$O(p^6)$ are of the form $$\label{eq:NNLOlag}
\mathcal{L}_6^{{\ensuremath{n_f=2}}}=\sum_{i=1,56} c_i o_i\,,
\qquad
\mathcal{L}_6^{{\ensuremath{n_f=3}}}=\sum_{i=1,94} C_i O_i\,,$$ The classification was done in [@Bijnens:1999sh] after an earlier attempt [@Fearing:1994ga]. The form of the operators $o_i$ and $O_i$ can be found in [@Bijnens:1999sh]. In [@Haefeli:2007ty] an extra relation for the [$n_f=2$]{} case was found reducing the number of terms there to 56.

Renormalization is done with a [ChPT]{} variant of $\overline{MS}$ introduced in [@Gasser:1983yg]. A detailed explanation valid to two-loop order can be found in [@Bijnens:1997vq; @Bijnens:1999hw].

The relevant subtraction coefficients for all cases are known. These are then used to split the coupling constants in the Lagrangian into an infinite and a renormalized part. This split is not unique, so below is the definition of the renormalized constants that we use: $$\label{eq:defLir}
\hat L_i = (c\mu)^{d-4}\left(\hat\Gamma_i\Lambda + \hat L_i^r(\mu)\right)\,.$$ The divergent part is contained in $\Lambda=1/(16\pi^2(d-4))$ and in [ChPT]{} we use as a standard $\ln c = -(1/2)\left(\ln 4\pi+\Gamma^\prime(1)+1\right)$. For [$n_f=2$]{}, $\hat L_i=l_i$ and $\hat \Gamma_i=\gamma_i$ are derived and listed in [@Gasser:1983yg]. For [$n_f=3$]{}, $\hat L_i=L_i$ and $\hat\Gamma_i = \Gamma_i$ are derived and listed in [@Gasser:1984gg]. For [$n_f=3$]{} the convention is to directly list the $L_i^r$ at a scale $\mu=0.77~$GeV. For [$n_f=2$]{} the convention is 