The Effect of Cancellation in Neutrinoless Double Beta Decay

In light of recent experimental results, we carefully analyze the effects of interference in neutrinoless double beta decay, when more than one mechanism is operative. We assume a complete cancellation is at work for $^{136}\rm{Xe}$, and find its implications on the half-life of other isotopes, such as $^{76}\rm{Ge}$. For definiteness, we consider the role of light and heavy sterile neutrinos. In this case, the effective Majorana mass parameter can be redefined to take into account all contributions and its value gets suppressed. Hence, larger values of neutrino masses are required for the same half-life. The canonical light neutrino contribution can not saturate the present limits of half-lives or the positive claim of observation of neutrinoless double beta decay, once the stringent bounds from cosmology are taken into account. For the case of cancellation, where all the sterile neutrinos are heavy, the tension between the results from neutrinoless double beta decay and cosmology becomes more severe. We show that the inclusion of light sterile neutrinos in this set up can resolve this issue. Using the recent results from GERDA, we derive upper limits on the active-sterile mixing angles and compare it with the case of no cancellation. The required values of the mixing angles become larger, if a cancellation is at work. A direct test of destructive interference in $^{136}\rm{Xe}$ is provided by the observation of this process in other isotopes and we study in detail the correlation between their half-lives. Finally, we discuss the model realizations which can accommodate light and heavy sterile neutrinos and the cancellation. We show that sterile neutrinos of few hundred MeV or GeV mass range, coming from an Extended seesaw framework or a further extension, can satisfy the required cancellation.