Neutrinoless double $\beta$ decay in four-neutrino models

The most stringent constraint on the so-called effective electron neutrino mass from the present neutrinoless double beta decay experiments is |M_{ee}| < 0.2 eV, while the planned next generation experiment GENIUS is anticipated to reach a considerably more stringent limit |M_{ee}|< 0.001 eV. We investigate the constraints these bounds set on the neutrino masses and mixings of neutrinos in four-neutrino models where there exists a sterile neutrino along with the three ordinary neutrinos. We find that the GENIUS experiment would be sensitive to the electron neutrino masses down to the limit m_{\nu_e}\lsim 0.024 eV in such a scenario