Does the hierarchy problem generate the seesaw scale?

Abstract

We find that minimizing the number of fine tuning relations in non-supersymmetric models can determine the scales at which some gauge symmetries beyond the standard model must break. We show that $SU(2)_R$ and $B-L$ gauge symmetries of the minimal left-right symmetric model must break at a scale $10^{15} GeV$ or higher, determined by the hierarchy problem and small ratios of quark masses, if parameters that break chiral or $\mu$-symmetries (and therefore can be naturally small), are not fine-tuned. This provides the $raison \ d'\hat{e}tre$ for the seesaw scale $\sim 10^{15}GeV$ indicated by neutrino experiments. Small ratios of fermion (quark) masses, which are natural in the standard model due to approximate chiral symmetry, will have to be fine tuned in minimal left right model if $SU(2)_R \times U(1)_{B-L}$ breaks at a lower scale.