Discussion on possible effects of the Barbero-Immirzi parameter at the TeV-scale particle physics

In this paper, we analyze a curvature- and torsion-square quantum gravity action with an additional Holst term minimally coupled to a massive Dirac field in four dimensions. The main purpose here is to try to estimate and compare the value of the Barbero-Immirzi parameter with its currently known results. To do that, we work out the physical mass of the fermion as a function of this parameter in a perturbative one-loop calculation, assuming the scenario of a physics at the TeV scale.

Figure 1

The running of $\beta$, with $\mathrm{\Lambda }=250\mathrm{MeV}$, $\mu =1\mathrm{MeV}$, $m_0=250\mathrm{MeV}$.