Complex-mass scheme and effective field theory

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Quantum chromodynamics 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 are hadrons which are color-neutral, composite objects made out of 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 corresponding EFT in terms of pions is mesonic chiral perturbation theory. Given a consistent power counting scheme, the EFT may be extended by additional fields such as the nucleon resulting in baryon chiral perturbation theory. In order to take also excited, unstable states into account, we propose the application of the complex-mass scheme (CMS) to the evaluation of physical characteristics of hadron resonances. The chiral limit of the masses and widths of the unstable particles serve as input parameters. With the aid of suitably chosen renormalization conditions, the CMS allows for a perturbative treatment of physical observables of unstable particles.