Renormalization Scheme Ambiguities in the Models with More than One Coupling

TL;DR

This paper investigates how finite renormalization ambiguities affect models with multiple couplings, like the Standard Model, showing non-uniqueness of beta-functions beyond one loop but their physical irrelevance at higher orders.

Contribution

It extends the analysis of renormalization ambiguities to models with more than two couplings, such as the Standard Model, highlighting the non-uniqueness of beta-functions beyond one loop.

Findings

Beta-functions are not unique beyond one loop in multi-coupling models.

Higher-order contributions can be absorbed into beta-functions for physical processes.

Mass independent renormalization leads to non-uniqueness in these models.

Abstract

The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making such finite renormalizations have been examined in the case of there being one or two couplings. In this paper we consider how finite renormalizations can affect more general models in which there are more than two couplings. In particular, we consider the Standard Model in which there are essentially five couplings. We show that in this model (when neglecting all mass parameters) if we use mass independent renormalization, then the renormalization group beta-functions are not unique beyond one loop order, that it is not in general possible to eliminate all terms beyond certain order for all these beta-functions, but that for a physical process all contributions beyond one loop order can be subsumed into the beta-functions.