Measurement of D0-D 0 mixing in D0 → K0
− decays
L. M. Zhang,37 Z. P. Zhang,37 I. Adachi,7 H. Aihara,45 V. Aulchenko,1 T. Aushev,18, 13 A. M. Bakich,40
V. Balagura,13 E. Barberio,21 A. Bay,18 K. Belous,12 U. Bitenc,14 A. Bondar,1 A. Bozek,27 M. Bračko,20,14
J. Brodzicka,7 T. E. Browder,6 P. Chang,26 Y. Chao,26 A. Chen,24 K.-F. Chen,26 W. T. Chen,24 B. G. Cheon,5
C.-C. Chiang,26 I.-S. Cho,50 Y. Choi,39 Y. K. Choi,39 J. Dalseno,21 M. Danilov,13 M. Dash,49 A. Drutskoy,3
S. Eidelman,1 D. Epifanov,1 S. Fratina,14 N. Gabyshev,1 G. Gokhroo,41 B. Golob,19, 14 H. Ha,16 J. Haba,7
T. Hara,32 N. C. Hastings,45 K. Hayasaka,22 H. Hayashii,23 M. Hazumi,7 D. Heffernan,32 T. Hokuue,22 Y. Hoshi,43
W.-S. Hou,26 Y. B. Hsiung,26 H. J. Hyun,17 T. Iijima,22 K. Ikado,22 K. Inami,22 A. Ishikawa,45 H. Ishino,46
R. Itoh,7 M. Iwasaki,45 Y. Iwasaki,7 N. J. Joshi,41 D. H. Kah,17 H. Kaji,22 S. Kajiwara,32 J. H. Kang,50 H. Kawai,2
T. Kawasaki,29 H. Kichimi,7 H. J. Kim,17 H. O. Kim,39 S. K. Kim,38 Y. J. Kim,4 K. Kinoshita,3 S. Korpar,20, 14
P. Križan,19, 14 P. Krokovny,7 R. Kumar,33 C. C. Kuo,24 A. Kuzmin,1 Y.-J. Kwon,50 J. S. Lee,39 M. J. Lee,38
S. E. Lee,38 T. Lesiak,27 J. Li,6 A. Limosani,21 S.-W. Lin,26 Y. Liu,4 D. Liventsev,13 T. Matsumoto,47 A. Matyja,27
S. McOnie,40 T. Medvedeva,13 W. Mitaroff,11 H. Miyake,32 H. Miyata,29 Y. Miyazaki,22 R. Mizuk,13 Y. Nagasaka,8
I. Nakamura,7 E. Nakano,31 M. Nakao,7 Z. Natkaniec,27 S. Nishida,7 O. Nitoh,48 S. Ogawa,42 T. Ohshima,22
S. Okuno,15 S. L. Olsen,6 Y. Onuki,35 W. Ostrowicz,27 H. Ozaki,7 P. Pakhlov,13 G. Pakhlova,13 C. W. Park,39
H. Park,17 L. S. Peak,40 R. Pestotnik,14 L. E. Piilonen,49 A. Poluektov,1 H. Sahoo,6 Y. Sakai,7 O. Schneider,18
J. Schümann,7 C. Schwanda,11 A. J. Schwartz,3 R. Seidl,9, 35 K. Senyo,22 M. E. Sevior,21 M. Shapkin,12 H. Shibuya,42
S. Shinomiya,32 J.-G. Shiu,26 B. Shwartz,1 J. B. Singh,33 A. Sokolov,12 A. Somov,3 N. Soni,33 S. Stanič,30
M. Starič,14 H. Stoeck,40 K. Sumisawa,7 T. Sumiyoshi,47 S. Suzuki,36 O. Tajima,7 F. Takasaki,7 K. Tamai,7
N. Tamura,29 M. Tanaka,7 G. N. Taylor,21 Y. Teramoto,31 X. C. Tian,34 I. Tikhomirov,13 T. Tsuboyama,7
S. Uehara,7 K. Ueno,26 T. Uglov,13 Y. Unno,5 S. Uno,7 P. Urquijo,21 Y. Usov,1 G. Varner,6 K. Vervink,18
S. Villa,18 A. Vinokurova,1 C. H. Wang,25 M.-Z. Wang,26 P. Wang,10 Y. Watanabe,15 E. Won,16 B. D. Yabsley,40
A. Yamaguchi,44 Y. Yamashita,28 M. Yamauchi,7 C. Z. Yuan,10 C. C. Zhang,10 V. Zhilich,1 and A. Zupanc14
(The Belle Collaboration)
1Budker Institute of Nuclear Physics, Novosibirsk
2Chiba University, Chiba
3University of Cincinnati, Cincinnati, Ohio 45221
4The Graduate University for Advanced Studies, Hayama
5Hanyang University, Seoul
6University of Hawaii, Honolulu, Hawaii 96822
7High Energy Accelerator Research Organization (KEK), Tsukuba
8Hiroshima Institute of Technology, Hiroshima
9University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
10Institute of High Energy Physics, Chinese Academy of Sciences, Beijing
11Institute of High Energy Physics, Vienna
12Institute of High Energy Physics, Protvino
13Institute for Theoretical and Experimental Physics, Moscow
14J. Stefan Institute, Ljubljana
15Kanagawa University, Yokohama
16Korea University, Seoul
17Kyungpook National University, Taegu
18Swiss Federal Institute of Technology of Lausanne, EPFL, Lausanne
19University of Ljubljana, Ljubljana
20University of Maribor, Maribor
21University of Melbourne, School of Physics, Victoria 3010
22Nagoya University, Nagoya
23Nara Women’s University, Nara
24National Central University, Chung-li
25National United University, Miao Li
26Department of Physics, National Taiwan University, Taipei
27H. Niewodniczanski Institute of Nuclear Physics, Krakow
28Nippon Dental University, Niigata
29Niigata University, Niigata
30University of Nova Gorica, Nova Gorica
31Osaka City University, Osaka
32Osaka University, Osaka
Typeset by REVTEX
http://arxiv.org/abs/0704.1000v2
33Panjab University, Chandigarh
34Peking University, Beijing
35RIKEN BNL Research Center, Upton, New York 11973
36Saga University, Saga
37University of Science and Technology of China, Hefei
38Seoul National University, Seoul
39Sungkyunkwan University, Suwon
40University of Sydney, Sydney, New South Wales
41Tata Institute of Fundamental Research, Mumbai
42Toho University, Funabashi
43Tohoku Gakuin University, Tagajo
44Tohoku University, Sendai
45Department of Physics, University of Tokyo, Tokyo
46Tokyo Institute of Technology, Tokyo
47Tokyo Metropolitan University, Tokyo
48Tokyo University of Agriculture and Technology, Tokyo
49Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
50Yonsei University, Seoul
We report a measurement of D0-D 0 mixing in D0 → K0S π
+π− decays using a time-dependent
Dalitz plot analysis. We first assume CP conservation and subsequently allow for CP violation. The
results are based on 540 fb−1 of data accumulated with the Belle detector at the KEKB e+e− collider.
