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Inspired by the Goldstone equivalence gauge, we study the thermal correctionsto an originally massive vector boson by checking the poles and branch cuts. Wefind that part of the Goldstone boson is spewed out from the longitudinalpolarization, becoming a branch cut which can be approximated by the"quasi-poles" in the thermal environment. In this case, physical Goldstoneboson somehow partly recovers. We also show the Feynmann rules for the"external legs" of these vector boson as well as the recovered Goldstone boson,expecting to simplify the vector boson participated process calculations byadopting the similar "tree-level" logic as in the zero temperature situation.Gauge boson mixing case are also discussed. Similar results are shown in othergauges, especially in the $R_\xi$ gauge.

Structures of the Massive Vector Boson Propagators at Finite Temperature Illuminated by the Goldstone Equivalence Gauge