{\cal L}_{11} & = & {\alpha}_{11} Tr[({\cal D}_{\mu} V^{\mu})^2]
\nonumber  \\
{\cal L}_{12} & = & \frac{1}{2} {\alpha}_{12} Tr(T{\cal D}_{\mu}{\cal
D}_{\nu}V^{\nu}) Tr(TV^{\mu})  \nonumber  \\
{\cal L}_{13} & = & \frac{1}{2} {\alpha}_{13} [Tr(T{\cal D}_{\mu}
V^{\nu})]^2
\label{eq:lag2}\end{aligned}$$

As it is well known there is some arbitrariness in the choice of a particular base of invariants. Using the equations of motion it would be possible to eliminate the operators ${\cal L}_{11}$, ${\cal L}_{12}$ and ${\cal L}_{13}$ redefining the rest of the terms (see for example [@Fer]).

So, a set of $\alpha_k$ ($k=0,..13$) parameters have appeared in the definition of this effective Lagrangian. We display in Table \[tab:equiv\] the relations between some different sets of the chiral Lagrangian parameters used in the literature, i.e. by Longhitano [@Long], Feruglio [@Fer] and Dobado et.al. [@HeE2].

The theory defined by the Lagrangian above is non-renormalizable in the strict sense, but the divergences appearing when we calculate at one-loop with the chiral Lagrangian at lowest order eq.(\[eq:lag1\]) have the same form that some of the terms obtained at tree level in the following order in the chiral expansion. The counterterms needed to reabsorb the divergences generated to the one-loop level with ${\cal
L}^{(2)}$ in the Landau gauge were 