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High Energy Physics - Phenomenology, hep-ph,High Energy Physics - Theory, hep-th,
Abstract:
We perform a systematic one-loop renormalization of a general renormalizable
Yang-Mills theory coupled to scalars and fermions using a regularization scheme
with an explicit UV momentum cutoff $\Lambda$. We construct the necessary
finite counterterms restoring the BRST invariance of the effective action by
analyzing the relevant Slavnov-Taylor identities. We find the relation between
the renormalized parameters in our scheme and in the conventional
$\overline{\rm MS}$ scheme which allow us to obtain the explicit two-loop
renormalization group equations in our scheme from the known two-loop ones in
the $\overline{\rm MS}$ scheme. We calculate in our scheme the divergences of
two-loop vacuum graphs in the presence of a constant scalar background field
which allow us to rederive the two-loop beta functions for parameters of the
scalar potential. We also prove that consistent application of the proposed
regularization leads to counterterms which, together with the original action,
combine to a bare action expressed in terms of bare parameters. This, together
with treating $\Lambda$ as an intrinsic scale of a hypothetical underlying
finite theory of all interactions, offers a possibility of an unconventional
solution to the hierarchy problem if no intermediate scales between the
electroweak scale and the Planck scale exist.
