Matthias R. Schindler

Infrared regularization of baryon chiral perturbation theory reformulated

We formulate the infrared regularization of Becher and Leutwyler in a form analogous to our recently proposed extended on-mass-shell renormalization. In our formulation, IR regularization can be applied to multi-loop diagrams with an arbitrary number of particles with arbitrary masses.

Power counting in baryon chiral perturbation theory including vector mesons

It is demonstrated that using a suitable renormalization condition one obtains a consistent power counting in manifestly Lorentz-invariant baryon chiral perturbation theory including vector mesons as explicit degrees of freedom.

An effective-field-theory analysis of low-energy parity-violation in nucleon–nucleon scattering

Abstract We analyze parity-violating nucleon–nucleon scattering at energies E m π 2 / M using the effective field theory appropriate for this regime. The minimal Lagrangian for short-range parity-violating NN interactions is written in an operator basis that encodes the five partial-wave transitions that dominate at these energies. We calculate the leading-order relationships between parity-violating NN asymmetries and the coefficients in the Lagrangian and also discuss the size of sub-leading corrections. We conclude with a discussion of further observables needed to completely determine the leading-order Lagrangian.

Electromagnetic form-factors of the nucleon in chiral perturbation theory including vector mesons

Abstract.We calculate the electromagnetic form factors of the nucleon up to fourth order in manifestly Lorentz-invariant chiral perturbation theory with vector mesons as explicit degrees of freedom. A systematic power counting for the renormalized diagrams is implemented using both the extended on-mass-shell renormalization scheme and the reformulated version of infrared regularization. We analyze the electric and magnetic Sachs form factors, GE and GM, and compare our results with the existing data. The inclusion of vector mesons results in a considerably improved description of the form factors. We observe that the most dominant contributions come from tree-level diagrams, while loop corrections with internal vector meson lines are small.

Quantum Chromodynamics and Chiral Symmetry

Chiral perturbation theory (ChPT) provides a systematic framework for investigating strong-interaction processes at low energies, as opposed to a perturbative treatment of quantum chromodynamics (QCD) at high momentum transfers in terms of the “running coupling constant.” The basis of ChPT is the global \(\hbox{SU}(3)_L\times \hbox{SU}(3)_R\times{U}(1)_V\) symmetry of the QCD Lagrangian in the limit of massless \(u, d,\) and \(s\) quarks. This symmetry is assumed to be spontaneously broken down to \(\hbox{SU}(3)_V\times{U(1)}_V\) giving rise to eight massless Goldstone bosons. In this chapter we will describe in detail one of the foundations of ChPT, namely the symmetries of QCD and their consequences in terms of QCD Green functions.

Quantum electrodynamics for vector mesons

Quantum electrodynamics for rho mesons is considered. It is shown that, at the tree level, the value of the gyromagnetic ratio of the rho+ is fixed to 2 in a self-consistent effective quantum field theory. Further, the mixing parameter of the photon and the neutral vector meson is equal to the ratio of electromagnetic and strong couplings, leading to the mass difference M(rho0)-M(rho+/-) approximately 1 MeV at tree order.

Infrared and extended on-mass-shell renormalization of two-loop diagrams

Abstract Using a toy model Lagrangian we demonstrate the application of both infrared and extended on-mass-shell renormalization schemes to multiloop diagrams by considering as an example a two-loop self-energy diagram. We show that in both cases the renormalized diagrams satisfy a straightforward power counting.

Infrared renormalization of two-loop integrals and the chiral expansion of the nucleon mass

Abstract 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 ) .

Chiral expansion of the nucleon mass to order O(q6)

Abstract We present the results of a complete two-loop calculation at order O ( q 6 ) of the nucleon mass in manifestly Lorentz-invariant chiral perturbation theory. The renormalization is performed using the reformulated infrared renormalization, which allows for the treatment of two-loop integrals while preserving all relevant symmetries, in particular chiral symmetry.

The Theory of Parity Violation in Few-Nucleon Systems

Abstract We review recent progress in the theoretical description of hadronic parity violation in few-nucleon systems. After introducing the different methods that have been used to study parity-violating observables we discuss the available calculations for reactions with up to five nucleons. Particular emphasis is put on effective field theory calculations where they exist, but earlier and complementary approaches are also presented. We hope this review will serve as a guide for those who wish to know what calculations are available and what further calculations need to be completed before we can claim to have a comprehensive picture of parity violation in few nucleon systems.