Perturbations to the $\mu -\tau$ symmetry, leptogenesis, and lepton flavor violation with the type II seesaw mechanism

We study the possibility of generating nonzero reactor mixing angle ${\theta }_{13}$ by perturbing the $\mu -\tau$ symmetric neutrino mass matrix. The leading-order $\mu -\tau$ symmetric neutrino mass matrix originates from a type I seesaw mechanism, whereas the perturbations to $\mu -\tau$ symmetry originate from a type II seesaw term. We consider four different realizations of $\mu -\tau$ symmetry, bimaximal mixing, tribimaximal mixing, hexagonal mixing, and golden ratio mixing, all giving rise to ${\theta }_{13}=0,{\theta }_{23}=\frac{\pi }{4}$ but different nonzero values of solar mixing angle ${\theta }_{12}$. We assume a minimal $\mu -\tau$ symmetry breaking type II seesaw mass matrix as a perturbation and calculate the neutrino oscillation parameters as a function of type II seesaw strength. We then consider the origin of nontrivial leptonic $CP$ phase in the charged lepton sector and calculate the lepton asymmetry arising from the lightest right-handed neutrino decay by incorporating the presence of both type I and type II seesaws. We constrain the type II seesaw strength as well as the leptonic $CP$ phase (and hence the charged lepton sector) by comparing our results with experimental neutrino oscillation parameters as well as the Planck bound on the baryon-to-photon ratio. Finally, we extend our analysis on lepton flavor violating decays like $\mu \to e\gamma$ and $\mu \to eee$ due to the exchange of a TeV scale Higgs triplet scalar within the low scale type II seesaw framework. The branching ratios for these lepton flavor processes are examined with the small type II perturbation term $\omega$, and the estimated values are very close to the experimental bound coming from current search experiments.

Figure 1

Right-handed neutrino decay.

Figure 2

Right-handed neutrino decay.

Figure 3

Relevant Feynman diagram for $\mu \to e\gamma$ due to Higgs triplet exchange.

Figure 4

Relevant Feynman diagram for $\mu \to eee$ due to Higgs triplet exchange.

Figure 5

Variation of ${\sin }^2{\theta }_{13}$ with type II seesaw strength $w$ for BM and TBM with $m_1(m_3)=0.07(0.065)\mathrm{eV}$.

Figure 6

${\sin }^2{\theta }_{13}$ with type II seesaw strength $w$ for BM and TBM with $m_1(m_3)=0.07(0.065)\mathrm{eV}$.

Figure 7

${\sin }^2{\theta }_{13}$ with type II seesaw strength $w$ for HM and GRM with $m_1(m_3)=0.001\mathrm{eV}$.

Figure 8

${\sin }^2{\theta }_{13}$ with type II seesaw strength $w$ for HM and GRM with $m_1(m_3)=0.07(0.065)\mathrm{eV}$.

Figure 9

$\mathrm{\Delta }{m}_{21}^2$, $\mathrm{\Delta }{m}_{23}^2$, and $\mathrm{\Delta }{m}_{31}^2$ with ${\sin }^2{\theta }_{13}$ for BM with $m_1(m_3)=0.001\mathrm{eV}$.

Figure 10

$\mathrm{\Delta }{m}_{21}^2$, $\mathrm{\Delta }{m}_{23}^2$, and $\mathrm{\Delta }{m}_{31}^2$ with ${\sin }^2{\theta }_{13}$ for BM with $m_1(m_3)=0.07(0.065)\mathrm{eV}$.

Figure 11

${\sin }^2{\theta }_{23}$ and ${\sin }^2{\theta }_{12}$ with ${\sin }^2{\theta }_{13}$ for BM with $m_1(m_3)=0.001\mathrm{eV}$.

Figure 12

${\sin }^2{\theta }_{23}$ and ${\sin }^2{\theta }_{12}$ with ${\sin }^2{\theta }_{13}$ for BM with $m_1(m_3)=0.07(0.065)\mathrm{eV}$.

Figure 13

$\mathrm{\Delta }{m}_{21}^2$, $\mathrm{\Delta }{m}_{23}^2$, and $\mathrm{\Delta }{m}_{31}^2$ with ${\sin }^2{\theta }_{13}$ for TBM with $m_1(m_3)=0.001\mathrm{eV}$.

Figure 14

$\mathrm{\Delta }{m}_{21}^2$, $\mathrm{\Delta }{m}_{23}^2$, and $\mathrm{\Delta }{m}_{31}^2$ with ${\sin }^2{\theta }_{13}$ for TBM with $m_1(m_3)=0.07(0.065)\mathrm{eV}$.

