Probing new physics in the neutrinoless double beta decay using electron angular correlation

The angular correlation of the electrons emitted in the neutrinoless double beta decay ($0\nu 2\beta$) is presented using a general Lorentz invariant effective Lagrangian for the leptonic and hadronic charged weak currents. We show that the coefficient $K$ in the angular correlation $d\Gamma /d\cos \theta \propto (1-K\cos \theta )$ is essentially independent of the nuclear matrix element models and present its numerical values for the five nuclei of interest (${}^{76}\mathrm{Ge}$, ${}^{82}\mathrm{Se}$, ${}^{100}\mathrm{Mo}$, ${}^{130}\mathrm{Te}$, and ${}^{136}\mathrm{Xe}$), assuming that the $0\nu 2\beta$ decays in these nuclei are induced solely by a light Majorana neutrino, ${\nu }_M$. This coefficient varies between $K=0.81$ (for the ${}^{76}\mathrm{Ge}$ nucleus) and $K=0.88$ (for the ${}^{82}\mathrm{Se}$ and ${}^{100}\mathrm{Mo}$ nuclei), calculated taking into account the effects from the nucleon recoil, the $S$ and $P$ waves for the outgoing electrons and the electron mass. Deviation of $K$ from its values derived here would indicate the presence of new physics (NP) in addition to a light Majorana neutrino, and we work out the angular coefficients in several ${\nu }_M+\mathrm{NP}$ scenarios for the ${}^{76}\mathrm{Ge}$ nucleus. As an illustration of the correlations among the $0\nu 2\beta$ observables (half-life $T_{1/2}$, the coefficient $K$, and the effective Majorana neutrino mass $|⟨m⟩|$) and the parameters of the underlying NP model, we analyze the left-right symmetric models, taking into account current phenomenological bounds on the right-handed $W_R$-boson mass and the left-right mixing parameter $\zeta$.

Figure 1

Correlation between the neutrino effective mass $|⟨m⟩|$ (left) [$|{ϵ}_{V+A}^{V+A}|$ (right)], the angular correlation coefficient $K$, and the half-life $T_{1/2}$ for the $0\nu 2\beta$ decay of ${}^{76}\mathrm{Ge}$ for the case $\cos {\psi }_1=0$.

Figure 2

Correlation between the neutrino effective mass $|⟨m⟩|$ (left) [$|{ϵ}_{V-A}^{V+A}|$ (right)], the angular correlation coefficient $K$, and the half-life $T_{1/2}$ for the $0\nu 2\beta$ decay of ${}^{76}\mathrm{Ge}$ for the case $\cos {\psi }_1=0$.

Figure 3

Correlation between the right-handed $W$-boson mass $m_{W_R}$, the angular correlation coefficient $K$, and the half-life $T_{1/2}$ for the $0\nu 2\beta$ decay of ${}^{76}\mathrm{Ge}$ for the case $\cos {\psi }_1=0$ and $ϵ={10}^{-6}$ (left) and for $ϵ=5\times {10}^{-7}$ (right).

Figure 4

Correlation between the mixing parameter $\zeta$, the angular correlation coefficient $K$, and the half-life $T_{1/2}$ for the $0\nu 2\beta$ decay of ${}^{76}\mathrm{Ge}$ for the case $\cos {\psi }_1=0$ and $ϵ={10}^{-6}$ (left) and for $ϵ=5\times {10}^{-7}$ (right).

Figure 5

Left: Differential width in $\cos \theta$ for the $0\nu 2\beta$ decay of ${}^{76}\mathrm{Ge}$ for a fixed value of $ϵ={10}^{-6}$ and $|⟨m⟩|=20$, 30 meV. The straight and dotted lines correspond to $m_{W_R}=1\mathrm{TeV}$, $\infty$, respectively (the latter is the conventional case of the light Majorana neutrino exchange mechanism). Right: The same as the left figure but for smaller values of $|⟨m⟩|=5$, 10 meV. In addition, the dashed lines correspond to $m_{W_R}=1.5\mathrm{TeV}$.