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 (0ν2β) 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/dcosθ∝(1-Kcosθ) is essentially independent of the nuclear matrix element models and present its numerical values for the five nuclei of interest (⁷⁶Ge, ⁸²Se, ¹⁰⁰Mo, ¹³⁰Te, and ¹³⁶Xe), assuming that the 0ν2β decays in these nuclei are induced solely by a light Majorana neutrino, νM. This coefficient varies between $K=0.81$ (for the ⁷⁶Ge nucleus) and $K=0.88$ (for the ⁸²Se and ¹⁰⁰Mo 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 νM+NP scenarios for the ⁷⁶Ge nucleus. As an illustration of the correlations among the 0ν2β observables (half-life T1/2, 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 WR-boson mass and the left-right mixing parameter ζ.