Pure spin-3/2 propagator for use in particle and nuclear physics

Abstract

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.

arXiv comment5 pages, 2 figures

References in corpus (7)

• Effective theory of the Delta(1232) in Compton scattering off the nucleon
• Field theory of nucleon to higher-spin baryon transitions
• Gauge-invariant tree-level photoproduction amplitudes with form factors
• Correspondence of consistent and inconsistent spin-3/2 couplings via the equivalence theorem
• Consistent interactions for high-spin fermion fields
• Electromagnetic Couplings of Nucleon Resonances
• Bosonic and fermionic Weinberg-Joos (j,0)+ (0,j) states of arbitrary spins as Lorentz-tensors or tensor-spinors and second order theory

Cited by in corpus (6)

• Extracting the pole and Breit-Wigner properties of nucleon and $\Delta$ resonances from the $\gamma N\to K\Sigma$ photoproduction
• $K^0\Lambda$ photoproduction off the neutron with nucleon resonances
• Pure spin-3/2 representation with consistent interactions
• Photoproduction $\gamma p\to K^{+}\Lambda (1690)$ in an effective Lagrangian approach
• Baryons in the Nambu Jona-Lasinio models
• On the 256-dimensional gamma matrix representation of the Clifford algebra Cl(1,7) and its relation to the Lie algebra SO(1,9)