Uniqueness of the Interaction Involving Spin-32Particles

Abstract

The free-field Lagrangian as well as the propagator for spin-; particles contains an arbitrary parameter A . However, the S-matrix elements for the interaction of a spin-9 field with other fields are always independent of this parameter, provided the interaction Lagrangian is properly chosen. For a system of a spin-; field coupled to a nucleon field and a pion field, a two-parameter (A,Z) interaction Lagrangian is introduced in such a way that it is invariant under a point transformation of the spin-4 field. The transition amplitude for such an interaction is independent of the parameter A. However, it does depend on the second parameter Z. By requiring the interaction to be consistent with the principles of second quantization, the value of the second parameter has been fixed. Therefore, the A (1238) contribution to the elastic 7iN scattering amplitudes can be uniquely determined. Using this model for the evaluation of the A(1238) contribution and the chiralinvariant Lagrangians for the calculation of the nucleon pole and p-pole contributions, the TN scattering lengths have been computed and compared with the experimental data. The calculated results are in good agreement with experiment.

Elastic and radiative π+p scattering and properties of the Δ++ resonance

“…Feynman rules should be, however, independent of A [13]. A common mistake in some calculations [15] is to take the simplest form of the propagator for the ∆ ++ corresponding to A = −1 and, simultaneously, the vertex πN∆ for a different value of this parameter (for example A = −1/3).…”

“…where A ν (x) is the electromagnetic four-potential and e (κ p ) denotes the charge (anomalous The electromagnetic vertex of the ∆ ++ resonance is given by [13,18]:…”

“…As is well known, the Feynman rules involving the propagator and vertices of the ∆ ++ depend upon an arbitrary parameter A [13]. This arbitrary parameter is the trace left in the Lagrangian of the model by the contact transformations (see Eq.…”

“…Electromagnetic gauge invariance is a fundamental property related to electric charge conservation. On another hand, invariance under contact transformations ensures that physical amplitudes involving the ∆ resonance are independent of any arbitrariness in the Feynman rules of a given theoretical model for this resonance [12,13]. This invariance assures that spurious spin-1/2 components are removed from the field describing an on-shell ∆ particle.…”

The dispersion relation of the pion in nuclear matter

“…here f πN ∆ = 2f πN N , ξ is an arbitrary constant 20,21 ). It will contribute to the processes in which ∆-isobar is off-shell.…”