Abstract
We construct an effective action for "soft" gluons by integrating out hard thermal modes of topologically massive vector bosons at one loop order. The loop carrying hard gluons (momentum $\sim T$) are known as hard thermal loop (HTL). The gluons are massive in the non-Abelian topologically massive model (TMM) due to a quadratic coupling $B\wedge F$ where a 2-form field $B$ is coupled quadratically with the field strength $F$ of Yang-Mills (YM) field. The mass of the gluons plays an important role in the perturbative analysis of thermal field theory. Due to the presence of this infrared cut-off in the model, the color diffusion constant and conductivity can be analyzed in perturbative regime.
Highlights
Gauge theory plays a crucial role in the standard model of particle physics for the description of fundamental interactions in nature [1,2,3]
In the final form, we have clearly shown how the Debye mass is modified due to the presence of the bare mass of massive gauge bosons
The bare mass puts an infrared cutoff in quantum chromodynamics (QCD) at finite temperature
Summary
Gauge theory plays a crucial role in the standard model of particle physics for the description of fundamental interactions in nature [1,2,3]. We will construct an effective Lagrangian density by integrating out the hard modes of topologically massive gluons (with momentum ∼T) This procedure has been followed to obtain a general form of hard thermal loop (HTL) effective action for massless gauge fields [27]. The gauge bosons acquire longitudinal mode, which violates unitarity in the scattering processes at high energy limit This can be seen in any massive non-Abelian gauge theory, for example, the electroweak sector [37,38,39]. We have recently shown a significant characteristic of the non-Abelian TMM This is the same behavior of strong coupling at high energy limit (i.e., asymptotic freedom) as what is found in massless YM theory [54]. It is to be noted that the CP symmetry is not violated in this model
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