### How could the standard model (core theory) be natural?

**Taking into account neutrino mixing ...**

The problem of the Higgs boson naturalness as phrased according to the current consensus in theoretical physics community (as well as its ideological use in experimental high energy physics programs) has already been evocated in this blog. I propose today to report on last developments of a work conducted mainly by Bryan Lynn under the seemingly mathematical scrutiny of late Raymond Stora that sheds an original light on this issue.

We defined the ν_{D}SM^{G}as the global SU(3)_{C}×SU(2)_{L}×U(1)_{Y}model of a complex Higgs doublet, and Standard Model (SM) quarks and leptons, augmented by 3 right-handed neutrinos with Dirac masses. With SM isospin and hypercharge assignments for fermions, ν_{D}SM^{G}has zero axial anomaly. We showed that the weak-scale low-energy effective Lagrangian of the spontaneously brokenν_{D}SM^{G}is severely constrained by, and protected by, new rigid/global spontaneous symmetry breaking (SSB) axial-vector Ward-Takahashi identities (WTI) and a Goldstone theorem, In particular, the weakscale SSB ν. (Note that such decoupling is modulo special cases: e.g. heavy Majorana νR, and possibly .... dimension≤ 4 operators, non-analytic in momenta or a renormalization scale µ_{D}SM^{G}has an SU(2)L shift symmetry... which protects it from any Brout-Englert-Higgs fine-tuning problem, and causes the complete decoupling of certain heavy M2 Heavy m2 W eak BSM matter-particles^{2}, involve heavy particles, and are beyond the scope of this paper.)Renormalized observable <H>.^{2}, m^{2}_{h;pole}are therefore not fine-tuned, but instead Goldstone Exceptionally Natural, with far more powerful suppression of fine-tuning than G. ’t Hooft’s naturalness criteria [... 13] would demand

But such heavy-particle decoupling is historically (i.e. except for high-precision electro-weak S,T and U parameters [... 46]) the usual physics experience, at each energy scale, as experiments probed smaller and smaller distances. After all, Willis Lamb did not need to know the top quark or BEH mass [47] in order to interpret theoretically the experimentally observed O(m_{e}α^{5}ln α) splitting in the spectrum of hydrogen.Such heavy-particle decoupling may be the reason why the Standard Model, viewed as an effective low-energy weak-scale theory, is the most experimentally and observationally successfull and accurate theory of Nature known to humans, i.e. when augmented by classical General Relativity and neutrino mixing: that “Core Theory” [48] has no known experimental or observational counterexamples...

Imagine we are able to extend this work to the Standard Model itself...!With its local/gauge groupSU(3)_{Color}×SU(2)_{L}×U(1)_{Y}, we would build 3 sets of rigid/global WTIs: unbrokenSU(3)_{Color}; unbroken electromagneticU(1)_{QED}; and spontaneously brokenSU(2)_{L}. It is then amusing to elevate such rigid/global WTIs to a “Principle of Nature”, so as to give them predictive power for actual experiments and observations. TheSU(3)_{Color}andU(1)_{QED}WTIs are unbroken vector-current IDs, and will not yield information analogous with that of SSB extended-AHM here. But the axial-vector current inside the SSBSU(2)_{L}WTIs will require and demand a nonzero SSB Dirac mass for each and every one of the the weak-interaction eigenstatesm^{Dirac}νe,m^{Dirac}νµ ,m^{Dirac}ντ≠0. The observable PNMS mixing matrix would then rotate those to mass-eigenstates m^{Dirac}ν1 ,m^{Dirac}ν2 ,m^{Dirac}ν3≠0.Would we then claim that spontaneouly brokenSU(2)_{L}WTIs predict neutrino oscillations? To make possible connection with Nature, although current experimental neutrino mixing data cannot rule out an exactly-zero mass for the lightest neutrino..., the mathematical self-consistency ofSU(2)_{L}WTIs would!

(Submitted on 21 Sep 2015)

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