Table Of Content1
UCTP-112-00
CP Violation and Mixing Results from FNAL E791
A. J. Schwartza
(Representing the E791 Collaboration)
a Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221
1
0 Wereview results from FNALE791 concerningD0-D0 mixingand CP violation in D meson decays. Wehave
0 searched for mixing in semileptonic D0 →K+ℓ−ν¯ decays and in hadronic D0 →K+π− and D0 →K+π−π+π−
2 decays. WehavesearchedforCPviolationinD0 →K+K−/π+π−andD+ →φπ+/K∗0K+/K+K−π+/π+π−π+
n decays. Finally, we have measured the difference in decay widths ∆Γ between the two mass-eigenstates of the
a D0-D0 system. Thisparameteraffectstherateof D0-D0 mixing. Wecombineourresultswith thosefrom other
J
experimentsto obtain confidenceintervals incorporating all published experimentaldata.
0
3
2
v 1. INTRODUCTION cays;(d)measurementofthewidthdifference∆Γ
6 between the two mass-eigenstates of the D0-D0
0 FNAL E7911 is a hadroproductionexperiment
system. TheseresultsarepublishedinRefs.[4,6–
0 studying the weak decays of charm mesons and
2 9]. Throughout this paper, charge-conjugate
baryons. The charm particles were produced by
1 impinging a 500 GeV/c π− beam on five thin modes are included unless otherwise noted.
0 The experimental apparatus consisted of a sil-
0 target foils. The most upstream foil consisted
icon vertex detector followed by a two-magnet
/ of platinum; the other foils consisted of carbon.
x spectrometer, two segmented Cerenkov count-
All foils were separated by about 15 mm such
e ers for hadron identification, an electromagnetic
- that D mesons decayed predominately in the air
p calorimeter for electron identification, and iron
gaps between foils. The experiment took data
e shielding followed by scintillator counters for
from September, 1991 to January 1992, record-
h
muon identification. The silicon vertex detector
: ingthe world’slargestsampleofcharmdecaysat
v consisted of 17 planes of silicon and was used to
thattime. Thenumberofreconstructedeventsis
i reconstruct decay vertices downstream from the
X over 200000. With this data sample the experi-
interaction vertex. The spectrometer consisted
r ment has studied charm production [1,2], charm
a of 35 planes of drift chambers and two propor-
lifetimes [3,4], rare and forbidden D decays [5],
tional wire chambers. The two dipole magnets
D0-D0 mixing [6],CPviolation[7,8],andseveral
bent particles in the horizontal plane and had
other topics. Here we focus on the following: (a)
p kicks of +212 GeV/c and +320 GeV/c. The
searchesforD0-D0 mixinginsemileptonicD0 CTerenkov counters contained gases with differ-
K+ℓ−ν¯ decays and in hadronic D0 K+π→− ent indices of refraction; together they provided
and D0 K+π−π+π− decays; (b) mea→surement π/K/p discrimination over the momentum range
→
of the doubly-Cabibbo-suppressed decay D+ 6–60GeV/c. Moredetailsaboutthedetectorcan
K+π−π+; (c) search for CP violation in ne→u- be found in Ref. [2].
tral D0 K+K−/π+π− decays and in charged Data was recordedusing a loose transverseen-
D+ →φπ+/K∗0K+/K+K−π+/π+π−π+ de- ergy trigger. After reconstruction, events with
→
evidence of well-separated interaction and decay
1The collaboration consists of: CBPF(Brazil), Tel Aviv,
vertices were retained for further analysis. Some
CINVESTAV (Mexico), Puebla (Mexico), U. C. Santa
Cruz, Cincinnati, Fermilab, Illinois Institute of Technol- of the main criteria used to select charm decays
ogy,KansasState, Massachusetts, Mississippi,Princeton, are listed in Table 1. The most important crite-
SouthCarolina,Stanford,Tufts,Wisconsin,andYale.