Assuming negligible CP violation, we measure the mixing parameters x = (0.80± 0.29+0.09 +0.10−0.07 −0.14)%
and y = (0.33 ± 0.24+0.08 +0.06−0.12 −0.08)%, where the errors are statistical, experimental systematic, and
systematic due to the Dalitz decay model, respectively. Allowing for CP violation, we obtain the
CPV parameters |q/p| = 0.86+0.30 +0.06−0.29 −0.03 ± 0.08 and arg(q/p) = (−14
+16+5+2
−18−3−4)
PACS numbers: 13.25.Ft, 11.30.Er, 12.15.Ff
Mixing in the D0-D 0 system is predicted to be very
small in the Standard Model (SM) [1] and, unlike in K0,
B0, and B0s systems, has eluded experimental observa-
tion. Recently, evidence for this phenomenon has been
found in D0 → K+K−/π+π− [2] and D0 → K+π− [3]
decays. It is important to measure D0-D 0 mixing in
other decay modes and to search for CP -violating (CPV )
effects in order to determine whether physics contribu-
tions outside the SM are present. Here we study the
self-conjugate decay D0→K0S π+π−.
The time-dependent probability of flavor eigenstates
D0 and D 0 to mix to each other is governed by the
lifetime τD0 = 1/Γ, and the mixing parameters x =
(m1 − m2)/Γ and y = (Γ1 − Γ2)/2Γ. The parameters
m1,m2 (Γ1,Γ2) are the masses (decay widths) of the mass
eigenstates |D1,2〉 = p|D0〉±q|D 0〉, and Γ = (Γ1+Γ2)/2.
The parameters p and q are complex coefficients sat-
isfying |p|2 + |q|2 = 1. Various D0 decay modes have
been exploited to measure or constrain x and y [4]. For
D0→K0S π+π− decays, the time dependence of the Dalitz
plot distribution allows one to measure x and y directly.
This method was developed by CLEO [5] using 9.0 fb−1
of data; here we extend this method to a data sample 60
times larger.
The decay amplitude at time t of an initially produced
|D0〉 or |D 0〉 can be expressed as
,m2+, t) = A(m2−,m2+)
e1(t) + e2(t)
,m2+)
e1(t)− e2(t)
,m2+, t) = A(m2−,m2+)
e1(t) + e2(t)
,m2+)
e1(t)− e2(t)
, (1)
where A and A are the amplitudes for |D0〉 and |D 0〉
decays as functions of the invariant-masses-squared vari-
ables m2
≡ m2(K0S π±). The time dependence is con-
tained in the terms e1,2(t) = exp[−i(m1,2 − iΓ1,2/2)t].
Upon squaring M and M, one obtains decay rates con-
taining terms exp(−Γt) cos(xΓt), exp(−Γt) sin(xΓt), and
exp[−(1± y)Γt].
We parameterize the K0Sπ
+π− Dalitz distribution fol-
lowing Ref. [6]. The overall amplitude as a function of
m2+ and m
is expressed as a sum of quasi-two-body am-
plitudes (subscript r) and a constant non-resonant term
(subscript NR):
,m2+) =
iφrAr(m2−,m2+) + aNReiφNR , (2)
,m2+) =
iφ̄rAr(m2+,m2−) + āNReiφ̄NR . (3)
The functions Ar are products of Blatt-Weisskopf form
factors and relativistic Breit-Wigner functions [7].
The data were recorded by the Belle detector at the
KEKB asymmetric-energy e+e− collider [8]. The Belle
detector [9] includes a silicon vertex detector (SVD), a
central drift chamber (CDC), an array of aerogel thresh-
old Cherenkov counters (ACC), a barrel-like arrangement
of time-of-flight scintillation counters (TOF), and an elec-
tromagnetic calorimeter.
We reconstruct D0 candidates via the decay chain
D∗+ → π+s D0, D0 → K0Sπ+π− [10]. Here, πs denotes
a low-momentum pion, the charge of which tags the fla-
vor of the neutral D at production. The K0S candidates
are reconstructed in the π+π− final state; we require
that the pion candidates form a common vertex sepa-
rated from the interaction region and have an invariant
mass within ±10 MeV/c2 of m
. We reconstruct D0
candidates by combining the K0S candidate with two op-
positely charged tracks assigned as pions. These tracks
are required to have at least two SVD hits in both r-φ and
z coordinates. A D∗+ candidate is reconstructed by com-
bining the D0 candidate with a low momentum charged
track (the π+s candidate); the resulting D
∗+ momentum
in the e+e− center-of-mass (CM) frame is required to be
larger than 2.5 GeV/c in order to eliminate BB events
and suppress combinatorial background.
The charged pion tracks are refitted to originate from
a common vertex, which represents the decay point of
the D0. The D∗+ vertex is taken to be the intersection
of the D0 momentum vector with the e+e− interaction
region. The D0 proper decay time is calculated from
the projection of the vector joining the two vertices (~L)
onto the momentum vector: t = ~L · (~p/p)(m
/p). The
uncertainty in t (σt) is calculated event-by-event, and we
require σt < 1 ps (for selected events, 〈σt〉 ∼ 0.2 ps).
The signal and background yields are determined from
a two-dimensional fit to the variables m
and Q ≡
−mπ)·c2. The variableQ is the kinetic
energy released in the decay and equals only 5.9 MeV for
D∗+→π+s D0 decays. We parameterize the signal shape
by a triple-Gaussian function for m
, and the sum
of a bifurcated Student t distribution and a Gaussian
function for Q. The backgrounds are classified into two
types: random πs background, in which a random πs
is combined with a true D0 decay, and combinatorial
background. The shape of the m
distribution for
the random πs background is fixed to be the same as
that used for the signal. Other background distributions
are obtained from Monte Carlo (MC) simulation. We
perform a two-dimensional fit to the measured m
distributions in a wide range 1.81 GeV/c2 < m
1.92 GeV/c2 and 0<Q< 20 MeV. We define a smaller
signal region |m
− mD0 | < 15 MeV/c2 and |Q −
5.9 MeV| < 1.0 MeV, corresponding to 3σ intervals in
these variables. In this region we find 534410±830 signal
events and background fractions of 1% and 4% for the
random πs and combinatorial backgrounds, respectively.
and Q distributions are shown in Fig. 1 along
with projections of the fit result.
mKsππ (GeV)
1.825 1.85 1.875 1.9
Signal
Random π
Combinatorial
Q (MeV)
0 5 10 15 20
FIG. 1: The distribution of (a) m
with 0 < Q < 20 MeV;
(b) Q with 1.81 GeV/c2 < m
< 1.92 GeV/c2. Superim-
posed on the data (points with error bars) are projections of
the m
-Q fit.
