Spontaneously broken Standard Model (SM) symmetries and the Goldstone theorem protect the Higgs mass and ensure that it has no Higgs Fine Tuning Problem (HFTP)

TL;DR

This paper demonstrates that the Goldstone theorem and spontaneous symmetry breaking protect the Higgs mass from quadratic divergences, eliminating the need for fine-tuning and challenging the necessity of new physics beyond the Standard Model.

Contribution

It shows that the Higgs mass is protected by SM symmetries and Goldstone modes, removing the Higgs Fine Tuning Problem without requiring BSM physics.

Findings

UV quadratic divergences vanish in the Goldstone mode

Higgs mass remains stable and unfine-tuned at all loop orders

SM symmetries suffice to protect the Higgs mass

Abstract

B.W.Lee/K.Symanzik proved that Ward-Takahashi identities and tadpole renormalization force all ultra-violet quadratic divergences (UV-QD) to be absorbed into the physical renormalized pseudo-scalar pion mass in O(4)LSM (linear sigma models) across the Higgs-VEV vs. Pion-Mass-Squared half-plane. We show that all UV-QD vanish identically in the "Goldstone mode" Zero-Pion-Mass spontaneous symmetry breaking (SSB) limit. The Higgs mass is protected to all loop-orders and Goldstone-mode O(4)LSM has no Higgs fine-tuning problem (HFTP). We insist that self-consistent renormalization of the Standard Model (SM) requires that the scalar-sector UV-QD-corrected effective Lagrangians of the SM and Goldstone-mode O(4)LSM are smoothly identical in the zero-gauge-coupling limit. Lee/Symanzik's two conditions must be imposed on the SM: the Higgs cannot simply disappear into the vacuum; SM Nambu-Goldstone boson (NGB) masses (i.e. the pre-Higgs-mechanism longitudinal Wand Z masses) must vanish identically. At 1-loop, the Higgs-VEV is neither UV-QD divergent nor fine-tuned. Loop-induced-artefact NGB masses absorb all SM UV-QD, which vanish identically in the Zero-NGB-Mass limit, i.e. the SSB SM. Simply another (un-familiar) consequence of the Goldstone theorem, no fine-tuning is necessary for a weak-scale Higgs mass. Our SM results can (almost certainly) be extended to include all-orders perturbative electro-weak and QCD loops. SM symmetries (as realized by SSB and the Goldstone theorem) are sufficient to protect the Higgs mass, and ensure that the SM does not suffer a HFTP. It is un-necessary to impose any new Beyond the Standard-Model (BSM) symmetries. Mistaken belief in a 1-loop SM HFTP has historically driven an expectation that new BSM physics must appear < 14 TeV. But our results re-open the possibility that LHC discovery potential might be confined to SM physics.