Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2011-06-30
Physics
High Energy Physics
High Energy Physics - Phenomenology
Revised argument, in Section 2 and 3, follows renormalization of finite Pion-Mass and PCAC in O(4) linear sigma model. All res
Scientific paper
B.W.Lee/K.Symanzik proved that Ward-Takahashi identities and tadpole renormalization force all UV quadratic divergences (UV-QD) to be absorbed into the physical renormalized Pion-Mass in O(4) linear sigma models. We show that UV-QD thus vanish exactly in the Zero-Pion-Mass-Limit and that the "Higgs" mass is not "fine-tuned" there. Consistent renormalization of the Standard Model (SM) requires that the scalar-sector UV-QD-corrected effective Lagrangians of the SM and Zero-Pion-Mass-O(4)LSM are smoothly identical in the zero-gauge-coupling limit. Lee/Symanzik's two conditions must therefore be imposed: a Higgs Stability Condition (it must not disappear into the vacuum) and a Goldstone Symmetry Restoration Condition (Nambu-Goldstone Boson (NGB) masses must be exactly zero). Including all-orders perturbative electro-weak and QCD loops, and independent of regularization scheme, SM UV-QD are then all absorbed into NGB masses and vanish identically in the Zero-NGB-Mass-Limit: i.e. in the spontaneously broken SM. They are not absorbed into SM renormalized parameters. No fine-tuning, even with Planck scale UV cut-off, is necessary for a weak-scale Higgs mass, an un-familiar consequence of the Goldstone theorem. The SM does not suffer Naturalness, Weak Hierarchy or Higgs Fine Tuning Problems (N-WH-HFT/P) as defined here. Mistaken belief in non-vanishing UV-QD and N-WH-HFT/P in the 1-loop SM has historically driven an expectation that new Beyond the Standard Model physics must appear < 10 TeV. But our results re-open the possibility that LHC discovery potential might be confined to SM physics. The crucial SM make/break test (a win/win scenario!) is LHC discovery/exclusion of the SM Higgs at that mass indicated by high-precision 1-electroweak-loop LEP1/SLC physics.
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