For the events selected in the signal region we perform
an unbinned likelihood fit to the Dalitz plot variables
and m2+, and the decay time t. For D
0 decays, the
likelihood function is
fj(mK0
ππ,i, Qi)Pj(m2−,i,m2+,i, ti) , (4)
where j = {sig, rnd, cmb} denotes the signal or back-
ground components, and the index i runs over D0 candi-
dates. The event weights fj are functions of mK0
Q and are obtained from the m
-Q fit mentioned
above.
The probability density function (PDF)
Psig(m2−,m2+, t) equals |M(m2−,m2+, t)|2 convolved
with the detector response. Resolution effects in two-
particle invariant masses are significant only for m2ππ.
The latter, and variation of the efficiency across the
Dalitz plot, are taken into account using the method
described in Ref. [6]. The resolution in decay time t
is accounted for by convolving Psig with a resolution
function consisting of a sum of three Gaussians with a
common mean and widths σk = Sk · σt,i (k = 1− 3).
The scale factors Sk and the common mean are free
parameters in the fit.
The random πs background contains real D
0 and
D 0 decays; in this case the charge of the πs is un-
correlated with the flavor of the neutral D. Thus the
Prnd PDF is taken to be (1 − fw)|M(m2−,m2+, t)|2 +
fw|M(m2−,m2+, t)|2, convolved with the same resolution
function as that used for the signal, where fw is the
wrong-tag fraction. We measure fw = 0.452±0.005 from
fitting events in the Q sideband 3 MeV< |Q−5.9 MeV| <
14.1 MeV.
For the combinatorial background, Pcmb is the prod-
uct of Dalitz-plot and decay time PDFs. The latter is
parameterized as the sum of a delta function and an
exponential function convolved with a Gaussian resolu-
tion function. The timing and Dalitz PDF parameters
are obtained from fitting events in the mass sideband
30 MeV/c2< |m
−mD0 | < 55 MeV/c2.
The likelihood function for D 0 decays, L, has the same
form as L, with M and M (appearing in Psig and Prnd)
interchanged. To determine x and y, we maximize the
sum lnL+lnL. Table I lists the results from two separate
fits. In the first fit we assume CP is conserved, i.e.,
a = ā, φ = φ̄, and p/q = 1. We fit all events in the
signal region, where the free parameters are x, y, τ
the timing resolution parameters of the signal, and the
Dalitz plot resonance parameters ar(NR) and φr(NR). The
fit gives τ
= (409.9 ± 1.0) fs, which is consistent with
the world average [11]. The results for ar and φr for the
18 quasi-two-body resonances used (following the same
model as in Ref. [6]) and the NR contribution are listed
in Table II. The Dalitz plot and its projections, along
with projections of the fit result, are shown in Fig. 2. We
estimate the goodness-of-fit of the Dalitz plot through a
two-dimensional χ2 test [6] and obtain χ2/ndf = 2.1 for
3653−40 degrees of freedom (ndf). We find that the main
features of the Dalitz plot are well reproduced, with some
significant but numerically small discrepancies at peaks
and dips of the distribution in the very high m2
region.
The decay-time distribution for all events, and the ratio
of decay-time distribution for events in theK∗(892)+ and
K∗(892)− regions, are shown in Fig. 3.
TABLE I: Fit results and 95% C.L. intervals for x and y,
including systematic uncertainties. The errors are statisti-
cal, experimental systematic, and decay-model systematic,
respectively. For the CPV -allowed case, there is another so-
lution as described in the text.
Fit case Parameter Fit result 95% C.L. interval
No x(%) 0.80 ± 0.29 +0.09+0.10−0.07−0.14 (0.0, 1.6)
CPV y(%) 0.33 ± 0.24 +0.08+0.06−0.12−0.08 (−0.34, 0.96)
CPV x(%) 0.81 ± 0.30 +0.10+0.09−0.07−0.16 |x| <1.6
y(%) 0.37 ± 0.25 +0.07+0.07−0.13−0.08 |y| <1.04
|q/p| 0.86+0.30 +0.06−0.29 −0.03 ± 0.08 -
arg(q/p)(◦) −14+16+5+2−18−3−4 -
For the second fit, we allow for CPV . This introduces
the additional free parameters |p/q|, arg(p/q), ār(NR) and
φ̄r(NR). The fit gives two solutions: if {x, y, arg(p/q)} is
a solution, then {−x, −y, arg(p/q)+π} is an equally good
solution. From the fit to data, we find that the Dalitz plot
parameters are consistent for the D0 and D 0 samples;
hence we observe no evidence for direct CPV . Results
for |p/q| and arg(p/q), parameterizing CPV in mixing
and interference between mixed and unmixed amplitudes,
respectively, are also found to be consistent with CP con-
servation. If we fit the data assuming no direct CPV , the
values for x and y are essentially the same as those for the
TABLE II: Fit results for Dalitz plot parameters. The errors
are statistical only.
Resonance Amplitude Phase (◦) Fit fraction
K∗(892)− 1.629 ± 0.006 134.3 ± 0.3 0.6227
K∗0 (1430)
− 2.12 ± 0.02 −0.9± 0.8 0.0724
K∗2 (1430)
− 0.87 ± 0.02 −47.3 ± 1.2 0.0133
K∗(1410)− 0.65 ± 0.03 111± 4 0.0048
K∗(1680)− 0.60 ± 0.25 147± 29 0.0002
K∗(892)+ 0.152 ± 0.003 −37.5 ± 1.3 0.0054
K∗0 (1430)
+ 0.541 ± 0.019 91.8 ± 2.1 0.0047
K∗2 (1430)
+ 0.276 ± 0.013 −106± 3 0.0013
K∗(1410)+ 0.33 ± 0.02 −102± 4 0.0013
K∗(1680)+ 0.73 ± 0.16 103± 11 0.0004
ρ(770) 1 (fixed) 0 (fixed) 0.2111
ω(782) 0.0380 ± 0.0007 115.1 ± 1.1 0.0063
f0(980) 0.380 ± 0.004 −147.1 ± 1.1 0.0452
f0(1370) 1.46 ± 0.05 98.6 ± 1.8 0.0162
f2(1270) 1.43 ± 0.02 −13.6 ± 1.2 0.0180
ρ(1450) 0.72 ± 0.04 41± 7 0.0024
σ1 1.39 ± 0.02 −146.6 ± 0.9 0.0914
σ2 0.267 ± 0.013 −157± 3 0.0088
NR 2.36 ± 0.07 155± 2 0.0615
1 2 3
2 (GeV2/c4)
10000
1 2 3
2 (GeV2/c4)
20000
40000
1 2 3
2 (GeV2/c4)
10000
0 0.5 1 1.5 2
2 (GeV2/c4)
FIG. 2: Dalitz plot distribution and the projections for data
(points with error bars) and the fit result (curve). Here, m2±
corresponds to m2(K0Sπ
±) for D0 decays and to m2(K0Sπ
for D 0 decays.
