We describe details of the renormalization of two-loop integrals relevant to the calculation of the nucleon mass in the framework of manifestly Lorentz-invariant chiral perturbation theory using infrared renormalization. It is shown that the renormalization can be performed while preserving all relevant symmetries, in particular chiral symmetry, and that renormalized diagrams respect the standard power counting rules. As an application we calculate the chiral expansion of the nucleon mass to order O(q^6).
We discuss the application of the complex-mass scheme to multi-loop diagrams in hadronic effective field theory by considering as an example a two-loop self-energy diagram. We show that the renormalized two-loop diagram satisfies the power counting.
The vector form factor of the pion is calculated in the framework of chiral effective field theory with vector mesons included as dynamical degrees of freedom. To construct an effective field theory with a consistent power counting, the complex-mass scheme is applied.
We consider a symmetry-preserving approach to the nucleon-nucleon scattering problem in the framework of the higher-derivative formulation of baryon chiral perturbation theory. Within this framework the leading-order amplitude is calculated by solving renormalizable equations and corrections are taken into account perturbatively.
In the framework of effective field theory we show that, at two-loop order, the mass and width of the Delta resonance defined via the (relativistic) Breit-Wigner parametrization both depend on the choice of field variables. In contrast, the complex-valued position of the pole of the propagator is independent of this choice.
An effective field theory model of the massive Yang-Mills theory is considered. Assuming that the renormalized coupling constants of non-renormalizable interactions are suppressed by a large scale parameter it is shown that in analogy to the non-abelian gauge invariant theory the dimensionless coupling constant vanishes logarithmically for large values of the renormalization scale parameter.
