field theory the width is naturally included in the imaginary part of the self-energy of the particles and, the Ward identity is respected at all orders in perturbation theory. These facts are exploited in those schemes by including the resummation of the fermion/boson loops in the propagator and the corrections in the electromagnetic vertices. Then, the imaginary part of the fermion/boson loops introduces the tree level width in the gauge boson propagator and, the gauge invariance is not violated since the fermion/boson loops obey the Ward identity order by order. At tree level, the propagator for a vector boson of mass M$_{V}$ can be set as where T $^{µν}$( q ) ≡ g µν − q $^{µ}$q$^{ν}$/q 2 and L $^{µν}$( q ) ≡ q $^{µ}$q$^{ν}$/q $^{2}$, are the transversal and longitudinal projectors, respectively. The vertex for the process V ( q 1 ) → V ( q 2 ) γ ( k ) is defined from the electromagnetic current At tree level, the vertex can be set as that given by the standard model for the W boson: These expressions satisfy the Ward identity Upon the inclusion of the finite width of the boson, by considering the loop contributions, the propagator is modified in a generic form as: where Im Π $^{T}$( q $^{2}$) and Im Π $^{L}$( q $^{2}$), are the transverse and longitudinal part of the absortive contribution of the self-energy induced by the particles in the loop. Similarly, the vertex becomes where Γ µνλ 1 contains the loop corrections. The Ward identity relates the loop contributions by requiring to satisfy D µν 0 ( q ) = − ıT $^{µν}$( q ) q 2 − M 2 V + ıL $^{µν}$( q ) M 2 V , (1) < V ( q 2 ) | J $^{µ}$(0) | V ( q 1 ) > = A † $_{ν}$( q 2 ) A$_{λ}$ ( q 1 )Γ $^{µνλ}$. (2) Γ µνλ 0 = g $^{µν}$( q 1 + q 2 ) λ − g $^{µλ}$( q 1 + k ) ν − g $^{νλ}$( q 2 − k ) $^{µ}$; (3) k$_{µ}$ Γ µνλ 0 = [ ıD νλ 0 ( q 1 ) ] − 1 − [ ıD νλ 0 ( q 2 ) ] − $^{1}$; (4) D $^{µν}$( q ) = − ıT $^{µν}$( q ) q 2 − M 2 V + ıIm Π $^{T}$( q $^{2}$) + ıL $^{µν}$( q ) M 2 V − ıIm Π $^{L}$( q $^{2}$) , (5) ıe Γ µνλ = ıe (Γ µνλ 0 + Γ µνλ 1 ) , (6) k$_{µ}$ Γ µνλ 1 = ıIm Π $^{νλ}$( q 1 ) − ıIm Π $^{νλ}$( q 2 ) . (7) 3