Applications of analyticity to scalar meson phenomenology

Abstract

The scalar mesons have caused much debate amongst hadronic physicists for many years. Even today the number of scalars is hotly contested, and there is almost no agreement on the composition of any of the experimentally observed states, except perhaps for the K*(_0) (1430). This thesis attempts to shed light on both of these problems via the application of analyticity to two different quantities. Recently a number of authors have proposed the existence of a light, strange, scalar meson known as the k. We perform a direct search of the best available πK scattering data to determine whether or not this resonance exists. This is done by constructing contour integrals from these data and determining the number of poles present inside the contour. We do not need to model either the internal dynamics of the state nor the form of the background scattering. The number of poles found tells us the number of resonances present and their positions allow us to estimate the resonance parameters. We find that there is only one resonance in scalar πK scattering below 1800 MeV and this is identified with the established K*(_0)(1430). We find no evidence for the k. Secondly, applying Cauchy's Theorem to the vacuum polarisation function leads to a relation between experimental and theoretical integrals known as a Finite Energy Sum Rule (FESR). FESRs are used to explore the scalar, isoscalar non-strange current and allow us to determine which of the experimentally observed scalar, isoscalar mesons is most likely to be the uũ + dd state. We find that the lightest scalar, isoscalar uũ dd state is not the fo(980) as suggested by some authors, but is rather the light, broad object known as the fo(400 - 1200). We are also able to estimate the average light quark mass and find m(_q)(l GeV(^2)) = 4.7 ± 0.9 MeV which is consistent with the recent estimates of this quantity from unquenched lattice QCD.