At finite temperature, a massive vector boson's longitudinal mode sheds part of its Goldstone component, which reappears as a branch cut that can be approximated as a massless quasi-Goldstone with a computed wave-function factor.
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Structures of the Massive Vector Boson Propagators at Finite Temperature Illuminated by the Goldstone Equivalence Gauge
At finite temperature, a massive vector boson's longitudinal mode sheds part of its Goldstone component, which reappears as a branch cut that can be approximated as a massless quasi-Goldstone with a computed wave-function factor.