The Pauli sum rules imply BSM physics
Abstract
Some 67 years ago (1951) Wolfgang Pauli mooted the three sum rules: \[ Σn (-1)2Sn gn = 0; Σn (-1)2Sn gn \; mn2 =0; Σn (-1)2Sn gn \; mn4=0. \] These three sum rules are intimately related to both the Lorentz invariance and the finiteness of the zero-point stress-energy tensor. Further afield, these three constraints are also intimately related to the existence of finite QFTs ultimately based on fermi--bose cancellations. (Supersymmetry is neither necessary nor sufficient for the existence of these finite QFTs; though softly but explicitly broken supersymmetry or mis-aligned supersymmetry can be used as a book-keeping device to keep the calculations manageable.) In the current article I shall instead take these three Pauli sum rules as given, assume their exact non-perturbative validity, contrast them with the observed standard model particle physics spectrum, and use them to extract as much model-independent information as possible regarding beyond standard model (BSM) physics.