Dispersive determination of the fourth generation lepton masses

Abstract: We continue our previous determination of the masses of the sequential fourth generation quarks in an extension of the Standard Model, and predict the mass $m_4$ ($m_L$) of the fourth generation neutrino $\nu_4$ (charged lepton $L$) by solving the dispersion relation associated with heavy fermion decays. The results $m_4\approx 170$ GeV and $m_L\approx 270$ GeV are extracted from the dispersive analyses of the $t\to d e^+\nu_4$ and $L^-\to \nu_1 \bar t d$ decay widths, respectively, where $t$ ($d$, $e^+$, $\nu_1$) denotes a top quark (down quark, positron, light neutrino). The predictions are cross-checked by examining the $L^-\to \nu_4 \bar u d$ decay, $\bar u$ being an anti-up quark. It is shown that the fourth generation leptons with the above masses survive the current experimental bounds from Higgs boson decays into photon pairs and from the oblique parameters. We also revisit how the existence of the fourth generation leptons impacts the dispersive constraints on the neutrino masses and the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix elements. It is found that the unitarity of the $3\times 3$ PMNS matrix holds well up to corrections of $O(m_\nu^2/m_W^2)$, $m_\nu$ ($m_W$) being a light neutrino (the $W$ boson) mass, whose mixing angles and $CP$ phase prefer the values $\theta_{12}\approx 34^\circ$, $\theta_{23}\approx 47^\circ$, $\theta_{13}\approx 5^\circ$ and $\delta\approx 200^\circ$ in the normal-ordering scenario for neutrino masses.