Complex-mass scheme and effective field theory
Final Report Abstract
Quantum chromodynamics (QCD) is the fundamental field theory of the strong interactions with quarks as its matter constituents and gluons as the carriers of the strong force. However, the asymptotically observed states of the strong interactions are hadrons such as the nucleon and the pion, which are colorneutral, composite objects made out of (anti-) quarks and gluons. At low energies, the strong interactions among hadrons may be described in terms of an effective field theory (EFT) using hadron fields instead of quarks and gluons as dynamical degrees of freedom. The EFT program is based on the most general Lagrangian compatible with the symmetries of the underlying theory| in the present context QCD. In addition, one needs a power-counting scheme to perform perturbative calculations of observables. The corresponding EFT in terms of pions is (mesonic) chiral perturbation theory (ChPT). It is based on the chiral symmetry of the QCD Lagrangian in the limit of massless up and down quarks in combination with its spontaneous breakdown to isospin symmetry in the ground state. Perturbative calculations are performed in the framework of a quark-mass and momentum expansion. To describe the interaction of pions with nucleons, mesonic ChPT is extended by including the nucleon field, resulting in baryon chiral perturbation theory (BChPT). Here, the implementation of a consistent power-counting scheme is more complex and is intimately connected to finding a suitable renormalization condition. Including also excited, unstable states such as the ρ-meson or the Roper resonance in the EFT, calls for a new renormalization condition which takes account of the finite widths of resonances. Such a renormalization scheme – the so-called complex-mass scheme (CMS) – was developed in the context of the Standard Model for describing the resonant behavior of the massive gauge bosons (W and Z0). The present project applies the CMS to the evaluation of physical characteristics of hadron resonances. Taking the masses and widths in the chiral limit as input parameters and choosing suitable renormalization conditions, the method allows for a perturbative treatment of physical observables of unstable particles. Within a simple model describing the interaction of an unstable vector boson with a stable fermion it was shown at the one-loop level that the perturbative unitarity of the S-matrix is satisfied up to and including second order in the width. In the baryonic sector, electromagnetic properties of the Roper resonance such as its magnetic moment and the nucleon-to-Roper transition form factors were calculated at next-to-next-to-leading order. In conclusion, the implementation of the CMS into an effective field theory of the strong (and electromagnetic) interactions at low- and intermediate energies has turned out to be a successful method for extending the framework of ordinary chiral perturbation theory to a momentum region near the complex poles representing resonances.
Publications
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Anwendungen des Komplexe-Masse-Renormierungsschemas in effektiver Feldtheorie. 2012, Dissertation, Johannes Gutenberg-Universität Mainz.
T. Bauer
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Complex-mass scheme and perturbative unitarity. International Journal of Modern Physics A, Vol. 27.2012, No. 30, 1250178.
T. Bauer, J. Gegelia, G. Japaridze, S. Scherer
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Complex-mass scheme and resonances in EFT. In: The 8th International Workshop on the Physics of Excited Nucleons
NSTAR 2011. AIP Conference Proceedings, Vol. 1432. 2012, pp. 269.
T. Bauer, D. Djukanovic, J. Gegelia, S. Scherer, L. Tiator
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Magnetic moment of the Roper resonance. Physics Letters B, Vol. 715. 2012, Issues 1–3, pp. 234–240.
T. Bauer, J. Gegelia, S. Scherer
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Electromagnetic transition form factors of the Roper resonance in a phenomenological field Theory. Physical Review C (PRC), Vol. 90. 2014, 015201.
T. Bauer, S. Scherer, L. Tiator
