Chiral perturbative relation for neutrino masses in the type-I seesaw mechanism.

In this letter, we perform a perturbative analysis by the lightest singular value m D 1 of the Dirac mass matrix m D in the type-I seesaw mechanism. A mass relation M 1 = m D 1 2 / | (m ν) 11 | is obtained for the lightest mass M 1 of the right-handed neutrino ν R 1 and the mass matrix of the left-handed neutrinos m ν in the diagonal basis of m D. This relation is rather stable under renormalization because it is gauge-invariant in the SM and associates with the approximate chiral symmetry of ν R 1. If diagonalization of the Yukawa matrices of leptons Y ν , e has only small mixings, the value (m ν) 11 is close to the effective mass m e e of the neutrinoless double beta decay. By assuming m D 1 ≃ m u , e ≃ 0.5 MeV, the lightest mass is about M 1 ≳ O (100) TeV in the normal hierarchy and M 1 ∼ O (10) TeV in the inverted hierarchy. Such a ν R 1 with a tiny Yukawa coupling y ν 1 ∼ O (10 − 5) can indirectly influence various observations. On the other hand, the famous bound of the thermal leptogenesis M 1 ≳ 10 9 GeV that requires m D 1 ≳ 30 MeV seems to be difficult to reconcile with a simple unified theory without a special condition. [ABSTRACT FROM AUTHOR]