Proton Compton scattering in a unified proton-Δ+model

Abstract

We develop a field-theoretic model for the description of proton Compton scattering in which the proton and its excited state, the ∆ + resonance, are described as part of one multiplet with a single Rarita-Schwinger wavefunction. In order to describe the phenomena observed, it is necessary to incorporate both minimal and non-minimal couplings. The minimal coupling reflects the fact that the ∆ + is a charged particle, and in this model the minimal coupling contributes also to the γN ∆ magnetic transition. The non-minimal couplings consist of five electromagnetic form-factors, which are accessed at fixed and vanishing momentum-transfer squared with real photons in Compton scattering experiments, therefore it is possible to extract a rather well-determined set of optimal parameters which reasonably well fit the data in the resonance region 140-450 MeV. The crucial parameter which determines the γN ∆ transition amplitude and therefore the height of the resonance peak is equal to 3.66 ± 0.03, in units of µ N . We find that this parameter also primarily determines the contributions to magnetic polarizability in this model. In the low-energy region up to 140 MeV, we separately fit the electric and magnetic polarizabilities, while keeping the other parameters fixed and obtain values in line with previous approaches. The basic model is then extended with insights gained in the traditional approaches, namely incorporating the sigma-meson channel with the currently favored parameters, and the pion vertex corrections.

Energy-dependentℓ-wave confinement-induced resonances

“…Furthermore, we employ the framework of the K-matrix approach presented in [18,19,28,33] which we combined with the freespace collisional theoretical framework of Gao [39,46,50]. This permits us to obtain fully analytical results including adequate two-body interatomic interactions which possess a van der Waals tail.…”

“…Complementing the experimental studies, substantial theoretical efforts exhibit a kaleidoscope of confinement-induced processes, such as dual [17] and higher partial wave CIRs [18,19], multichannel [20][21][22][23] or anharmonic CIRs [24][25][26] and CIR molecule formation [27] or dipolar CIRs [28][29][30]. Further studies on CIR effects focus on the impact of various confining geometries, such as quasi-2D either harmonic [31,32] or square well [33], and lattice potentials [34][35][36], or collisions in mixed dimensions [37]. Evidently, most of the theoretical efforts focus either on single par- * bhess@physnet.uni-hamburg.de † pgiannak@physnet.uni-hamburg.de ‡ pschmelc@physnet.uni-hamburg.de tial wave collisions or on the low energy regime.…”

“…(2) interrelates the wave functions of the asymptotic and the inner region. Consequently, the corresponding K matrices are connected according to the relation 18,19,28,33], where the K 3D -Matrix is a diagonal matrix in the ℓ-wave representation with entries given by the tangent of the phase shifts.…”

Generalized local-frame-transformation theory for excited species in external fields

“…Furthermore, the LFT theory gives a compact description of a variety of physical processes such as dielectronic recombination [12], negative-ion photodetachment in magnetic [13] or electric fields [14][15][16] or under generic external confinement [17], or ultracold atomic and/or * pgiannak@purdue.edu † chgreene@purdue.edu ‡ robichf@purdue.edu dipolar collisions in the presence of external trapping potentials [18][19][20][21]. In molecular applications frame transformation theory has been decisive in describing the rich rovibrational Rydberg spectra of diatomic molecules [22], and the dissociative recombination of H + 3 [23,24].…”

Dipole Spin Polarizabilities and Gyrations of Spin-One Particles in the Duffin–Kemmer–Petiau Formalism

“…Effective covariant Lagrangian of interaction between electromagnetic field and spin-1/2 particles that takes into account the polarizabilities of the latter was introduced in [1,10] and has been recently used for fitting the photon-proton scattering experimental data at the energies close to resonance production [11]. Characterization of electrodynamic processes on the basis of relativistic theoretical and field approaches, which are focused on the obtaining of phenomenological Lagrangians, equations that describe interaction of electromagnetic field with hadrons, as well as the calculation of electrodynamic processes' amplitudes consistent with the Standard Model's low-energy theorems is one of the most effective methods of interaction processes investigation.…”