Lattice Investigation of the DMO Sum Rule

Abstract

An evaluation of charged pion polarizability using correlation functions measured on a 16^{3}\times 24 lattice in the context of the Das, Mathur, Okubo (DMO) sum rule is carried out. The calculation is limited to the so-called intrinsic part of the polarizability. This contribution, equivalent to a Euclidean time integral over vector and axial vector momentum-differentiated propagators, is evaluated in both a continuous and discrete sense. In the continuous case, the time behavior of the correlation functions is fit to the continuum quark model; the discrete case is handled by a straightforward application of Simpson's rule for integration after subtracting the pion contributions. A comparison of the implied vector meson and pion decay constants with phenomenological values is carried out. Results for the intrinsic polarizability are extrapolated across four quark mass values to the chiral limit. An extensive discussion of the lattice systematics in this calculation is given.