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Search for Majorana Neutrinos near the Inverted Mass Hierarchy Region with KamLAND-Zen

We present an improved search for neutrinoless double-beta ($0νββ$) decay of $^{136}$Xe in the KamLAND-Zen experiment. Owing to purification of the xenon-loaded liquid scintillator, we achieved a significant reduction of the $^{110m}$Ag contaminant identified in previous searches. Combining the results from the first and second phase, we obtain a lower limit for the $0νββ$ decay half-life of $T_{1/2}^{0ν} > 1.07 \times 10^{26}$ yr at 90% C.L., an almost sixfold improvement over previous limits. Using commonly adopted nuclear matrix element calculations, the corresponding upper limits on the effective Majorana neutrino mass are in the range 61-165 meV. For the most optimistic nuclear matrix elements, this limit reaches the bottom of the quasi-degenerate neutrino mass region.