CP -conservation case, and the values for the CPV pa-
rameters are further constrained: |q/p| = 0.95+0.22
−0.20 and
arg(q/p) = (−2+10
◦. A check with independent fits to
theD0 andD 0 tagged samples gives consistent results for
x (y): 0.58%±0.41% (0.45%±0.33%) and 1.04%±0.41%
(0.21%± 0.34%), respectively.
We consider systematic uncertainties arising from both
experimental sources and from the D0→K0S π+π− decay
Proper time (fs)
-2000 0 2000 4000
FIG. 3: (a) The decay-time distribution for events in the
Dalitz plot fit region for data (points with error bars), and
the fit projection for the CP -conservation fit (curve). The
hatched area represents the combinatorial background contri-
bution. (b) Ratio of decay-time distributions for events in the
K∗(892)+ and K∗(892)− regions.
model. We estimate these uncertainties by varying rel-
evant parameters by their ±1σ errors and interpreting
the change in x and y as the systematic uncertainty due
to that source. The main sources of experimental uncer-
tainty are the modeling of the background, the efficiency,
and the event selection criteria. We vary the background
normalization and timing parameters within their uncer-
tainties, and we also set fw equal to its expected value
of 0.5 or alternatively let it float. To investigate possi-
ble correlations between the Dalitz plot (m2+,m
) dis-
tribution and the t distribution of combinatorial back-
ground, the Dalitz plot distribution is obtained for three
bins of decay time; these PDFs are then used accord-
ing to the reconstructed t of individual events. We also
try a uniform efficiency function, and we apply a “best-
candidate” selection to check the effect of the small frac-
tion of multiple-candidate events. We add all variations
in x and y in quadrature to obtain the overall experimen-
tal systematic error.
The systematic error due to our choice of D0 →
+π− decay model is evaluated as follows. We
vary the masses and widths of the intermediate res-
onances by their known uncertainties [11], and we
also try fits with Blatt-Weisskopf form factors set to
unity and with no q2 dependence in the Breit-Wigner
widths. We perform a series of fits successively exclud-
ing intermediate resonances that give small contributions
(ρ(1450), K∗(1680)+), and we also exclude the NR con-
tribution. We account for uncertainty in modeling of
the S-wave ππ component by using K-matrix formal-
ism [12]. We include an uncertainty due to the effect of
around 10-20% bias in the amplitudes for theK∗(1410)±,
K∗0 (1430)
+ andK∗2 (1430)
+ intermediate states, which we
observe in MC studies. Adding all variations in quadra-
ture gives the final results listed in Table I.
We obtain a 95% C.L. contour in the (x, y) plane
by finding the locus of points where −2 lnL increases
by 5.99 units with respect to the minimum value (i.e.,
−2∆ lnL=5.99). All fit variables other than x and y are
allowed to vary to obtain best-fit values at each point
on the contour. To include systematic uncertainty, we
rescale each point on the contour by a factor
1 + r2,
where r2 is a weighted average of the ratios of systematic
to statistical errors for x and y, where the weights de-
pend on the position on the contour. Both the statistical-
only and overall contours for both the CPV -allowed and
the CP -conservation case are shown in Fig. 4. We note
that for the CPV -allowed case, the reflection of these
contours through the origin (0, 0) are also allowed re-
gions. Projecting the overall contour onto the x, y axes
gives the 95% C.L. intervals listed in Table I. After
the systematics-rescaling procedure, the no-mixing point
(0,0) has a value −2∆ lnL = 7.3; this corresponds to a
C.L. of 2.6%. We have confirmed this value by generat-
ing and fitting an ensemble of MC fast-simulated exper-
iments.
x (%)
no CPV (stat. only)
no CPV
CPV (stat. only)
-1 0 1 2
FIG. 4: 95% C.L. contours for (x, y): dotted (solid) corre-
sponds to statistical (statistical and systematic) contour for
no CPV , and dash-dotted (dashed) corresponds to statisti-
cal (statistical and systematic) contour for the CPV -allowed
case. The point is the best-fit result for no CPV .
In summary, we have measured the D0-D 0 mixing
parameters x and y using a Dalitz plot analysis of
D0 → K0S π+π− decays. Assuming negligible CP vi-
olation, we measure x = (0.80 ± 0.29+0.09+0.10
−0.07−0.14)% and
y = (0.33 ± 0.24+0.08+0.06
−0.12−0.08)%, where the errors are sta-
tistical, experimental systematic, and decay-model sys-
tematic, respectively. Our results disfavor the no-mixing
point x = y = 0 with a significance of 2.2σ, while the
one dimensional significance for x > 0 is 2.4σ. We have
also searched for CPV ; we see no evidence for this and
constrain the CPV parameters |q/p| and arg(q/p).
We thank the KEKB group for excellent operation of
the accelerator, the KEK cryogenics group for efficient
solenoid operations, and the KEK computer group and
the NII for valuable computing and Super-SINET net-
work support. We acknowledge support from MEXT and
JSPS (Japan); ARC and DEST (Australia); NSFC and
KIP of CAS (China); DST (India); MOEHRD, KOSEF
and KRF (Korea); KBN (Poland); MES and RFAAE
(Russia); ARRS (Slovenia); SNSF (Switzerland); NSC
and MOE (Taiwan); and DOE (USA).
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[7] S. Kopp et al. (CLEO Collaboration), Phys. Rev. D 63,
092001 (2001).
[8] S. Kurokawa, E. Kikutani et al., Nucl. Instrum. Methods
Phys. Res. Sect. A 499, 1 (2003), and other papers in
this volume.
[9] A. Abashian et al. (Belle Collaboration), Nucl. In-
strum. Methods Phys. Res. Sect. A 479, 117 (2002);
Z. Natkaniec et al. (Belle SVD2 Group), Nucl. Instrum.
Methods Phys. Res. Sect. A 560, 1 (2006).
[10] Charge conjugate decays are implied unless explicitly
stated otherwise.
[11] W.-M. Yao et al. (Particle Data Group), J. Phys. G 33,
1 (2006).
