We present limits on Majoron-emitting neutrinoless double-$\beta$ decay modes based on an exposure of 112.3 days with 125 kg of ${}^{136}$Xe. In particular, a lower limit on the ordinary (spectral index $n=1$) Majoron-emitting decay half-life of ${}^{136}$Xe is obtained as $T_{1/2}^{0\nu {\chi }^0}>2.6\times {10}^{24}$ yr at 90$\%$ C.L., a factor of five more stringent than previous limits. The corresponding upper limit on the effective Majoron-neutrino coupling, using a range of available nuclear matrix calculations, is $\langle g_{ee}\rangle <(0.8–1.6)\times {10}^{-5}$. This excludes a previously unconstrained region of parameter space and strongly limits the possible contribution of ordinary Majoron emission modes to $0\nu \beta \beta$ decay for neutrino masses in the inverted hierarchy scheme.

• Received 29 May 2012

DOI:https://doi.org/10.1103/PhysRevC.86.021601