Figure 15

${\sin }^2{\theta }_{23}$, and ${\sin }^2{\theta }_{12}$ with ${\sin }^2{\theta }_{13}$ for TBM with $m_1(m_3)=0.001\mathrm{eV}$.

Figure 16

${\sin }^2{\theta }_{23}$, and ${\sin }^2{\theta }_{12}$ with ${\sin }^2{\theta }_{13}$ for TBM with $m_1(m_3)=0.07(0.065)\mathrm{eV}$.

Figure 17

$\mathrm{\Delta }{m}_{21}^2$, $\mathrm{\Delta }{m}_{23}^2$, and $\mathrm{\Delta }{m}_{31}^2$ with ${\sin }^2{\theta }_{13}$ for HM with $m_1(m_3)=0.001\mathrm{eV}$.

Figure 18

$\mathrm{\Delta }{m}_{21}^2$, $\mathrm{\Delta }{m}_{23}^2$, and $\mathrm{\Delta }{m}_{31}^2$ with ${\sin }^2{\theta }_{13}$ for HM with $m_1(m_3)=0.07(0.065)\mathrm{eV}$.

Figure 19

${\sin }^2{\theta }_{23}$ and ${\sin }^2{\theta }_{12}$ with ${\sin }^2{\theta }_{13}$ for HM with $m_1(m_3)=0.001\mathrm{eV}$.

Figure 20

${\sin }^2{\theta }_{23}$ and ${\sin }^2{\theta }_{12}$ with ${\sin }^2{\theta }_{13}$ for HM with $m_1(m_3)=0.07(0.065)\mathrm{eV}$.

Figure 21

$\mathrm{\Delta }{m}_{21}^2$, $\mathrm{\Delta }{m}_{23}^2$, and $\mathrm{\Delta }{m}_{31}^2$ with ${\sin }^2{\theta }_{13}$ for GRM with $m_1(m_3)=0.001\mathrm{eV}$.

Figure 22

$\mathrm{\Delta }{m}_{21}^2$, $\mathrm{\Delta }{m}_{23}^2$, and $\mathrm{\Delta }{m}_{31}^2$ with ${\sin }^2{\theta }_{13}$ for GRM with $m_1(m_3)=0.07(0.065)\mathrm{eV}$.

Figure 23

${\sin }^2{\theta }_{23}$ and ${\sin }^2{\theta }_{12}$ with ${\sin }^2{\theta }_{13}$ for GRM with $m_1(m_3)=0.001\mathrm{eV}$.

Figure 24

${\sin }^2{\theta }_{23}$ and ${\sin }^2{\theta }_{12}$ with ${\sin }^2{\theta }_{13}$ for GRM with $m_1(m_3)=0.07(0.065)\mathrm{eV}$.

Figure 25

$\sum _i|m_i|$ and $|m_{ee}|$ with ${\sin }^2{\theta }_{13}$ for BM with $m_1(m_3)=0.001\mathrm{eV}$.

Figure 26

$\sum _i|m_i|$ and $|m_{ee}|$ with ${\sin }^2{\theta }_{13}$ for BM with $m_1(m_3)=0.07(0.065)\mathrm{eV}$.

Figure 27

$\sum _i|m_i|$ and $|m_{ee}|$ with ${\sin }^2{\theta }_{13}$ for TBM with $m_1(m_3)=0.001\mathrm{eV}$.

Figure 28

$\sum _i|m_i|$ and $|m_{ee}|$ with ${\sin }^2{\theta }_{13}$ for TBM with $m_1(m_3)=0.07(0.065)\mathrm{eV}$.

Figure 29

$\sum _i|m_i|$ and $|m_{ee}|$ with ${\sin }^2{\theta }_{13}$ for HM with $m_1(m_3)=0.001\mathrm{eV}$.

Figure 30

$\sum _i|m_i|$ and $|m_{ee}|$ with ${\sin }^2{\theta }_{13}$ for HM with $m_1(m_3)=0.07(0.065)\mathrm{eV}$.

Figure 31

$\sum _i|m_i|$ and $|m_{ee}|$ with ${\sin }^2{\theta }_{13}$ for GRM with $m_1(m_3)=0.001\mathrm{eV}$.

Figure 32

$\sum _i|m_i|$ and $|m_{ee}|$ with ${\sin }^2{\theta }_{13}$ for GRM with $m_1(m_3)=0.07(0.065)\mathrm{eV}$.

Figure 33

Variation of baryon asymmetry with $\delta$ for BM and HM.

Figure 34

Variation of baryon asymmetry with $\delta$ for TBM.