On the definition of the \Delta mass and width

TL;DR

This paper demonstrates that, within effective field theory at two-loop order, the elta resonance's mass and width depend on field variable choices, whereas the pole position remains invariant, clarifying their physical significance.

Contribution

It shows that the pole position of the elta resonance is a field-variable independent, physically meaningful quantity, unlike the Breit-Wigner parameters.

Findings

Mass and width depend on field variables at two-loop order.

Pole position of the propagator is invariant under field redefinitions.

Clarifies the physical interpretation of resonance parameters.

Abstract

In the framework of effective field theory we show that, at two-loop order, the mass and width of the \Delta resonance defined via the (relativistic) Breit-Wigner parametrization both depend on the choice of field variables. In contrast, the complex-valued position of the pole of the propagator is independent of this choice.