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Resonance exchange graph for the two-step approximation. The blob on the left contains the K + Λ * photoproduction amplitude.
Source publication
We present a formalism for the low-energy analysis of the $\gamma p\rightarrow K^{+}\pi\Sigma$ photoproduction reaction in the $\Lambda^{\ast}(1405)$ resonance region. In particular, the constraints arising from unitarity, gauge invariance and chiral perturbation theory are discussed in some detail.
Contexts in source publication
Context 1
... we will be mainly concerned with the extraction of the Λ * properties from πΣ invariant mass distributions dσ/dM πΣ , it seems worthwhile to consider a simplified hadronic model, illustrated in Fig. 2, where the photoproduction process is assumed to take place in two separable steps: first, the Λ * is produced together with a K + , and subsequently decays into a πΣ state. We invoke on-shell factorization here, so that the blob on the left-hand side of Fig. 2 stands for an on-shell Λ * photoproduction amplitude S µ Λ * , while the ...
Context 2
... dσ/dM πΣ , it seems worthwhile to consider a simplified hadronic model, illustrated in Fig. 2, where the photoproduction process is assumed to take place in two separable steps: first, the Λ * is produced together with a K + , and subsequently decays into a πΣ state. We invoke on-shell factorization here, so that the blob on the left-hand side of Fig. 2 stands for an on-shell Λ * photoproduction amplitude S µ Λ * , while the strength of the Λ * πΣ vertex on the right-hand side can be related to the width of the Λ * , Γ Λ * . The rationale behind this is that we are now interested mainly in the resonance pole terms in the variable M πΣ , so that we can neglect all kinds of background ...
Context 3
... the expression in Eq. (22). Indeed, computing amplitudes from graphs like the one in Fig. 2, one finds that the Λ * pole terms in the resulting A i 0+ are proportional to the combinations B i Λ * . In the same way, one could relate the terms involving the A i 1− to pole terms due to a S = −1, spin 1 2 p-wave resonance. Approaching the reaction threshold, only the combination A 1 0+ survives in (27), which explains the ...
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