Direct calculation of the K-matrix for pion electro-production in the delta channel

Abstract

Abstract. We present a method to calculate directly the K matrix for the pion electro-production processes in the framework of chiral quark models which allows for a clean separation of the resonant amplitudes from the background. The method is applied to the calculation of the multipole amplitudes M1+, E1+, and S1+ in the ∆ channel within the Cloudy Bag Model. A good overall description is found in a broad energy range.

Pion electro-production in the Roper region in chiral quark models

“…This is in marked contrast to the P33 case in the region of the ∆(1232) which have been extensively investigated in our previous works (see e.g. [21] and [22]). The photo-production amplitude in the case of the ∆(1232) is dominated by the resonant contribution and follows the shape of the elastic T matrix in accordance with (21).…”

“…the Coulomb multipole. The same formulas apply to the M K amplitudes that enter (21) and (22) provided…”

Eta and kaon production in a chiral quark model

“…4); the neutron amplitude turns out to be somewhat weaker in the region of the lower resonance, while the imaginary parts of both amplitudes are underestimated in the region of the upper resonance. 1 The sign of our amplitudes agrees with those of the MAID analysis but is opposite to that of the Bonn-Gatchina group -to facilitate the comparison we have reversed the sign of the latter in fig. 4.…”

“…We use a SU(3) extended version of the Cloudy Bag Model (CBM) which includes also the ρ and ω mesons. The method has been described in detail in our previous papers [1][2][3][4][5] where we have analysed the scattering and electro-production amplitudes in different partial waves. We studied the ηN channel in the S 11 partial wave [4], pointing out its important contribution in the region of the N (1535) resonance; we also considered the KΛ channel in this partial wave.…”

The Roper resonance as a meson-baryon molecular state

“…Our recent investigation on the nature of the Roper resonance [1] has been motivated by the results of lattice QCD simulation in the P11 partial wave by the Graz-Ljubljana and the Adelaide groups [2,3] that have included beside threequark interpolating fields also operators for πN in relative p-wave and σN in s-wave, and have found no evidence for a dominant three-quark configuration below 1.65 GeV. In our research we use a coupled channel approach which has been previously successfully applied to describe meson scattering and photoand electro-production in several partial waves in the intermediate energy region [4,5,6,7,8,9]. In the present analysis of the Roper resonance we include the πN, π∆, and σN channels and solve the Lippmann-Schwinger equation for the meson amplitudes to all orders in the approximation of a separable kernel.…”