The condition 0 < Z < 1 and an intrinsic mass scale in Quantum Field Theory

TL;DR

This paper introduces a method to identify an intrinsic mass scale in Quantum Field Theories using nonlocal quantum field theories and the condition 0 < Z < 1, independent of specific dynamical details.

Contribution

It proposes a novel approach to determine an intrinsic mass scale in QFTs through a general principle applied to nonlocal quantum field theories, without relying on a specific framework.

Findings

Derives a nonlocal analogue of the 0 < Z < 1 condition.

Shows the intrinsic scale Lambda can be determined from this condition.

Suggests nonlocal QFTs as effective theories breaking at the intrinsic scale.

Abstract

In this work, we suggest a view-point that leads to an intrinsic mass scale in Quantum Field Theories. This view-point is fairly independent of dynamical details of a QFT and does not rely on any particular framework to go beyond the standard Model. We use the setting of the nonlocal quantum field theories NLQFT with a finite scale parameter Lambda, which are unitary for finite Lambda. We propose that the condition 0 < Z < 1 [wherever proven] can be rigorously implemented/imposed in such theories and that it implies the existence of a mass scale Lambda that can be determined from this condition. We derive the nonlocal analogue of the above relation [which is a finite relation in NLQFT] and demonstrate that it can be arrived at only from general principles. We further propose that the nonlocal formulation should be looked as an effective field theory that incorporates the effect of dynamics beyond an energy scale and which breaks at the intrinsic scale Lambda so obtained. Beyond this scale it should be replaced by another [perhaps, a more fundamental] theory. We provide a heuristic justification for this view-point.