Electroweak splitting functions in the Standard Model and beyond

TL;DR

This paper derives polarized electroweak splitting functions in the Standard Model and beyond, addressing mass singularities and providing a general, frame-independent formulation applicable to various gauge theories.

Contribution

It introduces a novel, general method for deriving electroweak splitting functions that handles mass singularities without frame-dependent assumptions.

Findings

Derived polarized splitting functions for all 1->2 processes

Addressed mass singularities in longitudinal polarizations

Validated results in the Standard Model and massless limits

Abstract

We derive quasi-collinear factorization formulas in generic spontaneously broken gauge theories with scalars, fermions, and vector bosons. Specifically, we obtain polarized leading-order splitting functions for all possible final-state and initial-state 1->2 processes in the considered gauge theory. The main complication lies in the presence of mass-singular terms in longitudinal polarization vectors, prohibiting the direct application of the usual factorization procedure known from Quantum Electrodynamics and Quantum Chromodynamics. We overcome this issue with two different strategies, using gauge invariance and Ward identities as guiding principle. Our derivations do not use any explicit component-wise parametrizations of momenta and wave functions and bear no reference to a particular Lorentz frame. Furthermore, our results are valid for completely general definitions of the spin reference axes of the individual external particles. The various massless limits, the special case of the Electroweak Standard Model, the reproduction of existing literature results, and symmetry relations among our splitting functions are discussed in detail.