Allowed region for the (second) lightest mass $M_{1,2}$ of right-handed neutrino ${\nu }_{R1,2}$ with $SO(10)$-inspired relations and sequential dominance

Abstract

In this paper, we evaluate the (second) lightest mass $M_{1,2}$ of right-handed neutrino ${\nu }_{R1,2}$ in grand unified theories with the type-I seesaw mechanism that predicts an almost massless neutrino $m_{1\mathrm{or}3}\sim 0$. By chiral perturbative treatment, the masses $M_{1,2}$ are expressed as $M_1=m_{D1}^2/m_{11},M_2=m_{D2}^2{m}_{11}/(m_{11}{m}_{22}-m_{12}^2)$ with the mass matrix of left-handed neutrinos $m$ in the diagonal basis of the Dirac mass matrix $m_D$. Assuming $m_{Di}$ and the unitary matrix $V$ in the singular value decomposition $(m_D{)}_{ij}=V_{ik}{m}_{Dk}{U}_{kj}^{†}$ are close to observed fermion masses and the CKM matrix, $M_{1,2}$ and their allowed regions are expressed by parameters in the low energy and unknown phases. As a result, for $m_{D1}\simeq 0.5$ MeV and $m_{D2}\simeq 100$ MeV, we obtain $M_1^{\mathrm{NH}}\simeq 3\times 10^{4-6}$ GeV and $M_2^{\mathrm{NH}}\simeq 3\times 10^{6-8}$ GeV in the NH, $M_1^{\mathrm{IH}}\simeq 5\times 10^{3-4}$ GeV and $M_2^{\mathrm{IH}}\simeq 4\times 10^{8-9}$ GeV in the IH. These upper and lower bounds are proportional to $m_{Di}^2$ or $m_{D1}{m}_{D2}$.

Comments: 16 pages, 2 figures