Right-handed weak currents in neutrinoless $ββ$ decays and ton scale $ββ$ detectors
Right handed weak-currents (RHCs) in the left-right (L-R) symmetric model for neutrinoless double beta decays (DBDs) of both the $0^+~\to~0^+$ and $0^+~\to~2^+$ transitions are discussed from both theoretical and experimental view points. $<λ>$ and $<η>$-terms are related by $<λ>/<η> \approx \tanβ$, which is constrained in the regions of $1-60$ for SUSY grand unified theories (GUTs) and of $1-165$ for non-SUSY GUTs. The enhancement mechanisms of the $<η>$ term over the $<λ>$ term in the $0^+$ transition are shown, and the $Δ$ isobar contribution to the NME for the transition to the 2$^+$ state is found to be of the order of $20\%$ of the NME with the quenched weak coupling. The new and interesting RHC regions of $<λ>\approx 5\times10^{-8}$ and $<η>\approx 1.5\times 10^{-10}$ are shown to be exclusively explored by measuring both the $ββ$ and $γ$ rays associated with the ground and excited DBDs by means of the ton-scale DBD detectors for the IH (inverted hierarchy) $ν$-masses. The actual RHCs to be studied depend on the RHC NMEs.