Transcript D0-D0 Mixing at BaBar Abe Seiden University of California at Santa Cruz for The BaBar Collaboration Charm 2007 August, 2007

D0-D0 Mixing at BaBar
Abe Seiden
University of California at
Santa Cruz
for
The BaBar Collaboration
Charm 2007 August, 2007
1
Status of Mixing Studies
• Mixing among the lightest neutral mesons of each flavor
has traditionally provided important information on the
electroweak interactions, the CKM matrix, and the
possible virtual constituents that can lead to mixing.
• Among the long-lived mesons, the D meson system
exhibits the smallest mixing phenomena.
• The B-factories have now accumulated sufficient
luminosity to observe mixing in the D system and we
can expect to see more detailed results as more
luminosity is accumulated and additional channels
sensitive to mixing are analyzed.
2
BaBar Charm Factory: 1.3 million Charm events per fb-1
• BaBar integrated luminosity ~384 fb-1 (Runs 1-5) used for evidence for
mixing result I will present. Corresponds to about 0.5 billion charm events
produced. Present BaBar integrated luminosity is approximately 500 fb-1.
BaBar Detector
BaBar is a high acceptance general
purpose detector providing excellent
tracking, vertexing, particle ID, and
neutrals detection.
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Mixing Measurables
The propagation eigenstates, including the electroweak
interactions are:
D1, 2  p D 0  q D 0
p
2
 q
2
1
Propagation parameters for the two states are given by:

1
2
 1  2 
M  M1  M 2
  1   2
With the observable oscillations determined by the
scaled parameters:
x
M


, y
 .

2
In the case of CP conservation the two D eigenstates are the
CP even and odd combinations. I will choose D1 to be the
CP even state. The sign choice for the mass and width
difference varies among papers, I will use the choice above.
4
Assuming CP conservation, small mixing parameters, and an initial
state tagged as a D0, we can write the time dependence to first order



 ( / 2  i m ) t
D(t) = (D  D ( y  ix) t )e
.
2
0
0
in x and y:
Projecting this onto a
final state f gives to first order the amplitude for finding f:
  ( / 2i m )t
(  f   f ( y  ix) t )e
2

This leads to a number of ways to measure the effect of mixing, for
example:
1) Wrong sign semileptonic decays. Here Af is zero and we measure
directly the quantity, after integrating over decay times:
RM = (x2 + y2)/2
Limits using this measurement however, are not yet sensitive
enough to get down to the 10-4 level for RM. Using 334 fb-1 of data,
electron decays only, and a double tag technique, BaBar measures
RM = 0.4x10-4, with a 68% confidence interval (-5.6, 7.4)x10-4.
2) Cabibbo favored, right sign (RS) hadronic decays (for example Kp.
These are used to measure the average lifetime, with the correction
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from the term involving x and y usually ignored (provides a correction on
O(10-3)).
3) Singly suppressed decays (for example KK or pp). In this case
tagging the initial state isn’t necessary. For CP even final states:
Af =Af. This provides the most direct way to measure y. With tagging we
can also check for CP violation, by looking at the value of y for each tag
type. BaBar will be updating this measurement with the full statistics later
this year. The initial measurement was based on 91 fb-1 and gave the
result y = 0.8, with statistical and systematic errors each about 0.4,
consistent with the published Belle measurement.
4) Doubly suppressed and mixed, wrong sign (WS) decays (for example
Kp). Mixing leads to an exponential term multiplied by both a linear and
a quadratic term in t. The quadratic term has a universal form depending
on RM . For any point in the decay phase space the decay rate is given by:
(t )2 t
2
2
( A f  A f A f y ' t  A f RM
)e
2
Here y ’ = y cosd – x sind, where d is a strong phase difference between
the Cabibbo favored and Doubly suppressed amplitudes. For the Kp
decay there is just the one phase.
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For multibody decays the phase d varies over the phase space and the
term proportional to t will involve a sum with different phases if we add
all events in a given channel.
BaBar has analyzed the decay channel Kpp0, with a mass cut that
selects mostly Kr decays, the largest channel for the Cabibbo allowed
amplitude arising from mixing. Based on 230 fb-1, BaBar measures:
0.18
a y '  (1.20.6

