Bryan W. Lynn, Glenn D. Starkman, Katherine Freese, Dmitry I. Podolsky
More than four decades ago, B.W. Lee and K. Symanzik proved that, in a
generic set of O(4) linear sigma models (LSM) in the f-pi vs.
mpi-squared-by-lambda-squared half-plane, Ward-Takahashi identities, along with
tadpole renormalization, i.e. a Higgs Vacuum Stability Condition, force all
S-matrix ultra-violet quadratic divergences (UV-QD) to be absorbed into the
physical renormalized pseudo-scalar pion mass squared. We show that all such
UV-QD, together with any finite remnants, therefore vanish identically in the
"Goldstone-mode" limit, where pions are Nambu-Goldstone Bosons (NGB) and
axial-vector current conservation is restored (i.e. when Lee and Symanzik's
Goldstone Symmetry Restoration Condition is enforced, as required by
Goldstone's theorem for the spontaneously broken theory). The scalar "Higgs"
mass is therefore not "quadratically fine-tuned" in the spontaneously broken
theory. Hence Goldstone-mode O(4) LSM symmetries are sufficient to ensure that
any finite remnant, after UV-QD cancellation, does not suffer from the Higgs
Fine Tuning Problem or Naturalness Problem. This is contrary to the lore that
quadratic divergences in the Higgs mass, observable already at 1-loop, lead to
such problems in the O(4) LSM, and are then directly inherited by the Standard
Model.
It was recently shown that, including all-orders perturbative electro-weak
and QCD loops, and independent of 1-loop ultraviolet regularization scheme, all
finite remnants of UV-QD in the Standard Model (SM) S-Matrix are absorbed into
NGB mass-squareds and vanish identically in the spontaneously broken SM. The SM
Higgs mass is therefore not fine-tuned. This paper's results on the O(4) LSM
lead us to a simple and intuitive understanding of that SM result, arising from
the embedding of O(4) LSM into the SM.
View original:
http://arxiv.org/abs/1112.2150
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