Transport-theoretical Description of Nuclear Reactions

The physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativistic $3\to 3$ amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. The corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.

Three-body Unitarity in the Finite Volume

Recent results for the photoproduction of mesons off nuclei are reviewed. These experiments have been performed for two major lines of research related to the properties of the strong interaction. The investigation of nucleon resonances requires light nuclei as targets for the extraction of the isospin composition of the electromagnetic excitations. This is done with quasi-free meson photoproduction off the bound neutron and supplemented with the measurement of coherent photoproduction reactions, serving as spin and/or isospin filters. Furthermore, photoproduction from light and heavy nuclei is a very efficient tool for the study of the interactions of mesons with nuclear matter and the in-medium properties of hadrons. Experiments are currently rapidly developing due to the combination of high quality tagged (and polarized) photon beams with state-of-the-art 4π detectors and polarized targets.

/pdf/photoproduction-of-mesons-off-nuclei-3dvfbcj7p4.pdf

Photoproduction of mesons off nuclei

▪ Abstract The Gerasimov-Drell-Hearn sum rule is one of several dispersive sum rules that connect the Compton scattering amplitudes to the inclusive photoproduction cross sections of the target under investigation. Being based on such universal principles as causality, unitarity, and gauge invariance, these sum rules provide a unique testing ground to study the internal degrees of freedom that hold the system together. The present article reviews these sum rules for the spin-dependent cross sections of the nucleon by presenting an overview of recent experiments and theoretical approaches. The generalization from real to virtual photons provides a microscope of variable resolution: At small virtuality of the photon, the data sample information about the long-range phenomena, which are described by effective degrees of freedom (Goldstone bosons and collective resonances), whereas the primary degrees of freedom (quarks and gluons) become visible at the larger virtualities. Through a rich body of new data and...

https://www.annualreviews.org/doi/pdf/10.1146/annurev.nucl.54.070103.181159

The gerasimov-drell-hearn sum rule and the spin structure of the nucleon

Masses, widths and photocouplings of baryon resonances are determined in a coupled-channel partial wave analysis of a large variety of data. The Bonn-Gatchina partial wave formalism is extended to include a decomposition of t- and u-exchange amplitudes into individual partial waves. The multipole transition amplitudes for p ! p� 0 and p ! n� + are given and compared to results from other analyses.

/pdf/photoproduction-of-pions-and-properties-of-baryon-resonances-2eqagso4j3.pdf

Photoproduction of pions and properties of baryon resonances from a Bonn-Gatchina partial-wave analysis

Helicity dependence of the (gamma)over-right-arrow (p)over-right-arrow -> n pi(+) pi(0) reaction in the second resonance region

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Helicity dependence of the (gamma)over-right-arrow (p)over-right-arrow -> n pi(+) pi(0) reaction in the second resonance region