| Summary: | In this letter, we perform a perturbative analysis by the lightest singular value mD1 of the Dirac mass matrix mD in the type-I seesaw mechanism. A mass relation M1=mD12/|(mν)11| is obtained for the lightest mass M1 of the right-handed neutrino νR1 and the mass matrix of the left-handed neutrinos mν in the diagonal basis of mD. This relation is rather stable under renormalization because it is gauge-invariant in the SM and associates with the approximate chiral symmetry of νR1.If diagonalization of the Yukawa matrices of leptons Yν,e has only small mixings, the value (mν)11 is close to the effective mass mee of the neutrinoless double beta decay. By assuming mD1≃mu,e≃0.5 MeV, the lightest mass is about M1≳O(100) TeV in the normal hierarchy and M1∼O(10) TeV in the inverted hierarchy. Such a νR1 with a tiny Yukawa coupling yν1∼O(10−5) can indirectly influence various observations.On the other hand, the famous bound of the thermal leptogenesis M1≳109 GeV that requires mD1≳30 MeV seems to be difficult to reconcile with a simple unified theory without a special condition.
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