The Pauli sum rules imply BSM physics

Abstract

Some 67 years ago (1951) Wolfgang Pauli mooted the three sum rules: n (−1) 2Sn g n = 0; n (−1) 2Sn g n m 2 n = 0; n (−1) 2Sn g n m 4 n = 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.

Vacuum Polarization Instead of “Dark Matter” in a Galaxy

“…( 7) by virtue of the equation of state (9). Bosons and fermions contribute with opposite signs into a vacuum energy density (8) [43,44]. Here, we do not consider the supersymmetry hypotheses N boson − N f erm due to the absence of evidence for supersymmetric partners to date [45].…”

“…For the mass contributions of particles and condensates, we imply the Pauli sum rules [44,46]. These rules are not fulfilled at this moment due to the incompleteness of the standard model.…”

Dark Matter in a Galaxy as Vacuum Polarization

“…In the formula (8), the UV cut-off k max and the difference between bosonic and fermionic degrees of freedom of the quantum fields appear since the zero-point stress-energy tensor is an additive quantity [26]. Here, we do not consider the supersymmetry hypotheses [27] due to absence of evidence of the supersymmetric particles to date. Other contributors to the vacuum energy density are the terms depending on the derivatives of the universe expansion rate [9,24,25,28].…”

A Vacuum of Quantum Gravity That is Ether.

“…The sense of renormalization is that one changes some infinite (or very large, if k max is taken finite) pieces in the operator of the mean values by some finite ones. We hope that in the future, when all the necessary particles will be discovered, the sum rules [25] will provide a mutual compensation of these infinite (or very large) pieces. That is, k max will give the actual UV completions of QG without the need for renormalization.…”