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Theory Seminar (High Energy/Cosmology)
The Goldstone Exception: Spontaneously broken global symmetry, i.e. the Goldstone theorem, protects the Higgs from a Fine Tuning (FT) Problem
Date: Tuesday, September 23rd
Time: 3:00 pm - 4:00 pm
Place: 5280 Chamberlin Hall
Speaker: Bryan Lynn, University College London and Case Western University
Abstract: More than four decades ago, B.W. Lee and K. Symanzik proved that, in the O(4) Gell-Mann Levy (GML) model with Partially Conserved Axial-vector Currents (PCAC), global Ward Takahashi Identities (WTI) force all Ultra-Violet Quadratic Divergences (UVQD) into the renormalized pseudo Nambu-Goldstone-Boson (NGB) pion mass-squared. Tadpole renormalization is un-necessary.

We prove (to all-orders perturbations) that all UVQD, together with all other relevant operators, therefore vanish identically in GML’s spontaneous symmetry broken (SSB) Goldstone-mode, where pions are true NGB (i.e. exactly massless). A weak-scale Higgs mass is natural in SSB GML, the Higgs mass and vacuum expectation value (VEV) are stable against quantum corrections and not FT: SSB GML has no Higgs FT problem. Neither do the SSB O(4) Schwinger model (PCAC=0) or the Standard Model (SM). No-Higgs-FT is simply another (albeit unfamiliar) consequence of WTI and the Goldstone Theorem.

A huge class of high-mass-scale (M_{Heavy}>>m_{Higgs}) extensions of GML, Schwinger and SM also demonstrate naturalness, no-FT and heavy particle decoupling. We display two examples: a heavy (M_S >> m_{Higgs}) real scalar field; and a right-handed Type 1 See-Saw Majorana neutrino with M_R >> m_{Higgs}. We prove that for |q^2| << M_{Heavy}^2, the heavy degrees of freedom contribute only irrelevant and marginal operators. Phenomenological consequences include the renewed possibility of thermal lepto-genesis in the neutrino-MSM. It is also easy to construct no-Higgs-FT models with very high-scale SUSY breaking.

We conjecture that, since classical General Relativity (GR) couples democratically to spin=0, ½ and 1 quantum particles, GR+SM (and maybe certain quantum gravity theories) will also retain naturalness, avoiding FT problems. Absent a SM FT problem, there should be no expectation that LHC14 will discover physics beyond the SM which is unrelated to neutrino mixing, the only known experimental failure of the SM.
Host: Ran Lu
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