Uncertainties in nuclear transition matrix elements for $β^{+}β^{+}$ and $\varepsilon β^{+}$ modes of neutrinoless positron double-$β$ decay within PHFB model

Uncertainties in the nuclear transition matrix elements $M^{(0ν)}$ and $M^{(0N)}$ of the double-positron emission $(β^{+}β^{+})_{0ν}$ and electron-positron conversion $(\varepsilon β^{+})_{0ν}$ modes due to the exchange of light and heavy Majorana neutrinos, respectively, are calculated for $^{96}$Ru, $^{102}$Pd, $^{106}$Cd, $^{124}$Xe, $^{130}$Ba and $^{156}$Dy isotopes by employing the PHFB model with four different parameterization of the pairing plus multipolar two-body interactions and three different parameterizations of the Jastrow short range correlations. In all cases but for $^{130}$Ba, the uncertainties are smaller than 14% for light Majorana neutrino exchange and 35% for the exchange of a heavy Majorana neutrino.

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