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

Understand

The angular correlation of the electrons emitted in the neutrinoless double beta decay ($0\nu2\beta$) 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 ($^{76}{Ge}$, $^{82}{Se}$, $^{100}{Mo}$, $^{130}{Te}$, and $^{136}{Xe}$), assuming that the $0\nu2\beta$-decays in these nuclei are induced solely by a light Majorana neutrino, $\nu_M$.
• This coefficient varies between $K=0.81$ (for the $^{76}{Ge}$ nucleus) and $K=0.88$ (for the $^{82}{Se}$ and $^{100}{Mo}$ 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 $\nu_M + {NP}$ scenarios for the $^{76}{Ge}$ nucleus.