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Abstract
We present a measurement of $π΅β‘(π^0βπ^+β’π^ββ’πΎ)/π΅β‘(π^0βπΎβ’πΎ)$, the Dalitz branching ratio, using data taken in 1999 by the E832 KTeV experiment at Fermi National Accelerator Laboratory. We use neutral pions from fully reconstructed πΎπΏ decays in flight; the measurement is based on βΌ60 thousand $πΎ_πΏβπ^0β’π^0β’π^0βπΎβ’πΎβ’πΎβ’πΎβ’π^+β’π^ββ’πΎ$ decays. We normalize to $πΎ_πΏβπ^0β’π^0β’π^0β6β’πΎ$ decays. We find $π΅β‘(π^0βπ^+β’π^ββ’πΎ)/π΅β‘(π^0βπΎβ’πΎ) (π_{π+β’π}β>15ββMeV/π^2)=[3.920Β±0.016β’(stat)Β±0.036β’(syst)]Γ10^{β3}$. Using the Mikaelian and Smith prediction for the $π^+β’π^β$ mass spectrum, we correct the result to the full $π^+β’π^β$ mass range. The corrected result is $π΅β‘(π^0βπ^+β’π^ββ’πΎ)/π΅β‘(π^0βπΎβ’πΎ)=[1.1559Β±0.0047β’(stat)Β±0.0106β’(syst)]%$. This result is consistent with previous measurements, and the uncertainty is a factor of 3 smaller than any previous measurement.