Scale of left-right symmetry

Unlike the standard model where neutrino masses can be made arbitrarily small, we find in the minimal left-right symmetric model that Dirac type Yukawa coupling $h_D \sim 10^{-4.2}$ for $\nu_\tau$ is generated from charged fermion Yukawa couplings through one loop Renormalization Group (RG) running. Using the seesaw relation this implies that the natural scale for right-handed neutrino's Majorana mass (seesaw scale) $M_N = f v_R \gtrsim 2000 TeV$. If we take the $SU(2)_R \times U(1)_{B-L}$ breaking scale $v_R$ to be below 50 TeV, so that it can be probed by LHC and a future collider, then the large $h_D$ generated on RG running increases the mass $m_\nu$ of the third generation light neutrino and severely suppresses the PMNS mixing angle $\theta_{23}$. We discuss the tuning needed for seesaw scales that can be probed by colliders and find the parameter space that can be tested by neutrino experiments for higher scales up to $10^{15} GeV$.