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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 ($0\nu2β$) 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 $dΓ/d\cos θ\propto (1-K\cos θ)$ 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 $0\nu2β$-decays in these nuclei are induced solely by a light Majorana neutrino, $ν_M$. 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 $ν_M + {NP}$ scenarios for the $^{76}{Ge}$ nucleus. As an illustration of the correlations among the $0\nu2β$ 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 $ζ$.