Unstable Particles and Resonances
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In the standard model all but the lightest particles are unstable. Any scattering process that proceeds by the production and subsequent decay of such an unstable particle, becomes enhanced when the center-of-mass energy s approaches its mass m2. Since self-energy corrections are also enlarged in this phase space region, perturbation theory breaks down. Several schemes have been developed to overcome this problem, including resumming the propagator, the narrow-width approximation, the complex mass scheme and setting up an effective field theory. The aim of this thesis is to explain and compare these schemes, with an emphasis on gauge invariance and unitarity. Resumming the propagator violates gauge invariance; the other schemes respect both and are compared at accuracy and functionality. The narrow-width approximation is typically the most straightforward scheme for calculating observables sufficiently integrated over s to leading order precision, for NLO calculations the complex mass scheme is especially convenient, and for even higher order precision the effective field theory seems most promising.