Consistence between πNΔ spin-3/2 gauge couplings and electromagnetic gauge invariance

D. BADAGNANI; C. BARBERO AND A. MARIANO

JOURNAL OF PHYSICS G. NUCLEAR PHYSICS

IOP PUBLISHING LTD

Año: 2015 vol. 42 p. 1 - 16

0305-4616

We review the consistency between the recently proposed spin-3/2 gaugeinteraction for Δ resonance with nucleons (N) and pions (π), and the fundamentalelectromagnetic gauge invariance in any radiative amplitude. We showthat: (1) the electromagnetic interaction introduced through minimal substitution in all derivatives breaks the spin-3/2 gauge invariance; (2) radiative corrections (in general not zero for any effective Lagrangian theory) of the spin-3/2 gauge strong vertexes at one loop reintroduce the conventional πderivative interaction. In fact, analyzing elastic and radiative pN scatteringamplitude, we show that chiral symmetric π-derivative pND couplings can besubstituted through a linear transformation to get Δ-derivative ones, whichhave the property of decoupling the 1/2 field components of the Δ propagator,plus contact terms where the Δ-field is absent. One could intend to apply newtransformations (now linear and nonlinear) to restore this property in theradiative case, but the electromagnetic gauge invariance does not survive andnonlinear transformations generate an infinite number of Δ-field terms in theLagrangian. We conclude that we can only content ourselves to fulfilapproximately the electromagnetic gauge invariance at a given order n withoutdestroying the spin-3/2 one, by dropping n + 1 order terms within an effectivefield theory framework, where the ?order n? is defined as a power countingexpansion applicable only in the resonance region. In addition, we show thatthe Ward identity for the DgD vertex cannot be fulfilled with a trimmed 3/2propagator?added ad hoc by some authors with the intention of avoiding 1/2propagation in the radiative case for the DgD amplitude.