Naturalness, Wilsonian renormalization, and “fundamental parameters” in quantum field theory

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.

The Classical Limit as an Approximation

“…For further remarks on error bounds in reductive explanations, seeScheibe (1986) or the discussion of "limits of validity" inRohrlich (1990Rohrlich ( , 2002.19 Recent philosophical work on renormalization describes theories related by renormalization group transformations as "alternative descriptions of the same physical system"(Fraser, 2019, p. 22). See also similar remarks inRosaler and Harlander (2019).…”

Dogmas of Effective Field Theory: Scheme Dependence, Fundamental Parameters, and the Many Faces of the Higgs Naturalness Principle

“…The analysis provided here serves to synthesize and expand upon the analysis of two previous articles, [23] and [14]. The first of these argues that the cancellations and sensitivities associated with bare formulations of the Higgs naturalness principle are formal artifacts associated with an arbitrary choice of bare parametrization, while the second argues that the cancellations and sensitivities arising in renormalized formulations are formal artifacts associated with an arbitrary choice of renormalization scheme.…”

Philosophical foundations of effective field theories

“…This suggests that in all situations the success of Cao and Schweber's argument about quasiautonomous domains may not rest on the validity of the decoupling theorem but on the success of Wilsonian RG methods. When the latter is considered, however, one faces a whole new set of issues beyond the scope of this review; most importantly, the problem of naturalness [4,24,40,47,49].…”