Chiral Symmetry Restoration, Naturalness and the Absence of Fine-Tuning I: Global Theories

The Standard Model (SM), and the scalar sector of its zero-gauge-coupling limit -- the chiral-symmetric limit of the Gell Mann-Levy Model (GML) -- have been shown not to suffer from a Higgs Fine-Tuning (FT) problem. All ultraviolet quadratic divergences (UVQD) are absorbed into the mass-squared of pseudo Nambu-Goldstone (pNGB) bosons, in GML. Since chiral SU(2)_{L-R} symmetry is restored as the pNGB mass-squared or as the Higgs vacuum expectation value (VEV) are taken to 0, small values of these quantities and of the Higgs mass are natural, and therefore not Fine-Tuned. In this letter, we extend our results on the absence of FT to a wide class of high-mass-scale (M_{Heavy}>>m_{Higgs}) extensions to a simplified SO(2) version of GML. We explicitly demonstrate naturalness and no-FT for two examples of heavy physics, both SO(2) singlets: a heavy (M_S >> m_{Higgs}) real scalar field (with or without a VEV); 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. The crucial common property of such high-mass-scale extensions is that they respect chiral SO(2)_{L-R} symmetry. GML is therefore natural and not FT, not just as a stand-alone renormalizable field theory, but also as a low energy effective theory with certain high-mass-scale extensions. We conjecture that, since gravity couples democratically to particles, quantum gravitational theories that respect chiral symmetry will also retain naturalness, and avoid FT problems for GML and the SM. Phenomenological consequences include the renewed possibility of thermal lepto-genesis in the neutrino-MSM. Absent a FT problem, there should be no expectation that LHC will discover physics beyond the SM unrelated to neutrino mixing.