We present the first model-independent measurement of the CKM unitarity triangle angle ϕ3 using B±→ D(KS0\ {K}_{\mathrm{S}}^0 \π+π−π0) K± decays, where D indicates either a D0 or D¯\ \overline{D} \0 ...meson. Measurements of the strong-phase difference of the D →KS0\ {K}_{\mathrm{S}}^0 \π+π−π0 amplitude obtained from CLEO-c data are used as input. This analysis is based on the full Belle data set of 772 × 106BB¯\ \overline{B} \ events collected at the Υ(4S) resonance. We obtain ϕ3 = (5.7−8.8+10.2\ {5.7}_{-8.8}^{+10.2} \±3.5±5.7)° and the suppressed amplitude ratio rB = 0.323±0.147±0.023±0.051. Here the first uncertainty is statistical, the second is the experimental systematic, and the third is due to the precision of the strong-phase parameters measured from CLEO-c data. The 95% confidence interval on ϕ3 is (−29.7, 109.5)°, which is consistent with the current world average.
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