Hadron Observables from Functional Methods

The main objective of this proposal is to investigate meson phenomenology, in particular that which is explored through leptonic probes frequently used in experiment, and give descriptions in terms of the underlying degrees of freedom: the quarks, and gluons. The means to accomplish this are provided by Quantum Chromodynamics (QCD) in combination with non-perturbative methods. The non-perturbative tools that will be used for this investigation are the Dyson-Schwinger and Bethe-Salpeter equations (DSEs and BSEs, respectively). With the solution of the BSEs giving the fully covariant description of meson bound-states, the DSEs allow calculation of the Green`s functions that are required input. Since the DSEs, exact in principle, constitute an infinite tower of coupled integral equations a truncation must be performed. It is the implications of this that will be investigated here. Traditionally, the binding that is required to form a quark-antiquark bound-state is provided by an iterated one- gluon exchange; commonly referred to as the rainbow--ladder truncation (RL). However, such a model is phenomenological at best and is liable to give a poor description of the underlying physics aside from that which arises due to dynamical chiral symmetry breaking (DCSB), an intrinsic and vitally important feature of most QCD studies. The proposed programme of investigation aims to make several key extensions of the RL approximation, with the subsequent calculation of form-factors and decay processes accessible in experiment. These extensions will allow a connection to higher n-point Green`s functions of QCD, i.e. the vertices, and will also include unquenching effects. In addition to providing pion-cloud effects and the possibility for the inclusion of decay channels, one such extension can aid in the inclusion of the UA (1)-anomaly and flavour-singlet mixing within this approach. The main target of application will be towards the calculation of the MM and MM vertex functions, for a meson M. Additionally, the possibility of extracting generalised parton distributions (GPDs) will be looked into, together with an investigation of soft-collinear factorisation in deeply virtual compton scattering (DVCS), and possible violations that may give rise to Regge behaviour in the appropriate deep inelastic scattering (DIS) limit. At the same time, application of the proposed methods to calculation of the hadronic light-by-light scattering contribution to the muon g-2 will be explored.