Two Notions of Naturalness

Abstract

My aim in this paper is twofold: (i) to distinguish two notions of naturalness employed in Beyond the Standard Model (BSM) physics and (ii) to argue that recognizing this distinction has methodological consequences. One notion of naturalness is an "autonomy of scales" requirement: it prohibits sensitive dependence of an effective field theory's low-energy observables on precise specification of the theory's description of cutoff-scale physics. I will argue that considerations from the general structure of effective field theory provide justification for the role this notion of naturalness has played in BSM model construction. A second, distinct notion construes naturalness as a statistical principle requiring that the values of the parameters in an effective field theory be "likely" given some appropriately chosen measure on some appropriately circumscribed space of models. I argue that these two notions are historically and conceptually related but are motivated by distinct theoretical considerations and admit of distinct kinds of solution.

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

“…It appears that separation of scales in the sense is unaffected by the numerical sensitivity of the physical Higgs mass to cutoff scale parameters, far from being critically threatened by it. 3 A third rationale for worrying about sensitivity of the physical Higgs mass to cutoff-scale parameters has been articulated by Williams, who argues that the numerical sensitivities of the Higgs mass are problematic because they violate the "spirit" of the Decoupling Theorem and the expectation that natural phenomena be describable in terms of "quasi-autonomous domains," where a quasi-autonomous domain is a realm of phenomena characterized by the applicability of some particular effective theory [34,36]. The existence of quasi-autonomous domains corresponds roughly to what Giudice describes as separation of scales-the fact nature exhibits regimes of phenomena governed by different effective theories, which accurately describe the behavior of coarse-grained degrees of freedom without reference to detailed state or dynamics governing the more fine-grained degrees of freedom on which they depend.…”

“…See[7] for a characterization of the naturalness principle along these lines2 This distinction has previously been highlighted by[1,33,36].…”

Naturalness in nuclear effective field theories

“…This unnaturalness could be a reflection of fine tuning in the underlying theory. Again, the simple toy model (29) provides an example [15]: when α ≃ (2n + 1)π/2 ≡ α cn with n ≥ 0 an integer, we have |a 2 | ≃ R|α cn (α − α cn )| −1 ≃ |κ −1 2 | ≫ R while still |r 2 | ∼ . .…”

Naturalness and Emergence

“…I simplify here, though not in a way that essentially alters the main point: C depends on the values of all of the other parameters.4Williams (2018) is an insightful recent discussion of the difference between these two conceptions of naturalness, though he draws the distinction somewhat differently than I do here.…”