The Pauli sum rules imply BSM physics

Abstract

Some 68 years ago (1951) Wolfgang Pauli mooted the three sum rules:∑n(−1)2Sngn=0;∑n(−1)2Sngnmn2=0;∑n(−1)2Sngnmn4=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.