We present a framework to combine data from the latest neutrinoless double-$\beta$ decay experiments for multiple isotopes and derive a limit on the effective neutrino mass $m_{\beta \beta }$ using the experimental energy distributions. The combined limits on $m_{\beta \beta }$ range between 130 and 310 meV, where the spread is due to different model calculations of nuclear matrix elements. The statistical consistency ($p$ values) between this result and the signal observation claimed by the Heidelberg-Moscow experiment is derived. The limits on $m_{\beta \beta }$ are also evaluated in a ($3+1$) sterile neutrino model, assuming all neutrinos are Majorana particles.

• Received 21 April 2015

DOI:https://doi.org/10.1103/PhysRevD.92.012002