  In this letter, we perform a perturbative analysis by the lightest singular
value $m_{D1}$ of the Dirac mass matrix $m_{D}$ in the type-I seesaw mechanism.
A mass relation $M_{1} = m_{D1}^{2}/ |(m_{\nu})_{11}|$ is obtained for the
lightest mass $M_{1}$ of the right-handed neutrino $\nu_{R1}$ and the mass
matrix of the left-handed neutrinos $m_{\nu}$ 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 $\nu_{R1}$.
  If diagonalization of the Yukawa matrices of leptons $Y_{\nu, e}$ has only
small mixings, the element $(m_{\nu})_{11}$ is close to the effective mass
$m_{ee}$ of the neutrinoless double beta decay. By assuming $m_{D1} \simeq
m_{u,e} \simeq 0.5$ MeV, the lightest mass is about $M_{1} \gtrsim O(100)$ TeV
in the normal hierarchy and $M_{1} \sim O(10)$ TeV in the inverted hierarchy.
Such a $\nu_{R1}$ with a tiny Yukawa coupling $y_{\nu 1} \sim O(10^{-5})$ can
indirectly influence various observations.
  On the other hand, the famous bound of the thermal leptogenesis $M_{1}
\gtrsim 10^{9}$ GeV that requires $m_{D1} \gtrsim 30$ MeV seems to be difficult
to reconcile with a simple unified theory without a special condition.
