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The uncertainty in the nuclear matrix elements (NMEs) of $0\nu\beta\beta$decay for $^{76}$Ge, $^{82}$Se, $^{128}$Te, $^{130}$Te, and $^{136}$Xe in theself-consistent quasiparticle random phase approximation (QRPA) method isinvestigated by using eighteen Skyrme interactions supplemented with either avolume- or surface-type of pairing interactions. The NMEs for the isotopesconcerned (except $^{136}$Xe) are less sensitive to the particle-hole ($ph$)interactions, while strongly dependent on the employed isovectorparticle-particle ($pp$) pairing interactions even though the pairing strengthsare optimized to the same pairing gap. The results indicate that a precisedetermination of the isovector $pp$ pairing interaction in the Skyrme energydensity functional is of importance to reduce the uncertainty in the NMEswithin the QRPA framework.

$0\nu\beta\beta$-decay nuclear matrix elements in self-consistent Skyrme  quasiparticle random phase approximation: uncertainty from pairing  interaction