Rare meson decays with three pairs of quasidegenerate heavy neutrinos

We consider a low-scale seesaw scenario where the masses of its heavy Majorana neutrinos are arranged in a pattern of three quasidegenerate pairs, in the range of $\mathcal{O}(1–6\mathrm{GeV})$. Since they can violate lepton number by two units, they contribute to rare decays of $D_s$ and $B_c$ mesons, providing the conditions for maximal $CP$ violation. We find that new phenomenology is possible depending on how many of on-shell pairs mediate these decays. In particular, we present new constraints on muon-heavy neutrino mixing parameters.

Figure 1

Schematic representation of the pair distribution in the on-shell mass range for Scenario III.

Figure 2

The $s$-channel of the lepton-number-violating decay $M^{+}\to {\ell }_1^{+}{\ell }_2^{+}{M}^{\prime -}$.

Figure 3

Effective mixing coefficients for Majorana neutrinos.

Figure 4

Left: ${\delta }_{ij}$ parameter which measures the $N_i-N_j$ overlap. Right: Some values of ${\delta }_{ij}$ and their respective errors.

Figure 5

Effective branching ratio divided by $|B_{\ell N}{|}^4$, for the processes (a) $D_s^{+}\to {\mu }^{+}{\mu }^{+}{\pi }^{-}$, (b) $D_s^{+}\to {\mu }^{+}{\mu }^{+}{K}^{-}$, (c) $B_C^{+}\to {\mu }^{+}{\mu }^{+}{\pi }^{-}$, and (d) $B_C^{+}\to {\mu }^{+}{\mu }^{+}{D}_s^{-}$, as a function of sterile neutrino mass, for $L=1[\mathrm{m}]$, ${\gamma }_N=2$, and $\eta =0.1m_N$. The dashed line represents the values for Scenario I, the solid line represents the value for Scenario II, and the dotted line represents the values for Scenario III. We regard the cases with $CP$ violation (${\delta }_{ij}=0.5$) and $\cos {\theta }_{jk}=\frac{1}{\sqrt{2}}$.

Figure 6

Quotients of the effective branching ratios for different values of $\eta$ using one pair and three pairs of $\mathrm{QDH}\nu$, for the processes (a) $D_s^{+}\to {\mu }^{+}{\mu }^{+}{\pi }^{-}$ and (b) $D_s^{+}\to {\mu }^{+}{\mu }^{+}{K}^{-}$, (c) $B_c^{+}\to {\mu }^{+}{\mu }^{+}{\pi }^{-}$, and (d) $B_c^{+}\to {\mu }^{+}{\mu }^{+}{D}_s^{-}$, as a function of sterile neutrino mass. We used $L=1[\mathrm{m}]$ and ${\gamma }_N=2$.

Figure 7

Limits for $|B_{\mu N}{|}^2$ from Ref. [39] vs the ones we get using one pair and three pairs of $\mathrm{QDH}\nu$ for the processes (a) $D_s^{+}\to {\mu }^{+}{\mu }^{+}{\pi }^{-}$, (b) $D_s^{+}\to {\mu }^{+}{\mu }^{+}{K}^{-}$, (c) $B_c^{+}\to {\mu }^{+}{\mu }^{+}{\pi }^{-}$, and (d) $B_c^{+}\to {\mu }^{+}{\mu }^{+}{D}_s^{-}$, based on expected luminosities for mesons. As before, we used $L=1[\mathrm{m}]$, ${\gamma }_N=2$, and $\eta =0.1m_N$.