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We consider finite volume effects on the electromagnetic form factor of thepion. We compute the peudoscalar-vector-pseudoscalar correlator in the$\epsilon$ expansion of chiral perturbation theory up to the next-to-leadingorder and find a way to remove the dominant part, which comes from acontribution of the pion zero-mode. Inserting non-zero momentum to relevantoperators (or taking a subtraction of the correlators at differenttime-slices), and taking an appropriate ratio of them, one can automaticallycancel the zero-mode's contribution, which becomes non-perturbatively large$\sim \mathcal{O}(100 \%)$ in the $\epsilon$ regime. The remaining finitevolume dependence, which comes from the non-zero momentum modes, is shown to beperturbatively small even in such an extremal case. Since the zero-mode'sdominance is universal in any finite volume scaling, and we do not rely on anyparticular feature of the $\epsilon$ expansion, our method has a wideapplication to many other correlators of QCD.

Extracting the electro-magnetic pion form factor from QCD in a finite volume