Using estimates of the low-energy constants: $g_A = 1.25, |g_{\D N}| = 1.5$, $M = 0.94 \, \texttt{GeV}$, $\Delta = 0.29 \, \texttt{GeV}$, and $\mu_1 = 3.38$; we plot the deviation from linearity of the one-loop result for the $F_2$ form factor in Fig. \[f:mom\] for various values of the pion mass. This is done using the function $\D F_2(q^2)$ defined by $$\D F_2(q^2) = \frac{F_2(q^2) - F_2(0)}{q^2 F'_2(0)}
.$$ The plot shows considerable deviation from linearity at the physical pion mass. For lattice pion masses around $0.25$ to $0.35 \, \texttt{GeV}$, there is a $\sim 5 - 10 \%$ deviation from linear behavior. As the lattice pion masses are brought down at fixed lattice spacing (so that the minimal $q^2$ remains fixed), there is a clear trend toward non-linear behavior in $q^2$.

We must keep in mind that the results plotted in the Figure receive $\sim 30 \%$ corrections for pion masses around $0.35 \, \texttt{GeV}$ due to higher-order terms in the chiral expansion that scale as $m_\pi / \Lambda_\chi$ [@Meissner:1997hn; @Puglia:1999th]. Such corrections are independent of $q^2$. Beyond $q^2 \sim 0.1 \, \texttt{GeV} \, {}^2$ there are $\sim 30 \%$ corrections from recoil $q^2 / M^2$ terms in 