Charge-changing weak interactions for right-handed particles in the Standard Model

Abstract

Experiments have shown that the charge-changing weak interaction is purely left-handed, which is taken into account in the Standard Model by the inclusion of a left-handed projection operator in the Lagrangian. Nevertheless, it will be shown here that the Standard Model predicts charge-changing weak interactions for right-handed fermions that can be larger than those for left-handed fermions if the mass is sufficiently large, as is the case for the top quark. Here we are using the conventional terminology in which a massive fermion with its spin parallel to its momentum is referred to as being right-handed in the relativistic limit, where it is in an approximate eigenstate of the chirality operator. These effects are due to the way in which the field of the W boson is quantized, which gives a divergent tensor product in the Feynman propagator in the unitary gauge. It will be shown that the off-diagonal terms in the propagator can convert a left-handed projection operator into a right-handed projection operator, which allows an interaction with right-handed fermions even though the Lagrangian is left-handed. Experiments to date have only demonstrated charge-changing weak interactions for left-handed particles, and an alternative quantization approach that eliminates the divergent off-diagonal terms in the W boson propagator and avoids these difficulties will be considered. The alternative approach appears to be in agreement with existing experiments, but additional high-energy experiments may be required in order to distinguish its predictions from those of the Standard Model.