Flavor mixing, gauge invariance, and wave-function renormalization

Abstract

We clarify some aspects of the LSZ formalism and wave-function renormalization for unstable particles in the presence of electroweak interactions when mixing and CP violation are considered. We also analyze the renormalization of the Cabibbo-Kobayashi-Maskawa ͑CKM͒ mixing matrix which is closely related to wavefunction renormalization. We critically review earlier attempts to define a set of ''on-shell'' wave-function renormalization constants. With the aid of extensive use of the Nielsen identities complemented by explicit calculations we corroborate that the counterterm for the CKM mixing matrix must be explicitly gauge independent and demonstrate that the commonly used prescription for the wave-function renormalization constants leads to gauge parameter dependent amplitudes, even if the CKM counterterm is gauge invariant as required. We show that a proper LSZ-compliant prescription leads to gauge independent amplitudes. The resulting wave-function renormalization constants necessarily possess absorptive parts, but we verify that they comply with the expected requirements concerning CP and CPT. The results obtained using this prescription are different ͑even at the level of the modulus squared of the amplitude͒ from the ones neglecting the absorptive parts in the case of top decay. The difference is numerically relevant.

New mathematical structures in renormalizable quantum field theories

“…Here and there one or the other technicality still demands clarification (see [2] for an example), but by now the dedicated group of practitioners of quantum field theory has the technical challenges implied by locality, causality and internal symmetries well under control.…”

Next-to-leading order corrections to single top quark production and decay at the Fermilab Tevatron:s-channel process

“…For example, one can study the Cabibbo-KobayashiMaskawa (CKM) matrix element V tb , new W -t-b couplings beyond the Standard Model (SM) [14,15,16,17,18,19,20,21,22,23,24,25], and CP violation [26,27,28] in single top quark production and decay. The angular correlations among the decay products of polarized top quarks also provide a useful handle on these couplings [29,30,31,32,33,34,35,36]. The t-channel production process can also provide us with information about the b quark distribution function inside the proton.…”

Mixing of fermions and spectral representation of propagator

“…, but in the presence of imaginary part in self-energy this condition becomes contradictory [29,30].…”