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arXiv · hep-ph/9603351

Gauge Invariance in the Process $e^+e^-\to \bar ν_e e^-W^+\to\barν_e e^-u\bar d$

Robin G. Stuart
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Abstract

The process $e^+e^-\rightarrow \bar ν_e e^-W^+ \rightarrow\barν_e e^-u\bar d$ is considered as an example of the problems associated with maintaining gauge invariance in matrix elements involving unstable particles. It is shown how to construct a matrix element that correctly treats width effects for the intermediate unstable $W$ boson and that is both $SU(2)_L$ and $U(1)_{\rm e.m.}$ gauge-invariant. $SU(2)_L$ gauge-invariance is maintained by Laurent expansion in kinematic invariants and $U(1)_{\rm e.m.}$ gauge-invariance is enforced by means of a projection operator under which the exact matrix element is invariant.

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Robin G. Stuart. 1996-05-04. Gauge Invariance in the Process $e^+e^-\to \bar ν_e e^-W^+\to\barν_e e^-u\bar d$. https://doi.org/10.1007/s100520050202

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