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 (${}^{76}Ge$, ${}^{82}Se$, ${}^{100}Mo$, ${}^{130}Te$, and ${}^{136}Xe$), 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 ${}^{76}Ge$ 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. As an illustration of the correlations among the $0\nu 2\beta$ observables (half-life $T_{1\mathrm{/}2}$, the coefficient $K$, and the effective Majorana neutrino mass $\mathrm{\mid }<m>\mathrm{\mid }$) 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 $\zeta$.