the $u$ channel, and the kaon resonances($K^{*}$ and $K_{1}$) in the $t$ channel, which are present in the PDG having spin $\le \frac{3}{2}$ and mass $<2$ GeV with significant branching ratio in $K\Lambda$ decay mode have been considered. In the case of the nucleon resonances($R$), the couplings $\gamma NR$ at the electromagnetic vertices are determined in terms of the helicity amplitudes and the $RK\Lambda$ couplings at the strong vertices are determined by the partial decay width of the resonances($R$) decaying to $K\Lambda$. The strong and the electromagnetic couplings of $u$ and $t$ channel resonances are fitted to reproduce the experimental data of CLAS and SAPHIR. The numerical results are presented for the total and differential scattering cross sections and are compared with the available experimental data from CLAS and SAPHIR as well as with some of the recent theoretical models.