[12] J. M. Link et al. (FOCUS Collaboration), Phys. Lett. B
585, 200 (2004); B. Aubert et al. (BaBar Collaboration),
arXiv: hep-ex/0507101.
http://arxiv.org/abs/hep-ex/0503045
http://arxiv.org/abs/hep-ex/0507101

  We report a measurement of D0-D0bar mixing in D0->Ks pi+ pi- decays using a
time-dependent Dalitz plot analysis. We first assume CP conservation and
subsequently allow for CP violation. The results are based on 540 fb$^{-1}$ of
data accumulated with the Belle detector at the KEKB $e^+e^-$ collider.
Assuming negligible CP violation, we measure the mixing parameters
$x=(0.80\pm0.29^{+0.09 +0.10}_{-0.07 -0.14})%$ and $y=(0.33\pm0.24^{+0.08
+0.06}_{-0.12 -0.08})%$, where the errors are statistical, experimental
systematic, and systematic due to the Dalitz decay model, respectively.
Allowing for CP violation, we obtain the $CPV$ parameters $|q/p|=0.86^{+0.30
+0.06}_{-0.29 -0.03}\pm0.08$ and $\arg(q/p)=(-14^{+16 +5 +2}_{-18 -3
-4})^\circ$.

Measurement of D0-D 0 mixing in D0 → K0
− decays
L. M. Zhang,37 Z. P. Zhang,37 I. Adachi,7 H. Aihara,45 V. Aulchenko,1 T. Aushev,18, 13 A. M. Bakich,40
V. Balagura,13 E. Barberio,21 A. Bay,18 K. Belous,12 U. Bitenc,14 A. Bondar,1 A. Bozek,27 M. Bračko,20,14
J. Brodzicka,7 T. E. Browder,6 P. Chang,26 Y. Chao,26 A. Chen,24 K.-F. Chen,26 W. T. Chen,24 B. G. Cheon,5
C.-C. Chiang,26 I.-S. Cho,50 Y. Choi,39 Y. K. Choi,39 J. Dalseno,21 M. Danilov,13 M. Dash,49 A. Drutskoy,3
S. Eidelman,1 D. Epifanov,1 S. Fratina,14 N. Gabyshev,1 G. Gokhroo,41 B. Golob,19, 14 H. Ha,16 J. Haba,7
T. Hara,32 N. C. Hastings,45 K. Hayasaka,22 H. Hayashii,23 M. Hazumi,7 D. Heffernan,32 T. Hokuue,22 Y. Hoshi,43
W.-S. Hou,26 Y. B. Hsiung,26 H. J. Hyun,17 T. Iijima,22 K. Ikado,22 K. Inami,22 A. Ishikawa,45 H. Ishino,46
R. Itoh,7 M. Iwasaki,45 Y. Iwasaki,7 N. J. Joshi,41 D. H. Kah,17 H. Kaji,22 S. Kajiwara,32 J. H. Kang,50 H. Kawai,2
T. Kawasaki,29 H. Kichimi,7 H. J. Kim,17 H. O. Kim,39 S. K. Kim,38 Y. J. Kim,4 K. Kinoshita,3 S. Korpar,20, 14
P. Križan,19, 14 P. Krokovny,7 R. Kumar,33 C. C. Kuo,24 A. Kuzmin,1 Y.-J. Kwon,50 J. S. Lee,39 M. J. Lee,38
S. E. Lee,38 T. Lesiak,27 J. Li,6 A. Limosani,21 S.-W. Lin,26 Y. Liu,4 D. Liventsev,13 T. Matsumoto,47 A. Matyja,27
S. McOnie,40 T. Medvedeva,13 W. Mitaroff,11 H. Miyake,32 H. Miyata,29 Y. Miyazaki,22 R. Mizuk,13 Y. Nagasaka,8
I. Nakamura,7 E. Nakano,31 M. Nakao,7 Z. Natkaniec,27 S. Nishida,7 O. Nitoh,48 S. Ogawa,42 T. Ohshima,22
S. Okuno,15 S. L. Olsen,6 Y. Onuki,35 W. Ostrowicz,27 H. Ozaki,7 P. Pakhlov,13 G. Pakhlova,13 C. W. Park,39
H. Park,17 L. S. Peak,40 R. Pestotnik,14 L. E. Piilonen,49 A. Poluektov,1 H. Sahoo,6 Y. Sakai,7 O. Schneider,18
J. Schümann,7 C. Schwanda,11 A. J. Schwartz,3 R. Seidl,9, 35 K. Senyo,22 M. E. Sevior,21 M. Shapkin,12 H. Shibuya,42
S. Shinomiya,32 J.-G. Shiu,26 B. Shwartz,1 J. B. Singh,33 A. Sokolov,12 A. Somov,3 N. Soni,33 S. Stanič,30
M. Starič,14 H. Stoeck,40 K. Sumisawa,7 T. Sumiyoshi,47 S. Suzuki,36 O. Tajima,7 F. Takasaki,7 K. Tamai,7
N. Tamura,29 M. Tanaka,7 G. N. Taylor,21 Y. Teramoto,31 X. C. Tian,34 I. Tikhomirov,13 T. Tsuboyama,7
S. Uehara,7 K. Ueno,26 T. Uglov,13 Y. Unno,5 S. Uno,7 P. Urquijo,21 Y. Usov,1 G. Varner,6 K. Vervink,18
S. Villa,18 A. Vinokurova,1 C. H. Wang,25 M.-Z. Wang,26 P. Wang,10 Y. Watanabe,15 E. Won,16 B. D. Yabsley,40
A. Yamaguchi,44 Y. Yamashita,28 M. Yamauchi,7 C. Z. Yuan,10 C. C. Zhang,10 V. Zhilich,1 and A. Zupanc14
(The Belle Collaboration)
1Budker Institute of Nuclear Physics, Novosibirsk
2Chiba University, Chiba
3University of Cincinnati, Cincinnati, Ohio 45221
4The Graduate University for Advanced Studies, Hayama
5Hanyang University, Seoul
6University of Hawaii, Honolulu, Hawaii 96822
7High Energy Accelerator Research Organization (KEK), Tsukuba
8Hiroshima Institute of Technology, Hiroshima
9University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
10Institute of High Energy Physics, Chinese Academy of Sciences, Beijing
11Institute of High Energy Physics, Vienna
12Institute of High Energy Physics, Protvino
13Institute for Theoretical and Experimental Physics, Moscow
14J. Stefan Institute, Ljubljana
15Kanagawa University, Yokohama
16Korea University, Seoul
17Kyungpook National University, Taegu
18Swiss Federal Institute of Technology of Lausanne, EPFL, Lausanne
19University of Ljubljana, Ljubljana
20University of Maribor, Maribor
21University of Melbourne, School of Physics, Victoria 3010
22Nagoya University, Nagoya
23Nara Women’s University, Nara
24National Central University, Chung-li
25National United University, Miao Li
26Department of Physics, National Taiwan University, Taipei
27H. Niewodniczanski Institute of Nuclear Physics, Krakow
28Nippon Dental University, Niigata
29Niigata University, Niigata
30University of Nova Gorica, Nova Gorica
31Osaka City University, Osaka
32Osaka University, Osaka
Typeset by REVTEX
http://arxiv.org/abs/0704.1000v2
33Panjab University, Chandigarh
34Peking University, Beijing
35RIKEN BNL Research Center, Upton, New York 11973
36Saga University, Saga
37University of Science and Technology of China, Hefei
38Seoul National University, Seoul
39Sungkyunkwan University, Suwon
40University of Sydney, Sydney, New South Wales
41Tata Institute of Fundamental Research, Mumbai
42Toho University, Funabashi
43Tohoku Gakuin University, Tagajo
44Tohoku University, Sendai
45Department of Physics, University of Tokyo, Tokyo
46Tokyo Institute of Technology, Tokyo
47Tokyo Metropolitan University, Tokyo
48Tokyo University of Agriculture and Technology, Tokyo
49Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
50Yonsei University, Seoul
We report a measurement of D0-D 0 mixing in D0 → K0S π
+π− decays using a time-dependent
Dalitz plot analysis. We first assume CP conservation and subsequently allow for CP violation. The
results are based on 540 fb−1 of data accumulated with the Belle detector at the KEKB e+e− collider.
