Measurement of the relative branching ratio of positive D meson going to antipion-pion-pion to positive D meson going to negative K meson-antipion-pion.

We present a measurement of the relative branching ratio of the Cabibbo-suppressed D+ meson decay into three charged pions using 193 pb-1 of data collected by CDF II detector at Fermilab's Tevatron. We determine BR(D+ → pi -pi+pi+)/BR( D+ → K-pi +pi+) = (3.461 +/- 0.038(stat) +/- 0.040(syst))%. This value agrees with the present world average and is about three times more precise than any current measurement. Using the world average branching ratio BR(D + → K-pi+pi +)=(9.51 +/- 0.34)%, we find BR(D + → pi-pi+pi+)= (3.29 +/- 0.11) x 10-3.