2
rion is that of SDZ, defined as the distance be- 2.1. Semileptonic D0 → K+ℓ−ν¯ Decays
tween the interaction and decay vertices divided
SemileptonicD0 K+ℓ−ν¯candidateswerese-
by the errorinthis quantity. Values usedfor this →
lected by requiringthatthere be a two-trackver-
criterion ranged from 8 (for D0 and D+ decays)
s tex with SDZ > 8. One track was required to
to 20 (for longer-lived D+ decays).
pass kaon identification criteria in the Cerenkov
counters, and the other track was required to
pass either electron identification criteria in the
Table 1 calorimeter or muon identification criteria in the
Main criteria used to select D decays. scintillator counters following the iron shielding.
Selection criteria Typ. value Tracks identified as muons were required to have
p > 10 GeV/c to reduce background from de-
SDZ
≡ cays in flight. We define a quantity Mmin ≡
(z z )/ σ2 +σ2 8–20 p + p2 +M2 ,wherep isthetransversemo-
dec− int p dec int T p T Kℓ T
mentumofthe Kℓsystemwithrespecttothe D0
p (transverse to D direction) <250 MeV/c
T direction-of-flight (obtained from the interaction
min|zdec−ztarget edge|/σsec >5 and decay vertex positions), and MKℓ is the in-
D impact parameter variant mass of the Kℓ pair. To reduce back-
grounds,M is requiredto be inthe range1.6–
w/r/t int. vertex <60 µm min
2.1 GeV/c2, and M is required to be in the
Kℓ
χ2 <5 range 1.15–1.80 GeV/c2. The upper cut on M
track Kℓ
removesbackgroundfromD0 K−π+ decaysin
t ≡ mD × (zdec−zint)/p <5 ps which the pion is misidentified→as a lepton. After
these cuts, the candidate D0 is paired with a π±
trackoriginatingfromtheinteractionvertex(and
having p>2 GeV/c) to form a D∗±.
Since there is an undetected neutrino in the fi-
2. SEARCH FOR D0-D0 MIXING nalstate,thecandidateD0 momentumcannotbe
E791 has searched for D0-D0 mixing via measured directly. However, using the direction
semileptonic D0 K+ℓ−ν¯ decays and hadronic of the D0, the measured K and ℓ momenta, and
D0 K+π− an→d D0 K+π−π+π− decays. assumingthe parentparticlemasstobe thatofa
Fort→hesesearcheswereq→uirethatthe D0 bepro- D0,onecansolveforthe neutrinomomentumup
duced via D∗+ D0π+ decay, and thus the fla- to a two-fold ambiguity. We use the solution re-
vor of the D0 (o→r D0) when created is identified sulting in higher D0 momentum, as Monte Carlo
(MC) studies indicate that this provides a bet-
by the charge of the associated pion. The flavor
ter estimate of the true momentum. From MC
ofthe D0 whenit decaysis identifiedby the final
studies we determine that the r.m.s. difference
state. Withthisinformationwemeasuretheratio
r Γ(D0 D0 f¯)/Γ(D0 f). Eachtype betweenthecalculatedandthetrueD0 momenta
mix ≡ → → → is about 15%.
ofdecaystudied(semileptonicorhadronic)hasan
To search for a mixing signal, we divide the
advantage and a disadvantage: the Kℓν decays
electronandmuonsamplesinto“right-sign”(RS)
cannot be fully reconstructed due to the missing
and“wrong-sign”(WS) decays. The formerhave
neutrino, and thus the decay-time resolution is
the charge of the kaon being opposite to that of
degraded. TheKπ/Kπππ decaysarefullyrecon-
the pion from the D∗, whereas the latter have
structed and thus have good time resolution, but
the charge of the kaon being the same as that
they contain “background” arising from doubly-
of the pion. A WS decay would indicate D0-D0
Cabibbo-suppressed (DCS) amplitudes that pro-
mixing. To determine the numbers of events in
duce the same final state. The DCS amplitudes
the four samples (e and µ, RS and WS), we per-
do not contribute to the semileptonic decays.
3
form an unbinned maximum likelihood fit using An example ofthe time dependences ofthe three
the Q value (m m m ) and decay- terms is plotted in Fig. 1.
