
Physics 2014
Extracting the electromagnetic pion form factor from QCD in a finite volumeDOI: 10.1103/PhysRevD.90.114508 Abstract: We consider finite volume effects on the electromagnetic form factor of the pion. We compute the peudoscalarvectorpseudoscalar correlator in the $\epsilon$ expansion of chiral perturbation theory up to the nexttoleading order and find a way to remove the dominant part, which comes from a contribution of the pion zeromode. Inserting nonzero momentum to relevant operators (or taking a subtraction of the correlators at different timeslices), and taking an appropriate ratio of them, one can automatically cancel the zeromode's contribution, which becomes nonperturbatively large $\sim \mathcal{O}(100 \%)$ in the $\epsilon$ regime. The remaining finite volume dependence, which comes from the nonzero momentum modes, is shown to be perturbatively small even in such an extremal case. Since the zeromode's dominance is universal in any finite volume scaling, and we do not rely on any particular feature of the $\epsilon$ expansion, our method has a wide application to many other correlators of QCD.