Assuming negligible CP violation, we measure the mixing parameters x = (0.80± 0.29+0.09 +0.10−0.07 −0.14)%
and y = (0.33 ± 0.24+0.08 +0.06−0.12 −0.08)%, where the errors are statistical, experimental systematic, and
systematic due to the Dalitz decay model, respectively. Allowing for CP violation, we obtain the
CPV parameters |q/p| = 0.86+0.30 +0.06−0.29 −0.03 ± 0.08 and arg(q/p) = (−14
+16+5+2
−18−3−4)
PACS numbers: 13.25.Ft, 11.30.Er, 12.15.Ff
Mixing in the D0-D 0 system is predicted to be very
small in the Standard Model (SM) [1] and, unlike in K0,
B0, and B0s systems, has eluded experimental observa-
tion. Recently, evidence for this phenomenon has been
found in D0 → K+K−/π+π− [2] and D0 → K+π− [3]
decays. It is important to measure D0-D 0 mixing in
other decay modes and to search for CP -violating (CPV )
effects in order to determine whether physics contribu-
tions outside the SM are present. Here we study the
self-conjugate decay D0→K0S π+π−.
The time-dependent probability of flavor eigenstates
D0 and D 0 to mix to each other is governed by the
lifetime τD0 = 1/Γ, and the mixing parameters x =
(m1 − m2)/Γ and y = (Γ1 − Γ2)/2Γ. The parameters
m1,m2 (Γ1,Γ2) are the masses (decay widths) of the mass
eigenstates |D1,2〉 = p|D0〉±q|D 0〉, and Γ = (Γ1+Γ2)/2.
The parameters p and q are complex coefficients sat-
isfying |p|2 + |q|2 = 1. Various D0 decay modes have
been exploited to measure or constrain x and y [4]. For
D0→K0S π+π− decays, the time dependence of the Dalitz
plot distribution allows one to measure x and y directly.
This method was developed by CLEO [5] using 9.0 fb−1
of data; here we extend this method to a data sample 60
times larger.
The decay amplitude at time t of an initially produced
|D0〉 or |D 0〉 can be expressed as
,m2+, t) = A(m2−,m2+)
e1(t) + e2(t)
,m2+)
e1(t)− e2(t)
,m2+, t) = A(m2−,m2+)
e1(t) + e2(t)
,m2+)
e1(t)− e2(t)
, (1)
where A and A are the amplitudes for |D0〉 and |D 0〉
decays as functions of the invariant-masses-squared vari-
ables m2
≡ m2(K0S π±). The time dependence is con-
tained in the terms e1,2(t) = exp[−i(m1,2 − iΓ1,2/2)t].
Upon squaring M and M, one obtains decay rates con-
taining terms exp(−Γt) cos(xΓt), exp(−Γt) sin(xΓt), and
exp[−(1± y)Γt].
We parameterize the K0Sπ
+π− Dalitz distribution fol-
lowing Ref. [6]. The overall amplitude as a function of
m2+ and m
is expressed as a sum of quasi-two-body am-
plitudes (subscript r) and a constant non-resonant term
(subscript NR):
,m2+) =
iφrAr(m2−,m2+) + aNReiφNR , (2)
,m2+) =
iφ̄rAr(m2+,m2−) + āNReiφ̄NR . (3)
The functions Ar are products of Blatt-Weisskopf form
factors and relativistic Breit-Wigner functions [7].
The data were recorded by the Belle detector at the
KEKB asymmetric-energy e+e− collider [8]. The Belle
detector [9] includes a silicon vertex detector (SVD), a
central drift chamber (CDC), an array of aerogel thresh-
old Cherenkov counters (ACC), a barrel-like arrangement
of time-of-flight scintillation counters (TOF), and an elec-
tromagnetic calorimeter.
We reconstruct D0 candidates via the decay chain
D∗+ → π+s D0, D0 → K0Sπ+π− [10]. Here, πs denotes
a low-momentum pion, the charge of which tags the fla-
vor of the neutral D at production. The K0S candidates
are reconstructed in the π+π− final state; we require
that the pion candidates form a common vertex sepa-
rated from the interaction region and have an invariant
mass within ±10 MeV/c2 of m
. We reconstruct D0
candidates by combining the K0S candidate with two op-
positely charged tracks assigned as pions. These tracks
are required to have at least two SVD hits in both r-φ and
z coordinates. A D∗+ candidate is reconstructed by com-
bining the D0 candidate with a low momentum charged
track (the π+s candidate); the resulting D
∗+ momentum
in the e+e− center-of-mass (CM) frame is required to be
larger than 2.5 GeV/c in order to eliminate BB events
and suppress combinatorial background.
The charged pion tracks are refitted to originate from
a common vertex, which represents the decay point of
the D0. The D∗+ vertex is taken to be the intersection
of the D0 momentum vector with the e+e− interaction
region. The D0 proper decay time is calculated from
the projection of the vector joining the two vertices (~L)
onto the momentum vector: t = ~L · (~p/p)(m
/p). The
uncertainty in t (σt) is calculated event-by-event, and we
require σt < 1 ps (for selected events, 〈σt〉 ∼ 0.2 ps).
