expression for the form factor has been worked out long time ago both for ${\rm SU(2)_L \times SU(2)_R}$ [@gasserleutwyler] and ${\rm SU(3)_L \times SU(3)_R}$ [@gasserleutwyler_2] cases, which is given by $$G_\pi^{SU(2),NLO}(Q^2)  = 1 + \frac{2Q^2}{f^2}l^r_6 + \frac{2M_\pi^2}{f^2} \left[ - \frac{sL}{6} + \frac{H(s)}{N} \right],
\label{PFF_SU2_NLO}$$ and $$G_\pi^{SU(3),NLO}(Q^2) = 1  - \frac{4Q^2}{f^2_0}L^r_9 + \frac{2M_\pi^2}{f_0^2} \left[  - \frac{sL}{6} + \frac{H(s)}{N} \right] 
                            +  \frac{M_K^2}{f_0^2} \left[ - \frac{s_KL_K}{6} + \frac{H(s_K)}{N} \right],
\label{PFF_SU3_NLO}$$ where $$H(x) = -\frac{4}{3} + \frac{5}{18}x - \frac{x-4}{6} \sqrt{\frac{x-4}{x}}{\rm log} \left( \frac{\sqrt{\frac{x-4}{x}}+1}{\sqrt{\frac{x-4}{x}}-1}\right),$$ and $f$ and $f_0$ are the decay constant in the SU(2) and SU(3) chiral limit, respectively. In the above equations, we made use of the following definitions: $$\begin{aligned}
\label{eq:constants}
N &=& (4\pi)^2,\\\nonumber
s &=& \frac{-Q^2}{M_\pi^2}, s_K = \frac{-Q^2}{M_K^2},\nonumber\\
L &=& \frac{1}{N}{\rm log}(\frac{M^2_\pi}{\mu^2}),L_K = \frac{1}{N}{\rm log}(\frac{M^2_K}{\mu^2}).\nonumber\end{aligned}$$ Besides the decay constant at the chiral limit, the SU(2) formula (\[PFF\_SU2\_NLO\]) involves $l^r_6$ as the only unknown LEC, and the same situation holds for the SU(3) case, (\[PFF\_SU3\_NLO\]), with $L^r_9$ as the unknown LEC. Calculating the slope at the origin of the momentum transfer yields the expressions for the charge radius: $$\left< r^2\right>_{SU(2),NLO} = -\frac{2}{f^2} \left( 6l^r_6 + \frac{1}{N} + L \right),
\label{r2_SU2_NLO}$$ $$\left< r^2\right>_{SU(3),NLO} = -\frac{2}{f_0^2} \left( -12L^r_9 + \frac{3}{2N} + L + \frac{L_K}{2}\right).
