Study of two quasidegenerate heavy sterile neutrinos in rare meson decays

In this work, we study the lepton-number-violating processes of $K^{\pm }$ and $D^{\pm }$ mesons. Two quasidegenerate sterile neutrinos are assumed to induce such processes. Different from the case where only one sterile neutrino is involved, here, the $CP$ phases of the mixing parameters could give a sizable contribution. This, in turn, would affect the absolute values of the mixing parameters determined by the experimental upper limits of the branching fractions. A general function which expresses the difference between the mixing parameters for two-generation and one-generation cases is presented. Special cases with specific relations of the parameters are discussed. Besides, we also thoroughly investigate the $CP$ violation effect of such processes. It is shown that generally ${\mathcal{A}}_{CP}$ is a function of the sterile neutrino mass.

Figure 1

(a) Decay width of heavy sterile neutrino with $m_N\in [0.140,5.279]\mathrm{GeV}$; (b) the portion of the contribution made by $U_e$, $U_{\mu }$, and $U_{\tau }$, respectively.

Figure 2

Feynman diagram of the LNV process $K^{+}\to e^{+}{e}^{+}{\pi }^{-}$.

Figure 3

$y$ function in the two-generation case with parameters chosen as: (a) $k=1.0,x_0=0.1,\mathrm{\Delta }\phi =\pi /2$, (b) $k=1.0,x_0=1.0,\mathrm{\Delta }\phi =\pi$, (c) $k=1.0,x_0=1.0,\mathrm{\Delta }\phi =\pi /2$, (d) $k=2.0,x_0=1.0,\mathrm{\Delta }\phi =\pi /2$.

Figure 4

$R_{21}$ as a function of (a) $\mathrm{\Delta }\phi$ and (b) $x_0$.

Figure 5

The dependence of $R_{21}$ on $k$ and $k_e$ with $x_0=0.1$ and $\mathrm{\Delta }\phi =\pi$.

Figure 6

The dependence of $R_{21}$ on $m_4$ with (a) $k_{\tau }=0.1$, (b) $k_{\tau }=1.0$ and (c) $k_{\tau }=10.0$. Here we have chosen $k_e=k_{\mu e}=k_{\tau e}=1$, $x_0=0.1$, $\mathrm{\Delta }\phi =\pi$ and $k_{\mu }=0.1,1.0,10.0$ in each subfigure.

Figure 7

Experimental bounds on (a) ${|U_e|}^2$, (b)${|U_{\mu }|}^2$, and (c) $|U_e{U}_{\mu }|$ in one-generation and two-generation scenarios. For the later case, we choose $k_{\mu e}=k_{\tau e}=1$, $k_{\tau }=10.0$ and $x_0=0.1$.

Figure 8

(a) ${\mathcal{A}}_{CP}$ as a function of $x_0$ and $\mathrm{\Delta }\phi$ with $k=1$; (b) the region around the maximum.

Figure 9

The extremum of ${\mathcal{A}}_{CP}$ as a function of $k_e$ and $k$.

Figure 10

The mass dependency of the extremum value of $CP$ asymmetry in several choices of parameters, where $k_e=0.99$, $k_{\mu e}=k_{\tau e}=1$.