Novel Collective Excitations and the Quasi-Particle Picture of Quarks Coupled with a Massive Boson at Finite Temperature

Motivated by the observation that there may exist hadronic excitations evenin the quark-gluon plasma (QGP) phase, we investigate how the properties ofquarks, especially within the quasi-particle picture, are affected by thecoupling with bosonic excitations at finite temperature (T), employing Yukawa models with a massive scalar (pseudoscalar) and vector (axial-vector)boson of mass m. The quark spectral function and the quasi-dispersion relationsare calculated at one-loop order. We find that there appears a three-peakstructure in the quark spectral function with a collective nature when T iscomparable with m, irrespective of the type of boson considered. Such amulti-peak structure was first found in a chiral model yielding scalarcomposite bosons with a decay width. We elucidate the mechanism through whichthe new quark collective excitations are realized in terms of the Landaudamping of a quark (an antiquark) induced by scattering with the thermallyexcited boson, which gives rise to mixing and hence a level repulsion between aquark (antiquark) and an antiquark-hole (quark-hole) in the thermally excitedantiquark (quark) distribution. Our results suggest that the quarks in the QGPphase can be described within an interesting quasi-particle picture with amulti-peak spectral function. Because the models employed here are rathergeneric, our findings may represent a universal phenomenon for fermions coupledto a massive bosonic excitation with a vanishing or small width. The relevanceof these results to other fields of physics, such as neutrino physics, is alsobriefly discussed. In addition, we describe a new aspect of the plasminoexcitation obtained in the hard-thermal loop approximation.Comment: 41 pages, 39 eps figures, version to appear in Prog. Theor. Phys, comments on effects of the quark mass and the chemical potential added, typos corrected, some figures improve