The Pauli sum rules imply BSM physics

TL;DR

This paper explores how Pauli's sum rules, which relate to Lorentz invariance and zero-point energy finiteness, impose constraints on BSM physics by analyzing the standard model spectrum.

Contribution

It demonstrates that Pauli's sum rules can be used to derive model-independent constraints on BSM physics from the observed particle spectrum.

Findings

Pauli sum rules are exactly valid and non-perturbatively true.

Constraints on BSM particles derived from sum rules.

Implications for the structure of finite quantum field theories.

Abstract

Some 67 years ago (1951) Wolfgang Pauli mooted the three sum rules: \[ \sum_n (-1)^{2S_n} g_n = 0; \qquad \sum_n (-1)^{2S_n} g_n \; m_n^2 =0; \qquad \sum_n (-1)^{2S_n} g_n \; m_n^4=0. \] 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.