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Using Chiral Perturbation Theory, we obtain the kaon semi-leptonic vector form factor in finite volume at a generic momentum transfer, $q^2$, up to one loop order. At first we confirm the lattice observation that the contribution of the heavy Pseudo-Goldstone boson in the finite volume corrections at zero momentum transfer is unimportant. We then evaluate the form factor at $q^2=0$ numerically for two volumes with L = 1.83 fm and L = 2.74 fm and compare our results with the lattice data as quoted in Boyle et al. (Phys. Rev. Lett. 100 (2008) 141601). It turns out that our ChPT results in the smaller volume are in better agreement with the lattice data than those in the larger volume. This study suggests that SU(3) ChPT, concerning vector form factor at zero momentum transfer, is a reliable tool for lattice data in order to extrapolate at large lattice size.
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