First order electroweak radiative corrections to the decay of the polarised $W$ boson

TL;DR

This paper provides a complete analytic treatment of first-order electroweak radiative corrections to the decay of a polarised $W$ boson into heavy quarks, incorporating finite fermion masses and mass effects that can influence total rates and branching ratios. By formulating the decay in terms of the spin-density matrix and helicity bilinears, the authors derive the Born terms and compute both tree-level real-photon emissions and loop corrections, including a careful renormalisation of the CKM matrix and infrared subtraction. The results yield IR-finite analytic expressions for the helicity bilinears $H^{mm'}$ at $O(
)$, with explicit dependence on renormalisation schemes (e.g., $\,\

Abstract

Analytic results for the next-to-leading order electroweak radiative corrections to the decay of the polarised $W$ boson into a pair of heavy quarks are presented. Finite fermion masses are taken into account throughout this calculation, and in performing the collinear limit for the final quark states and all light fermions taking part in this process, the importance of mass effects is demonstrated. This gives hints for the deviation of the total decay rate and the branching ratios into massive fermions between experimental measurements and theoretical predictions.

Figures (7)

• Figure 1: Born-term contribution
• Figure 2: First order electroweak tree corrections
• Figure 3: Kinematics of the three (and two) particle decay
• Figure 4: Loop corrections
• Figure 5: Angular distribution in dependence on the subtraction scheme employed