We present the first measurements of the absolute branching fractions of $Xi_c^+$ decays into $Xi^- pi^+ pi^+$ and $p K^- pi^+$ final states. Our analysis is based on a data set of $(772pm 11)times 10^{6}$ $Bbar{B}$ pairs collected at the $Upsilon(4S)$ resonance with the Belle detector at the KEKB $e^+e^-$ collider. We measure the absolute branching fraction of $bar{B}^{0} to bar{Lambda}_{c}^{-} Xi_{c}^{+}$ with the $Xi_c^+$ recoiling against $bar{Lambda}_c^-$ in $bar{B}^0$ decays resulting in ${cal B}(bar{B}^{0} to bar{Lambda}_{c}^{-} Xi_{c}^{+}) = [1.16 pm 0.42(rm stat.) pm 0.15(rm syst.)] times 10^{-3}$. We then measure the product branching fractions ${cal B}(bar{B}^{0} to bar{Lambda}_c^- Xi_c^+){cal B}(Xi_c^+ to Xi^- pi^+ pi^+)$ and ${cal B}(bar{B}^{0} to bar{Lambda}_c^- Xi_c^+){cal B}(Xi_c^+ to p K^- pi^+)$. Dividing these product branching fractions by $bar{B}^{0} to bar{Lambda}_{c}^{-} Xi_{c}^{+}$ yields: ${cal B}(Xi_c^+ to Xi^- pi^+ pi^+) = [2.86 pm 1.21(rm stat.) pm 0.38(rm syst.)]%$ and ${cal B}(Xi_c^+ to p K^- pi^+)=[0.45 pm 0.21(rm stat.) pm 0.07(rm syst.)]%$. Our result for ${cal B}(Xi_c^+ to Xi^- pi^+ pi^+)$ can be combined with $Xi_c^+$ branching fractions measured relative to $Xi_c^+ to Xi^- pi^+ pi^+$ to set the absolute scale for many $Xi_c^+$ branching fractions.
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