Study of the D0 \to Pi Pi- Pi0 Decay at BaBar Page: 4 of 8
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Amplitude an
0.823 0.000 0.004
0.512 0.005 0.011
0.588 0.007 0.003
0.033 0.011 0.018
0.055 0.010 0.006
0.134 0.008 0.004
0.202 0.017 0.017
0.224 0.013 0.022
0.179 0.011 0.017
0.091 0.006 0.006
0.050 0.004 0.004
0.061 0.009 0.007
0.062 0.006 0.006
0.056 0.006 0.007
0.115 0.003 0.004
0.092 0.011 0.007Phase #n ( )
0
16.2 0.6 0.4
-2.0 0.6 0.6
-146 18 14
10 8 13
16 3 3
-17 2 2
-17 2 3
-50 3 3
8 4 8
-59 5 4
156 9 6
12 9 4
51 8 7
-171 3 4
-11 4 2Fraction fn (%)
67.8 0.0 0.6
26.2 0.5 1.1
34.6 0.8 0.3
0.11 0.07 0.12
0.30 0.11 0.07
1.79 0.22 0.12
4.1 0.7 0.7
5.0 0.6 1.0
3.2 0.4 0.6
0.82 0.10 0.10
0.25 0.04 0.04
0.37 0.11 0.09
0.39 0.08 0.07
0.71 0.07 0.08
1.32 0.08 0.10
0.84 0.21 0.12Table 1: Result of the fit of the D0 Dalitz-plot showing the amplitude an, the
phase #2 and the fraction fn, an. The mass and width of the fo(400) are 400
and 600 MeV/c2. The masses and widths of the other mesons are taken by the
2006 issue of the Review of Particle Physics [8]. The phase of the p(770)+ - is
fixed at 00.
{p}+ -) = p(770)+i ) + p(1450)+ -) + p(1700)+i-){p}- +
{f} )( + 0-) - 0 + -)),
p(770) 0x) + p(1450)0 r0) + p(1700)%0) =
1
( +O) - + -0)),
p(770)-i+) + p(1450)-i+) + p(1700)-+
fo(-0+) - f0 +)),
fo(400)r ) + I fo(980)r ) + I fo(1370)r ) +(4)
fo(1500)r0) + Ifo(1710)ir0) + If2(1710)r0)
1
( + -0) + +O)),
where gqiq2q3) indicates the state 7 -i) *) 7 q3), q= +, -, 0 being the charge
of the i.th pion. The amplitudes of these four states are obtained by summing
the amplitudes of the channels in the right side of (4).
We use the symbols I(I12); Iz) for the isospin eigenstates of the 3ir final4
Channel
p(770)+ -
p(770)0 0
p(770)-+
p(1450)+ -
p(1450)0i0
p(1450)-+
p(1700)+ -
p(1700)0i0
p(1700)- +
fo (400)>0
fo (980)ir0
fo(1370)ir0
fo(1500)ir0
fo(1710)7r0
f2(1270)ir0
nonresonant
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Gaspero, Mario. Study of the D0 \to Pi Pi- Pi0 Decay at BaBar, article, April 6, 2012; United States. (https://digital.library.unt.edu/ark:/67531/metadc837189/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.