On Perturbative Dynamics in Gauge Field Theories: an Investigation in Higgs Particle and an Anti-symmetric Tensor Field As an Alternative to Higgs Mechanism in Standard Model of Particle Physics

The contribution of a non-Abelian tensor field (already appearing in the spectrum of string theory) to the self energy of a vector field is examined for a theory which is one of the various attempts to find an alternative to the Higgs mechanism. By direct calculation of one-loop Feynman diagrams, we show that the anti-symmetric tensor field makes no contribution to the self-energy of the vector field at this order. This result is consistent with an analysis of the degrees of freedom which shows that there are no physical degrees of freedom associated with the tensor field. The coupling of this anti-symmetric tensor field to matter results in divergencies which are not consistent with renormalizability. If this tensor field were to exist though, it would necessarily couple to the gravitational field, contributing to 'dark matter'. As well the contribution of the non-Abelian vector field to the self-energy of the anti-symmetric tensor field is computed to see if a dynamically generated kinetic term arises for the tensor field. The effect of higher loop terms coming from scalar fields on the Standard Model $beta$-function, is also examined.