The signal and background yields are determined from
a two-dimensional fit to the variables m
and Q ≡
−mπ)·c2. The variableQ is the kinetic
energy released in the decay and equals only 5.9 MeV for
D∗+→π+s D0 decays. We parameterize the signal shape
by a triple-Gaussian function for m
, and the sum
of a bifurcated Student t distribution and a Gaussian
function for Q. The backgrounds are classified into two
types: random πs background, in which a random πs
is combined with a true D0 decay, and combinatorial
background. The shape of the m
distribution for
the random πs background is fixed to be the same as
that used for the signal. Other background distributions
are obtained from Monte Carlo (MC) simulation. We
perform a two-dimensional fit to the measured m
distributions in a wide range 1.81 GeV/c2 < m
1.92 GeV/c2 and 0<Q< 20 MeV. We define a smaller
signal region |m
− mD0 | < 15 MeV/c2 and |Q −
5.9 MeV| < 1.0 MeV, corresponding to 3σ intervals in
these variables. In this region we find 534410±830 signal
events and background fractions of 1% and 4% for the
random πs and combinatorial backgrounds, respectively.
and Q distributions are shown in Fig. 1 along
with projections of the fit result.
mKsππ (GeV)
1.825 1.85 1.875 1.9
Signal
Random π
Combinatorial
Q (MeV)
0 5 10 15 20
FIG. 1: The distribution of (a) m
with 0 < Q < 20 MeV;
(b) Q with 1.81 GeV/c2 < m
< 1.92 GeV/c2. Superim-
posed on the data (points with error bars) are projections of
the m
-Q fit.
For the events selected in the signal region we perform
an unbinned likelihood fit to the Dalitz plot variables
and m2+, and the decay time t. For D
0 decays, the
likelihood function is
fj(mK0
ππ,i, Qi)Pj(m2−,i,m2+,i, ti) , (4)
where j = {sig, rnd, cmb} denotes the signal or back-
ground components, and the index i runs over D0 candi-
dates. The event weights fj are functions of mK0
Q and are obtained from the m
-Q fit mentioned
above.
The probability density function (PDF)
Psig(m2−,m2+, t) equals |M(m2−,m2+, t)|2 convolved
with the detector response. Resolution effects in two-
particle invariant masses are significant only for m2ππ.
The latter, and variation of the efficiency across the
Dalitz plot, are taken into account using the method
described in Ref. [6]. The resolution in decay time t
is accounted for by convolving Psig with a resolution
function consisting of a sum of three Gaussians with a
common mean and widths σk = Sk · σt,i (k = 1− 3).
The scale factors Sk and the common mean are free
parameters in the fit.
The random πs background contains real D
0 and
D 0 decays; in this case the charge of the πs is un-
correlated with the flavor of the neutral D. Thus the
Prnd PDF is taken to be (1 − fw)|M(m2−,m2+, t)|2 +
fw|M(m2−,m2+, t)|2, convolved with the same resolution
function as that used for the signal, where fw is the
wrong-tag fraction. We measure fw = 0.452±0.005 from
fitting events in the Q sideband 3 MeV< |Q−5.9 MeV| <
14.1 MeV.
For the combinatorial background, Pcmb is the prod-
uct of Dalitz-plot and decay time PDFs. The latter is
parameterized as the sum of a delta function and an
exponential function convolved with a Gaussian resolu-
tion function. The timing and Dalitz PDF parameters
are obtained from fitting events in the mass sideband
30 MeV/c2< |m
−mD0 | < 55 MeV/c2.
The likelihood function for D 0 decays, L, has the same
form as L, with M and M (appearing in Psig and Prnd)
interchanged. To determine x and y, we maximize the
sum lnL+lnL. Table I lists the results from two separate
fits. In the first fit we assume CP is conserved, i.e.,
a = ā, φ = φ̄, and p/q = 1. We fit all events in the
signal region, where the free parameters are x, y, τ
the timing resolution parameters of the signal, and the
Dalitz plot resonance parameters ar(NR) and φr(NR). The
fit gives τ
= (409.9 ± 1.0) fs, which is consistent with
the world average [11]. The results for ar and φr for the
18 quasi-two-body resonances used (following the same
model as in Ref. [6]) and the NR contribution are listed
in Table II. The Dalitz plot and its projections, along
with projections of the fit result, are shown in Fig. 2. We
estimate the goodness-of-fit of the Dalitz plot through a
two-dimensional χ2 test [6] and obtain χ2/ndf = 2.1 for
3653−40 degrees of freedom (ndf). We find that the main
features of the Dalitz plot are well reproduced, with some
significant but numerically small discrepancies at peaks
and dips of the distribution in the very high m2
region.
The decay-time distribution for all events, and the ratio
of decay-time distribution for events in theK∗(892)+ and
K∗(892)− regions, are shown in Fig. 3.
TABLE I: Fit results and 95% C.L. intervals for x and y,
including systematic uncertainties. The errors are statisti-
cal, experimental systematic, and decay-model systematic,
respectively. For the CPV -allowed case, there is another so-
lution as described in the text.
Fit case Parameter Fit result 95% C.L. interval
No x(%) 0.80 ± 0.29 +0.09+0.10−0.07−0.14 (0.0, 1.6)
CPV y(%) 0.33 ± 0.24 +0.08+0.06−0.12−0.08 (−0.34, 0.96)
CPV x(%) 0.81 ± 0.30 +0.10+0.09−0.07−0.16 |x| <1.6
y(%) 0.37 ± 0.25 +0.07+0.07−0.13−0.08 |y| <1.04
|q/p| 0.86+0.30 +0.06−0.29 −0.03 ± 0.08 -
arg(q/p)(◦) −14+16+5+2−18−3−4 -
For the second fit, we allow for CPV . This introduces
the additional free parameters |p/q|, arg(p/q), ār(NR) and
φ̄r(NR). The fit gives two solutions: if {x, y, arg(p/q)} is
a solution, then {−x, −y, arg(p/q)+π} is an equally good
solution. From the fit to data, we find that the Dalitz plot
parameters are consistent for the D0 and D 0 samples;
hence we observe no evidence for direct CPV . Results
for |p/q| and arg(p/q), parameterizing CPV in mixing
and interference between mixed and unmixed amplitudes,
respectively, are also found to be consistent with CP con-
servation. If we fit the data assuming no direct CPV , the
values for x and y are essentially the same as those for the
TABLE II: Fit results for Dalitz plot parameters. The errors
are statistical only.
