Naturalness, Wilsonian Renormalization, and "Fundamental Parameters" in Quantum Field Theory

TL;DR

This paper examines the concept of naturalness and fundamental parameters in quantum field theory, contrasting two interpretations within the Wilsonian framework and arguing that the notion of fundamental parameters may be unnecessary in high energy physics.

Contribution

It clarifies the distinction between defining EFTs by fundamental parameters versus RG trajectories, challenging the necessity of fundamental parameters in high energy physics.

Findings

Wilsonian RG perspective shows no single fundamental parameter set is physically preferred.

Fine tuning of the Higgs mass is an artifact of arbitrary reference scales.

The concept of fundamental parameters may be superfluous in high energy physics.

Abstract

The Higgs naturalness principle served as the basis for the so far failed prediction that signatures of physics beyond the Standard Model (SM) would be discovered at the LHC. One influential formulation of the principle, which prohibits fine tuning of bare Standard Model (SM) parameters, rests on the assumption that a particular set of values for these parameters constitute the "fundamental parameters" of the theory, and serve to mathematically define the theory. On the other hand, an old argument by Wetterich suggests that fine tuning of bare parameters merely reflects an arbitrary, inconvenient choice of expansion parameters and that the choice of parameters in an EFT is therefore arbitrary. We argue that these two interpretations of Higgs fine tuning reflect distinct ways of formulating and interpreting effective field theories (EFTs) within the Wilsonian framework: the first takes an EFT to be defined by a single set of physical, fundamental bare parameters, while the second takes a Wilsonian EFT to be defined instead by a whole Wilsonian renormalization group (RG) trajectory, associated with a one-parameter class of physically equivalent parametrizations. From this latter perspective, no single parametrization constitutes the physically correct, fundamental parametrization of the theory, and the delicate cancellation between bare Higgs mass and quantum corrections appears as an eliminable artifact of the arbitrary, unphysical reference scale with respect to which the physical amplitudes of the theory are parametrized. While the notion of fundamental parameters is well motivated in the context of condensed matter field theory, we explain why it may be superfluous in the context of high energy physics.