D0π+ − D0 − π+
time t (m (z z )/p) for each event. The results of the fitting procedure depend
For D∗+ D0 ×D0π+decd−ecayinst, the Q distribution upon whether we allow interference between the
→
is sharply peaked at 5.8 MeV. We also include DCS and mixing amplitudes, and also whether
in the fits the Q and t distributions of back- we allow CP violation in any of the coefficients
ground. The results for the electron sample are: in Eq. (1). In the most general case of allow-
N =1237 45 and N =4.4+11.8. The re- ing CP violation in all coefficients, we obtain
saunRldtSsNfoWrSth=e 1m±.8uo−+n1112s..01a.mTphleWeraSerei:sNnoRSi−n=1d0i.c15a2t6io7n±of44a rrmix((DD00 →D0D)0=) (=0.70(0+.10.858−+00..34093.1±8)%0..17A)l%lowainndg
mixing signal. Combining results from both Keν¯ mix → −0.53 ±
CP violation in only the interference term gives
and Kµν¯ samples gives rmix = (0.11−+00..2370)% or r = (0.39+0.36 0.16)% or r < 0.85% at
r <0.50% at 90% C.L. mix −0.32 ± mix
mix 90% C.L.
2.2. Hadronic D0 → K+π− and D0 →
K+π−π+π− Decays
D0 K+π− candidates were selected from a
→
sample of two-prong decay vertices, and D0
K+π−π+π− candidates were selected from fou→r-
prongverticesandfromthree-prongverticeswith
an extra track added. For the final event selec-
tion, we use a two-layer neural network with 12
input variables (for Kπ) or 7 input variables (for
Kπππ). These variables include the p of the
T
D0 candidatewith respectto the π− beamdirec-
tion, the p of the D0 with respect to the D0 di-
T
rection (obtained from the interaction and decay
vertex positions), SDZ, the decay vertex fit χ2,
thetrackfitχ2s,theCerenkovcounters’response
forthe K,etc. Thisselectionresultsineightsep-
aratedatasets: D0 andD0, Kπ andKπππ final
states,RSandWSdecays. We subsequentlyper- Figure 1. An example of the time dependence
formasingleunbinnedmaximumlikelihoodfitto of D0 K+π− decays due to the DCS ampli-
→
alldata sets,constructing the likelihoodfunction tude (dashed), the mixing amplitude (dotted),
from the kinetic energy Q, the decay-time t, and and the interference between the two (dashed-
the reconstructed mass m of each event. Back- dotted). The sum of all three contributions is
grounds were carefully modeled and included in solid.
thefit. ForeachWSdataset,thefitincludedcon-
tributions from a possible DCS amplitude. This
amplituderesultsinadifferenttdependencethan
If we assume no mixing contribution (consis-
that due to mixing, and this allows one to par-
tentwithStandardModelpredictionsatourlevel
tially discriminate between the two sources. The
of sensitivity), we obtain a rate for DCS decays.
fullexpressionfortheWStdistribution(atsmall Theresultsare: r (Kπ)=(0.68+0.34 0.07)%
t where we have acceptance) is: DCS −0.33±
and r (Kπππ) = (0.25+0.36 0.03)%. These
DCS −0.34 ±
dNWS/dt ≈ e−Γt × (1) avaslueexspaecreteadp,paronxdimaaretelcyontasins4teθnCt×w(ipthhasoeusrpmaceea)-,
(cid:16)|ADCS|2+|Amix|2t2+2Re(ADCSA∗mix)t(cid:17). surement of the DCS charged decay D+ →
4
K+π−π+ [9]. For this latter measurement the to be largest. Because the incoming beam is π−,
final event sample is shown in Fig. 2. There are the production cross section for D0 and D− (in
substantial backgrounds arising from misidenti- our acceptance) is a few percent larger than that
fied charm decays such as D0 K−π+π+ and forD0 andD+; this productionasymmetrymust
Ds+ → K+K−π+ (both Cabib→bo-favored). We be corrected for in order to discern a CP asym-
simultaneously fit for these backgrounds and a metry. To do this we define the ratios:
D+ K+π−π+ signal, finding 59 13 candi-
→ ±
date events in the peak. This gives a measure- ηD→f ≡ ND→f/ND→K−π+(π+) (3)
ment rDCS(Kππ)=(0.77 ± 0.17 ± 0.08)%. ηD→f¯ ≡ ND→f¯/ND→K+π−(π−) . (4)
Then A = (η η )/(η + η )
CP D→f − D→f¯ D→f D→f¯
if ε /ε = ε /ε ,
D→f D→K−π+(π+) D→f¯ D→K+π−(π−)
where ε is the overalldetection efficiency for
D→f
D f (including acceptance). This relation-
→
ship among efficiencies holds well for E791. We
assume there is negligible CP violation in the
Cabibbo-favored decay modes used to normalize
theCabibbo-suppresseddecayrates[Eqs.(3)and
(4)].
