Abstract
We develop a covariant model for the $\gamma^\ast N \to N(1535)$ transition in the timelike kinematical region, the region where the square momentum transfer $q^2$ is positive. Our starting point is the covariant spectator quark model constrained by data in the spacelike kinematical region ($Q^2 = -q^2 >0$). The model is used to estimate the contributions of valence quarks to the transition form factors, and one obtains a fair description of the Dirac form factor at intermediate and large $Q^2$. For the Pauli form factor there is evidence that beyond the quark-core contributions there are also significant contributions of meson cloud effects. Combining the quark-core model with an effective description of the meson cloud effects, we derive a parametrization of the spacelike data that can be extended covariantly to the timelike region. This extension enabled us to estimate the Dalitz decay widths of the $N(1535)$ resonance, among other observables. Our calculations can help in the interpretation of the present experiments at HADES ($pp$ collisions and others).
Highlights
The creation and propagation of intermediate nucleonic excitations or Nà states, followed by virtual photon transitions leading to Nà → γÃN → eþe−N decays [1,2,3,4,5,6,7,8,9,10,11], can be probed with data on dielectron production from proton-proton and proton-nucleus collisions, as well as on inclusive and exclusive pion-nucleus reactions provided by secondary pion beams experiments
We present the observables associated with the timelike region
Theoretical models for the electromagnetic structure of the NÃ resonances in the timelike region are necessary for the interpretation of NÃ Dalitz decays measured currently in experiments at HADES [1,7,14]
Summary
The creation and propagation of intermediate nucleonic excitations or Nà states, followed by virtual photon transitions leading to Nà → γÃN → eþe−N decays [1,2,3,4,5,6,7,8,9,10,11], can be probed with data on dielectron production from proton-proton (pp) and proton-nucleus (pA) collisions, as well as on inclusive and exclusive pion-nucleus reactions provided by secondary pion beams experiments. The restriction to the large Q2 region was a consequence of the difficulty of the covariant spectator quark model in defining a covariant wave function of the Nð1535Þ compatible with the orthogonality of the states, and with a gauge invariant transition current. This happens because the baryon wave functions that we use are constructed by using symmetries alone, and not obtained from a dynamical calculation. The empirical data associated with the electromagnetic structure of the γÃN → Nð1535Þ transition are usually represented in terms of the helicity amplitudes in the resonance rest frame In this frame the momentum transfer is q. Our calculations are preferentially compared with the CLAS data, well distributed in the range Q2 1⁄4 0–4 GeV2, and Particle Data Group (PDG) at Q2 1⁄4 0 [52]
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