charge conservation.

We extract the form factor from a suitable ratio of the pion two- and three-point functions. We use a ratio, which has the advantage of simultaneously reducing fluctuations and renormalizing the current, defined as $$\label{eq:ratio}
R(\tau)=\frac{C^{3pt}(\vec{p'},t_f;\vec{p},0;\tau)}{C^{3pt}(\vec{p'},t_f;\vec{p'},0;\tau)} \frac{C^{2pt}(\vec{p'},\tau)}{C^{2pt}(\vec{p},\tau)}
\times \frac{2E_\pi(\vec{p'})}{E_\pi(\vec{p})+E_\pi(\vec{p'})},$$ which converges as $$R(\tau)\to \frac{G^{\rm bare}_\pi(Q^2)}{G^{\rm bare}_\pi(0)}=G_\pi(Q^2),$$ for large $\tau$ and $t_f$. $E_\pi(\vec{p})$ denotes pion energy for spatial momentum $\vec{p}$, $C^{3pt}(\vec{p'},t_f; \vec{p},0;\tau)$ is the three-point function with momenta $\vec{p}$ at the source and $\vec{p'}$ at the sink $t_f$, $$\label{eq:C3pt}
C^{3pt}(\vec{p'},t_f; \vec{p},0;\tau) = \left< \pi^+(\vec{p'},t_f) J_\mu(\tau) \pi^+(\vec{p},0)\right>,$$ and $C^{2pt}(\vec{p},\tau)$ is the two-point function, $$\label{eq:C2pt}
C^{2pt}(\vec{p},\tau) = \left< \pi^+(\vec{p},\tau) \pi^+(\vec{p},0)\right>.$$ After contraction of quark fields, the three-point function consists of the connected and disconnected contributions. The latter vanishes after the gauge field average due to charge conjugation invariance, and hence need not be calculated. Since we assume degeneracy of up and down quark masses in the present calculation, the connected contribution is equal to $$\label{eq:3pt}
C^{3pt}(\vec{p'},t_f; \vec{p},0;\tau) = \sum_{\vec{y},\vec{x}}e^{-i\vec{p'}\vec{y}+i\vec{q}\vec{x}} 
\left<Tr[\gamma_5 D^{-1}(0,x) \gamma_\mu D^{-1}(x,y) \gamma_5 D^{-1}(y,0)]\right>.$$ This contribution can be calculated by the traditional source method [@martinelli; @draper].

Choice of momenta carried by quarks
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The ratio (\[eq:ratio\]) makes use of two- and three-point functions in an appropriate combination to extract the 