3.1. Neutral D0 Decays
We measure A for D0 K+K− and D0
π+π−, where thCePD0 orig→inates from D∗+ →
→
D0π+ and thus the flavor of the D0 is identified
by the charge of the associated pion. The final
mass plots are shown in Fig. 3 along with those
for the normalizationchannel D0 K−π+. The
→
solid curves superimposed are our fits to the his-
Figure2. TheK+π−π+ invariantmassspectrum tograms. The integrals of the Gaussian distribu-
for events passing final selection criteria. A peak tions used for the signals determine the number
resulting from the DCS decay D+ K+π−π+ of D0 Kπ/KK/ππ decays. These eventyields
→ →
(andalsofromthesingly-Cabibbo-suppressedde- (listed in Fig. 3) are used to calculate ηD0 and
cay Ds+ →K+π−π+) is clearly visible. ηD0 and subsequently determine ACP. The re-
sults are:
A (K+K−) = 0.010 0.049 0.012 (5)
CP − ± ±
A (π+π−) = 0.049 0.078 0.030. (6)
3. SEARCH FOR CP VIOLATION CP − ± ±
These correspond to 90% confidence intervals
E791 has searched for CP violation in both
9.3% < A (K+K−) < 7.3% and 18.6% <
chargedandneutralD decays. Forthesesearches A− (π+π−)C<P8.8%. −
wemeasurethetime-integratedasymmetryA , CP
CP
defined as: 3.2. Charged D+ Decays
Γ(D f) Γ(D f¯)
A → − → . (2) We measure A for D+ decays into the fi-
CP ≡ Γ(D →f)+Γ(D →f¯) nal states φπ+ (φCP K+K−), K∗0K+ (K∗0
WestudyonlyCabibbo-suppressedfinalstates,as K−π+), K+K−π+→(nonresonant), and π+π−π→+.
forthesemodesCP-violatingeffects areexpected Forallmodes,thenormalizationchannelisD+
→
5
Figure 3. Final mass plots for D0 (left) and
0
D (right) decaysinto finalstates Kπ (top row),
K+K− (middle row), and π+π− (bottom row).
K−π+π+. For the φπ+ final state we require
m m <6MeV/c2; fortheK∗0K+ final
| K+K−− φ|
state we require m m < 45 MeV/c2.
| K−π+ − K∗|
The mass spectra for the final event samples are
shown in Fig. 4, and the measured asymmetries
A are listed in Table 2. We also list measure-
CP
mentsfromotherexperiments,andforeachdecay
mode we calculate a 90% confidence interval for
A incorporating all measurements listed. As
CP
the measurements are from independent experi-
ments,weassumetheirstatisticalandsystematic
errors uncorrelated. We observe that A for
CP
D+ K+K−π+ is relatively well-constrained:
→
the 90% CL interval is 1.6% to +2.0%. For
D0 π+π−π+, the E7−91 measurement is the Figure 4. Final mass plots for D+ (left) and D−
only→result available. ∗0
(right) decays into final states φπ, K K, KKπ
(nonresonant), and πππ.
6
Table 2
CPasymmetriesmeasuredforD0 andD+ decays. Alsolistedaremeasurementsfromotherexperiments,
and listed in boldface type are 90% confidence intervals incorporating all the experimental results.