Resonance Amplitude Phase (◦) Fit fraction
K∗(892)− 1.629 ± 0.006 134.3 ± 0.3 0.6227
K∗0 (1430)
− 2.12 ± 0.02 −0.9± 0.8 0.0724
K∗2 (1430)
− 0.87 ± 0.02 −47.3 ± 1.2 0.0133
K∗(1410)− 0.65 ± 0.03 111± 4 0.0048
K∗(1680)− 0.60 ± 0.25 147± 29 0.0002
K∗(892)+ 0.152 ± 0.003 −37.5 ± 1.3 0.0054
K∗0 (1430)
+ 0.541 ± 0.019 91.8 ± 2.1 0.0047
K∗2 (1430)
+ 0.276 ± 0.013 −106± 3 0.0013
K∗(1410)+ 0.33 ± 0.02 −102± 4 0.0013
K∗(1680)+ 0.73 ± 0.16 103± 11 0.0004
ρ(770) 1 (fixed) 0 (fixed) 0.2111
ω(782) 0.0380 ± 0.0007 115.1 ± 1.1 0.0063
f0(980) 0.380 ± 0.004 −147.1 ± 1.1 0.0452
f0(1370) 1.46 ± 0.05 98.6 ± 1.8 0.0162
f2(1270) 1.43 ± 0.02 −13.6 ± 1.2 0.0180
ρ(1450) 0.72 ± 0.04 41± 7 0.0024
σ1 1.39 ± 0.02 −146.6 ± 0.9 0.0914
σ2 0.267 ± 0.013 −157± 3 0.0088
NR 2.36 ± 0.07 155± 2 0.0615
1 2 3
2 (GeV2/c4)
10000
1 2 3
2 (GeV2/c4)
20000
40000
1 2 3
2 (GeV2/c4)
10000
0 0.5 1 1.5 2
2 (GeV2/c4)
FIG. 2: Dalitz plot distribution and the projections for data
(points with error bars) and the fit result (curve). Here, m2±
corresponds to m2(K0Sπ
±) for D0 decays and to m2(K0Sπ
for D 0 decays.
CP -conservation case, and the values for the CPV pa-
rameters are further constrained: |q/p| = 0.95+0.22
−0.20 and
arg(q/p) = (−2+10
◦. A check with independent fits to
theD0 andD 0 tagged samples gives consistent results for
x (y): 0.58%±0.41% (0.45%±0.33%) and 1.04%±0.41%
(0.21%± 0.34%), respectively.
We consider systematic uncertainties arising from both
experimental sources and from the D0→K0S π+π− decay
Proper time (fs)
-2000 0 2000 4000
FIG. 3: (a) The decay-time distribution for events in the
Dalitz plot fit region for data (points with error bars), and
the fit projection for the CP -conservation fit (curve). The
hatched area represents the combinatorial background contri-
bution. (b) Ratio of decay-time distributions for events in the
K∗(892)+ and K∗(892)− regions.
model. We estimate these uncertainties by varying rel-
evant parameters by their ±1σ errors and interpreting
the change in x and y as the systematic uncertainty due
to that source. The main sources of experimental uncer-
tainty are the modeling of the background, the efficiency,
and the event selection criteria. We vary the background
normalization and timing parameters within their uncer-
tainties, and we also set fw equal to its expected value
of 0.5 or alternatively let it float. To investigate possi-
ble correlations between the Dalitz plot (m2+,m
) dis-
tribution and the t distribution of combinatorial back-
ground, the Dalitz plot distribution is obtained for three
bins of decay time; these PDFs are then used accord-
ing to the reconstructed t of individual events. We also
try a uniform efficiency function, and we apply a “best-
candidate” selection to check the effect of the small frac-
tion of multiple-candidate events. We add all variations
in x and y in quadrature to obtain the overall experimen-
tal systematic error.
The systematic error due to our choice of D0 →
+π− decay model is evaluated as follows. We
vary the masses and widths of the intermediate res-
onances by their known uncertainties [11], and we
also try fits with Blatt-Weisskopf form factors set to
unity and with no q2 dependence in the Breit-Wigner
widths. We perform a series of fits successively exclud-
ing intermediate resonances that give small contributions
(ρ(1450), K∗(1680)+), and we also exclude the NR con-
tribution. We account for uncertainty in modeling of
the S-wave ππ component by using K-matrix formal-
ism [12]. We include an uncertainty due to the effect of
around 10-20% bias in the amplitudes for theK∗(1410)±,
K∗0 (1430)
+ andK∗2 (1430)
+ intermediate states, which we
observe in MC studies. Adding all variations in quadra-
ture gives the final results listed in Table I.
We obtain a 95% C.L. contour in the (x, y) plane
by finding the locus of points where −2 lnL increases
by 5.99 units with respect to the minimum value (i.e.,
−2∆ lnL=5.99). All fit variables other than x and y are
allowed to vary to obtain best-fit values at each point
on the contour. To include systematic uncertainty, we
rescale each point on the contour by a factor
1 + r2,
where r2 is a weighted average of the ratios of systematic
to statistical errors for x and y, where the weights de-
pend on the position on the contour. Both the statistical-
only and overall contours for both the CPV -allowed and
the CP -conservation case are shown in Fig. 4. We note
that for the CPV -allowed case, the reflection of these
contours through the origin (0, 0) are also allowed re-
gions. Projecting the overall contour onto the x, y axes
gives the 95% C.L. intervals listed in Table I. After
the systematics-rescaling procedure, the no-mixing point
(0,0) has a value −2∆ lnL = 7.3; this corresponds to a
C.L. of 2.6%. We have confirmed this value by generat-
ing and fitting an ensemble of MC fast-simulated exper-
iments.
x (%)
no CPV (stat. only)
no CPV
CPV (stat. only)
-1 0 1 2
FIG. 4: 95% C.L. contours for (x, y): dotted (solid) corre-
sponds to statistical (statistical and systematic) contour for
no CPV , and dash-dotted (dashed) corresponds to statisti-
cal (statistical and systematic) contour for the CPV -allowed
case. The point is the best-fit result for no CPV .
In summary, we have measured the D0-D 0 mixing
parameters x and y using a Dalitz plot analysis of
D0 → K0S π+π− decays. Assuming negligible CP vi-
olation, we measure x = (0.80 ± 0.29+0.09+0.10
−0.07−0.14)% and
y = (0.33 ± 0.24+0.08+0.06
−0.12−0.08)%, where the errors are sta-
tistical, experimental systematic, and decay-model sys-
tematic, respectively. Our results disfavor the no-mixing
point x = y = 0 with a significance of 2.2σ, while the
one dimensional significance for x > 0 is 2.4σ. We have
also searched for CPV ; we see no evidence for this and
constrain the CPV parameters |q/p| and arg(q/p).
We thank the KEKB group for excellent operation of
the accelerator, the KEK cryogenics group for efficient
solenoid operations, and the KEK computer group and
the NII for valuable computing and Super-SINET net-
work support. We acknowledge support from MEXT and
JSPS (Japan); ARC and DEST (Australia); NSFC and
KIP of CAS (China); DST (India); MOEHRD, KOSEF
and KRF (Korea); KBN (Poland); MES and RFAAE
(Russia); ARRS (Slovenia); SNSF (Switzerland); NSC
and MOE (Taiwan); and DOE (USA).
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http://arxiv.org/abs/hep-ex/0503045
http://arxiv.org/abs/hep-ex/0507101
