How could the standard model (core theory) be natural?
We defined the νDSMG 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, νDSMG has zero axial anomaly. We showed that the weak-scale low-energy effective Lagrangian of the spontaneously broken νDSMG 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 νDSMG 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. (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 µ2, involve heavy particles, and are beyond the scope of this paper.) Renormalized observable <H>2 , m2h;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  in order to interpret theoretically the experimentally observed O(meα5ln 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”  has no known experimental or observational counterexamples...
Imagine we are able to extend this work to the Standard Model itself...! With its local/gauge group SU(3)Color×SU(2)L×U(1)Y , we would build 3 sets of rigid/global WTIs: unbroken SU(3)Color; unbroken electromagnetic U(1)QED; and spontaneously broken SU(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. The SU(3)Color and U(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 SSB SU(2)L WTIs will require and demand a nonzero SSB Dirac mass for each and every one of the the weak-interaction eigenstates mDiracνe, mDiracνµ , mDiracντ ≠ 0. The observable PNMS mixing matrix would then rotate those to mass-eigenstates mDiracν1 , mDiracν2 , mDiracν3 ≠ 0. Would we then claim that spontaneouly broken SU(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 of SU(2)L WTIs would!
Global SU(3)CxSU(2)LxU(1)Y linear sigma model with Standard Model fermions: axial-vector Ward Takahashi identities, the absence of Higgs mass fine tuning, and the decoupling of certain heavy particles, due to the Goldstone theorem(Submitted on 21 Sep 2015)