The pion form factor from first principles

We calculate the electromagnetic form factor of the pion in quenched lattice QCD. The non-perturbatively improved Sheikoleslami-Wohlert lattice action is used together with the O(a) improved current. We calculate form factor for pion masses down to mπ = 360 MeV . We compare the mean square radius for the pion extracted from our form factors to the value obtained from the ’Bethe Salpeter amplitude’. Using (quenched) chiral perturbation theory, we extrapolate our results towards the physical pion mass. INTRODUCTION The pion, being the lightest and simplest particle in the hadronic spectrum has been studied intensively in the past. Using a variety of effective and phenemenological models, the properties of the pion have been desribed with varying succes. However, these models make assumptions, for example, confinement is put in by hand in contrast to being the result of the underlying dynamics. Lattice QCD (LQCD) doesn’t have this drawback since it is solves QCD directly. Using LQCD, global properties of the pion such as the mass and the decay width have been calculated to satisfying accuracy. The form factor, which directly reflects the internal structure, is clearly an important challenge. The first lattice results were obtained by Martinelli and Sachrajda [1]. It was followed by a more detailed study by Draper et al. [2], who showed that the form factor could be described by a simple monopole form as suggested by vector meson dominance [3]. We extend [4] these studies by adopting improved lattice techniques [10–14], which means that we include extra operators in order to systematically eliminate all the O(a) discretisation errors. Some aspects of the pion structure have been obtained [5–9] using ’the Bethe-Salpeter method’. We also use this approach and compare its predictions to the results of our direct calculation of the pion form factor. Finally we study a chiral extrapolation to reach the physical limit. THE METHOD To extract the form factor we calculate the twoand three point functions of the pion, analogously to [2]. The two point function is given by G2(t,p) = ∑ x 〈