We present the first measurements of absolute branching fractions of $Xi_c^0$ decays into $Xi^- pi^+$, $Lambda K^- pi^+$, and $p K^- K^- pi^+$ final states. The measurements are made using a data set comprising $(772pm 11)times 10^{6}$ $Bbar{B}$ pairs collected at the $Upsilon(4S)$ resonance with the Belle detector at the KEKB $e^+e^-$ collider. We first measure the absolute branching fraction for $B^- to bar{Lambda}_c^- Xi_c^0$ using a missing-mass technique; the result is ${cal B}(B^- to bar{Lambda}_c^- Xi_c^0) = (9.51 pm 2.10 pm 0.88) times 10^{-4}$. We subsequently measure the product branching fractions ${cal B}(B^- to bar{Lambda}_c^- Xi_c^0){cal B}(Xi_c^0 to Xi^- pi^+)$, ${cal B}( B^- to bar{Lambda}_c^- Xi_c^0) {cal B}(Xi_c^0 to Lambda K^- pi^+)$, and ${cal B}( B^- to bar{Lambda}_c^- Xi_c^0) {cal B}(Xi_c^0 to p K^- K^- pi^+)$ with improved precision. Dividing these product branching fractions by the result for $B^- to bar{Lambda}_c^- Xi_c^0$ yields the following branching fractions: ${cal B}(Xi_c^0 to Xi^- pi^+)= (1.80 pm 0.50 pm 0.14)%$, ${cal B}(Xi_c^0 to Lambda K^- pi^+)=(1.17 pm 0.37 pm 0.09)%$, and ${cal B}(Xi_c^0 to p K^- K^- pi^+)=(0.58 pm 0.23 pm 0.05)%.$ For the above branching fractions, the first uncertainties are statistical and the second are systematic. Our result for ${cal B}(Xi_c^0 to Xi^- pi^+)$ can be combined with $Xi_c^0$ branching fractions measured relative to $Xi_c^0 to Xi^- pi^+$ to yield other absolute $Xi_c^0$ branching fractions.
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