Mode A (E791) A (Others)
CP CP
+0.024 0.084 (E687 [10])
±
D0 K+K− 0.010 0.049 0.012 +0.080 0.061 (CLEO [11])
→ − ± ± ±
0.001 0.022 0.015 (E831 [12])
− ± ±
−2.6 < A < 4.4 %
CP
D0 π+π− 0.049 0.078 0.030 +0.048 0.039 0.025 (E831 [12])
→ − ± ± ± ±
−4.1 < A < 9.2 %
CP
0.031 0.068 (E687 [10])
D+ K+K−π+ 0.014 0.029 − ±
→ − ± +0.006 0.011 0.005 (E831 [12])
± ±
−1.6 < A < 2.0 %
CP
D+ φπ+ 0.028 0.036 0.066 0.086 (E687 [10])
→ − ± ±
−6.8 < A < 4.1 %
CP
D+ K∗0K+ 0.010 0.050 0.12 0.13 (E687 [10])
→ − ± − ±
−10 < A < 5.2 %
CP
D+ π+π−π+ 0.017 0.042
→ − ±
−8.6 < A < 5.2 %
CP
4. MEASUREMENT OF THE WIDTH previous limit r < 0.50% implies y < 0.10
DIFFERENCE ∆Γ or ∆Γ < 0.48 pmsi−x1, and thus cosh(∆|Γ|/2)t 1
| | ≈
for the range of lifetime t accepted by the ex-
E791 has measured the difference in decay periment. Thus dN /dt e−Γt, and ∆Γ =
widths between the two mass-eigenstates of the Kπ ∝
2(Γ Γ ). Equivalently, y = ∆Γ/(2Γ) =
D0-D0 system. This provides a measurement of KK − Kπ
τ /τ 1. From an experimental point of
the mixing parameter y ∆Γ/(2Γ). Theoreti- Kπ KK −
view, it is convenient that cosh(∆Γ/2)t 1 as
≡
cally, r = Γ(D0 D0 f¯)/Γ(D0 f) = we actually measure t t t′, and≈while
(x2+ym2)ix/2 for x,y s→mall, w→here x ∆m→/Γ. e−Γt′ e−Γt, cosh(∆Γ/−2)tc′uits ≡not proportional
≡
The method used to determine ∆Γ is as fol- ∝
to cosh(∆Γ/2)t.
lows: assuming no CP violation, the two mass- The D0 K−π+ and D0 K+K− final
eigenstates are CP eigenstates and can be writ- → →
event samples are shown in Fig. 5. The re-
ten D = (D0 + D0 )/√2 and D = (D0 sultant lifetime distributions (for t′) are shown
1 | i | i 2 | i−
D0 )/√2. Observing a K+K− final state in Fig. 6. These distributions have the back-
(|CPi= +1) denotes a D K+K− decay, and ground shape subtracted, and fitting to them
dfiNnaKlKs/tadtte∝dee−noΓt1et.sOabDse0r1vio→nrgDa K0 −deπc+ayo,rrKes+pπec−- y2.i4el4d1s: Γ0K.0π68=ps2−.412.0T±he0d.0iff1e9repnsc−e1inanwdidΓthKsK∆=Γ
is0.04± 0.14 0.05ps−1,wherethefirsterroris
tively(neglectingDCSamplitudesforsimplicity).
± ±
In this case dN /dt e−Γtcosh(∆Γ/2)t [13], statistical(resultingfromthefits)andthesecond
Kπ ∝ error is the sum in quadrature of the systematic
where Γ = (Γ +Γ )/2 and ∆Γ = Γ Γ . Our
1 2 1− 2
7
errors. These systematic errors are listed in Ta-
ble3. Theresultcorrespondstoa90%confidence
interval 0.20 < ∆Γ < 0.28 ps−1. For y we ob-
−
tain0.008 0.029 0.010or 0.042<y <0.058
± ± −
at 90% C.L. Combining this with a recent mea-
surementbyFNAL E831(y =0.0342 0.0139
± ±
0.0074 [14]) gives 0.006<y <0.052 at 90% C.L.
