Spectral function of a fermion coupled with a massive vector boson at finite temperature in a gauge invariant formalism
Abstract
We investigate spectral properties of a fermion coupled with a massive gauge boson with a mass m at finite temperature (T) in the perturbation theory. The massive gauge boson is introduced as a U(1) gauge boson in the Stueckelberg formalism with a gauge parameter α. We find that the fermion spectral function has a threepeak structure for T∼m irrespective of the choice of the gauge parameter, while it tends to have one faint peak at the origin and two peaks corresponding to the normal fermion and antiplasmino excitations familiar in QED in the hard thermal loop approximation for T≫m. We show that our formalism successfully describe the fermion spectral function in the whole T region with the correct highT limit except for the faint peak at the origin, although some care is needed for choice of the gauge parameter for T≫m. We clarify that for T∼m, the fermion pole is almost independent of the gauge parameter in the oneloop order, while for T≫m, the oneloop analysis is valid only for α≪1/g where g is the fermionboson coupling constant, implying that the oneloop analysis cannot be valid for large gauge parameters as in the unitary gauge.
 Publication:

Physical Review D
 Pub Date:
 February 2011
 DOI:
 10.1103/PhysRevD.83.045017
 arXiv:
 arXiv:1011.6452
 Bibcode:
 2011PhRvD..83d5017S
 Keywords:

 11.10.Wx;
 12.38.Mh;
 Finitetemperature field theory;
 Quarkgluon plasma;
 High Energy Physics  Phenomenology;
 Nuclear Theory
 EPrint:
 28pages, 11figures. v2: typos fixed