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Register a new userPure spin-3/2 representation with consistent interactions
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We have investigated the use of pure spin-3/2 propagator with consistent interaction Lagrangians to describe the property of spin-3/2 resonance. For this purpose we use the antisymmetric tensor spinor representation. By using the primary and secondary constraints we obtain the interaction fields that have the correct degrees of freedom. To visualize the result we calculate the contribution of spin-3/2 $Delta$ resonance to the total cross section of pion scattering and pion photoproduction off the nucleon. The result confirms that the scattering and photoproduction amplitudes obtained from the pure spin-3/2 representation with consistent interaction Lagrangians exhibit the required property of a resonance. Therefore, the formalism can be used for phenomenological investigations in the realm of nuclear and particle physics.
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We propose the use of pure spin-3/2 propagator in the $(3/2,0) oplus (0,3/2)$ representation in particle and nuclear physics. To formulate the propagator in a covariant form we use the antisymmetric tensor spinor representation and we consider the $Delta$ resonance contribution to the elastic $pi N$ scattering as an example. We find that the use of conventional gauge invariant interaction Lagrangian leads to a problem; the obtained scattering amplitude does not exhibit the resonance behavior. To overcome this problem we modify the interaction by adding a momentum dependence. As in the case of Rarita-Schwinger we find that a perfect resonance description could be obtained in the pure spin-3/2 formulation only if hadronic form factors were considered in the interactions.
Consistent interactions for off-shell fermion fields of arbitrary spin are constructed from the gauge-invariance requirement of the interaction Lagrangians. These interactions play a crucial role in the quantum hadrodynamical description of high-spin baryon resonances in hadronic processes. We find that the power of the momentum dependence of a consistent interaction rises with the spin of the fermion field. This leads to unphysical structures in the energy dependence of the computed tree-level cross sections when the short-distance physics is cut off with standard hadronic form factors. A novel, spin-dependent hadronic form factor is proposed that suppresses the unphysical artifacts.
We address the issue of consistent interactions for off-shell fermion fields of arbitrary spin. These interactions play a crucial role in the quantum hadrodynamical description of high-spin baryon resonances in hadronic processes. The Rarita-Schwinger description of high-spin fermion fields involves unphysical degrees of freedom, associated with their lower-spin content. These enter the interaction if not eliminated outright. The invariance condition of the interaction under the unconstrained Rarita-Schwinger gauge removes the lower-spin content of the fermion propagator and leads to a consistent description of the interaction. We develop the most general, consistent interaction structure for high-spin fermions. We find that the power of the momentum dependence of a consistent interaction rises with the spin of the fermion field. This leads to unphysical structures in the energy dependence of the computed cross sections when the short-distance physics is cut off with standard hadronic form factors. A novel, spin-dependent hadronic form factor is proposed that suppresses the unphysical artifacts.
We extend the self-consistent Greens functions formalism to take into account three-body interactions. We analyze the perturbative expansion in terms of Feynman diagrams and define effective one- and two-body interactions, which allows for a substantial reduction of the number of diagrams. The procedure can be taken as a generalization of the normal ordering of the Hamiltonian to fully correlated density matrices. We give examples up to third order in perturbation theory. To define nonperturbative approximations, we extend the equation of motion method in the presence of three-body interactions. We propose schemes that can provide nonperturbative resummation of three-body interactions. We also discuss two different extensions of the Koltun sum rule to compute the ground state of a many-body system.
The semi-inclusive deep inelastic electron scattering off transversely polarized $^3$He, i.e. the process, $e + vec{^3 {rm He}} to e + h+X$, with $h$ a detected fast hadron, is studied beyond the plane wave impulse approximation. To this end, a distorted spin-dependent spectral function of a nucleon inside an A=3 nucleus is actually evaluated through a generalized eikonal approximation, in order to take into account the final state interactions between the hadronizing system and the (A-1) nucleon spectator one. Our realistic description of both nuclear target and final state is a substantial step forward for achieving a reliable extraction of the Sivers and Collins single spin asymmetries of the free neutron. To illustrate how and to what extent the model dependence due to the treatment of the nuclear effects is under control, we apply our approach to the extraction procedure of the neutron single spin asymmetries from those measured for $^3$He for values of the kinematical variables relevant both for forthcoming experiments at Jefferson Lab and, with an exploratory purpose, for the future Electron Ion Collider.
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