The leading
non anomalous Lagrangian with one vector meson (i.e. of order 
) is:
and corresponds to the so called Conventional Vector model [3,4].
The parameters which enter the calculation of the vector two-point function
are the vector mass 
and the coupling 
to the external vector
source.
The full Lagrangian up to 
order which gives contribution to
and 
, the vector wave function renormalization constant,
(or equivalently to 
) is:
The first term defines the inverse free fermion propagator 
. The remaining part defines the local perturbation to the free Lagrangian
up to order 
.
There are five 
terms with new coefficients 
.
Each term can be traced back to the corresponding term in the list
(8) where the covariant derivative 
is defined in terms of the
covariant derivative 
as follows:
The covariant derivative on the vector-like fields 
is defined as:
The general formula resulting for 
and 
and including the leading
contribution from the ENJL model can be written as follows:
where the wave function renormalization constant 
is given by:
The 
coefficients must be determined from experimental
data.
The function 
is equal to 
.
The 
are polynomials in the Feynman
parameter 
.
Their explicit expression is given by:
From eq.(16) one obtains that the purely divergent contribution
(i.e. 
) to
terms is identically zero.
We are left with two independent coefficients: 
.