Figure 6. Reduced lifetime (t′) distributions for
D0 K−π+ (top) and D0 K+K− (bot-
→ →
tom). The contributions from background have
been subtracted.
for the DCS charged decay D+ K+π−π+:
→
r (Kππ)=(0.77 0.17 0.08)%.
DCS ± ±
We have alsosearchedfor CP violationin neu-
FrainiggdhutrDeo0f5.t→hFeinKDa0+lmKa−sKs(+pblKoottt−sofmpoer)a.DkT0(bh→oetKptoe−maπk+ptloo(tto)thpies) Dtra+l D→0 →φπK++/KK−∗0/Kπ++π/−K+deKca−yπs+a/nπd+iπn−cπh+argdeed-
duetoD0 K−→π+ decaysinwhichthepionhas cays. WeseenoevidenceforCPviolation,andfor
→ each mode we set 90% C.L. limits on the asym-
been misidentified as a kaon.
metryparameterA . Theseresultsarelistedin
CP
Table 2.
Finally, we measure the difference in decay
widths ∆Γ between the two mass-eigenstates of
5. SUMMARY
the D0-D0 system. We convert this into a mea-
We have searched for D0-D0 mixing in both surement of the mixing parameter y =∆Γ/(2Γ).
semileptonic and hadronic D0 decays and see no Our result is y = 0.008 0.029 0.010 or
± ±
evidence for it. We subsequently set 90% CL 0.042<y <0.058 at 90% C.L. Combining this
−
upper limits r <0.50% and r <0.85%, re- with a recent measurement by FNAL E831 gives
mix mix
spectively. Assuming the mixing amplitude to 0.006<y <0.052 at 90% C.L.
be negligibly small (as predicted by the Stan-
dard Model), we fit our data for the rate of DCS
REFERENCES
decays D0 K+π− and D0 K+π−π+π−,
obtaining rD→CS(Kπ) = (0.68−+00..33→43 ±0.07)% and 1. E. M. Aitala et al., Phys. Lett. B371 (1996)
r (Kπππ) = (0.25+0.36 0.03)%. These re- 157;Phys.Lett.B379(1996)292;Phys.Lett.
DCS −0.34 ±
sults are consistent with the rate we measure B403(1997)185;Phys.Lett.B411(1997)230;
8
Table 3
Systematic errors contributing to the measure-
ment of ∆Γ.
τ τ ∆Γ
Kπ KK
Systematic error (ps) (ps) (ps−1)
Fit range 0.002 0.003 0.024
Selection criteria 0.001 0.002 0.020
Particle ID weighting 0.001 0.003 0.024
MC production model 0.003 0.003 0.000
Fixed width 0.001 0.002 0.030
Total 0.004 0.006 0.050
Phys. Lett. B462 (1999) 225.
2. E. M. Aitala et al., Eur. Phys. J.direct C4
(1999) 1.
3. E. M. Aitala et al., Phys. Lett. B440 (1998)
435.
4. E.M.Aitalaetal.,Phys.Rev.Lett.83(1999)
32.
5. E. M. Aitala et al., Phys. Rev. Lett.
76 (1996) 364; Phys. Lett. B462 (1999)
401; FERMILAB-Pub-00/280-E(2000), hep-
ex/0011077(submitted to Phys. Rev. Lett.).
6. E.M.Aitalaetal.,Phys.Rev.Lett.77(1996)
2384; Phys. Rev. D57 (1998) 13.
7. E. M. Aitala et al., Phys. Lett. B421 (1998)
405.
8. E. M. Aitala et al., Phys. Lett. B403 (1997)
377.
9. E. M. Aitala et al., Phys. Lett. B404 (1997)
187.
10. P. L. Frabetti et al., Phys. Rev. D50 (1994)
R2953.
11. J.Barteltet al., Phys.Rev.D52(1995)4860.
12. J.M.Linketal.,Phys.Lett.B491(2000)232.
13. A. J. Schwartz, UCTP-104-99 (1999), hep-
ph/0011226(unpublished).
14. J.M.Linket al., Phys.Lett.B485(2000)62.