0.2)%,
R

(0.023
0.8
M
0.14  0.004)%
The parameter a allows for the phase variation over the region summed
over. Better would be a fit to the full Dalitz plot. This, however, requires
a model for all the resonant and smooth components that contribute to
the given channel, which may introduce uncertainties. BaBar is working
on such a fit; will be based on approximately 1500 signal events.
Another important 3-body channel is the KSpp decay channel. This
contains: CP-even, CP-odd, and mixed-CP resonances. Must get
relative amounts of CP-odd and CP-even contributions correct
(including smooth components) to get the correct lifetime difference.
Provides the possibility to measure x. BaBar also working on this
channel, Belle has published their results.
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Expectations for Mixing Parameters
Final general comments: In the Standard Model y and x are due to
long-distance effects. They may be comparable in value but this
depends on physics that is difficult to model. Also, the sign of x/y
provides an important measurement. Long-distance effects control
how complete the SU(3) cancellation is, which would make the
parameters vanish in the symmetry limit. Depends on SU(3) violations
in matrix elements and phase space. One might expect the x and y
parameters to be in the range O(10-3 to 10-2). Thus the present data
are consistent with the Standard Model. Searches for CP violation are
important goals of the B-factories, since observation at a non-neglible
level would signify new physics.
I will turn now to the strongest Evidence for D-Mixing from BaBar, using
the Kp final state.
(PRL 98, 211802 (2007))
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Event Selection: Kp Decay of the D
• Beam-constrained vertex fits
of K, p, ptag tracks as shown
in figure. ptag charge gives D
flavor at production.
– Require fit probability > 0.001
• D0 selection
–
–
–
–
–
–
CMS p* > 2.5 GeV/c
K, p particle identification
DCH hits > 11
1.81 < M(Kp) < 1.92 GeV/c2
decay time error < 0.5 ps
-2 < decay time < 4 ps
• ptag
– CMS p* < 0.45 GeV/c
– lab p > 0.1 GeV/c
– SVT hits > 5
y
beam spot
x
interaction
point
• 0.14 < M < 0.16 GeV/c2,
where M = M(Kpptag) –
M(Kp).
• Select candidate with best
vertex fit probability for
multiple D*+ candidates
sharing tracks
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RS(top)/WS(bottom) Datasets After Event Selection
Integrated Luminosity Approximately 384 fb-1
x103
BaBar Data
mKp
BaBar Data
events/1 MeV/c2
BaBar Data
mKp
events/0.1 MeV/c2



m
1,229,000
RS candidates
BaBar Data
m
64,000
WS candidates

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Analysis Strategy
• Blind analysis of D*+ → D0(→Kp) ptag
– Event selection and fitting methodology determined before looking at
the mixing results.
• Unbinned maximum likelihood fit to the data using four variables per event.
– First, correlated fit to the M(Kp), M = M(Kpptag) – M(Kp) distributions
(two of the variables) to establish shapes for different components
(signal and backgrounds) of the two dimensional distribution. Highstatistics RS and WS data samples fit simultaneously. These shapes
used in later time dependent fits.
• Fit RS proper-time distribution in the four variables, where the two
additional variables are the event-by-event lifetime and its error.
Establishes proper-time resolution function for signal and backgrounds.
– The WS data are fit using the RS resolution functions.
• Several WS proper time fits are performed.
– no mixing
– mixing, no CP violation
– mixing, CP violation
• Monte Carlo used to search for systematics and validate statistical
significance of results.
11
RS/WS M(Kp), M Distributions
BaBar Data
Fit RS/WS M(Kp), M distributions with signal and three background PDFs,
correlation between M and M in signal events taken into account in PDF.
Signal: peaks in M(Kp), M
True D0 combined with random ptag: peaks in M(Kp) only
Misreconstructed D0: peaks in M only
Purely combinatoric: non-peaking in either variable
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Simultaneous Fit to RS/WS Data
BaBar Data
RS signal:
1,141,500±1200
Events.
BaBar Data
BaBar Data
WS signal:
4030±90
Events.
BaBar Data
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Proper Time Analysis
• Use M(Kp) and M PDF shapes from mass fits
• Fit RS decay time and error distribution to determine signal lifetime and
resolution model
Signal, background D0 PDF: exponential convolved with resolution
function , which is the sum of three gaussians with widths proportional
to the event-by-event lifetime errors.
Random combinatoric PDF: sum of two gaussians, one of which has a
power-law tail.
• Fix WS resolution and DCS lifetime from RS fit
Signal PDF: theoretical mixed lifetime distribution, which is
proportional to: (RD + RD½ y’ (t) + (x’ 2+y’ 2)(t)2/4) et ,
convolved with the resolution model from RS fit. RD is the ratio of WS to
RS D0 decays. With CP violation fit separately for D and D.
• Search for and quantify systematic errors by looking at results after:
Variations in functional form of signal and background PDFs.
Variations in the fit parameters.
Variations in the event selection.
Adding a small non-zero mean in the proper-time signal resolution PDF.
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RS Decay Time Fit
BaBar Data
The D0 lifetime is consistent
with the Particle Data Group
value, within the statistical and
systematic errors of the
measurement.
Plot selection:
1.843<m<1.883 GeV/c2
0.1445<m< 0.1465 GeV/c2
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WS Mixing Fit: No CP Violation
• Varied fit parameters
BaBar Data
– Mixing parameters
– Fit class
normalizations
– Combinatoric shape
Mixing minus No mixing PDF
Data minus No mixing PDF
BaBar Data
Plot selection:
1.843<m<1.883 GeV/c2
0.1445<m< 0.1465
GeV/c2
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Mixing Contours: No CP Violation
• y’, x’2 contours
computed by change
in log likelihood
BaBar Data
– Best-fit point is in
non-physical region
x’2 < 0, but one-sigma
contour is in physical
region
– correlation: -0.95
• Accounting for
systematic errors, the
no-mixing point is at the
3.9-sigma contour
RD: (3.030.160.06) x 10-3
x’2: (-0.220.300.21) x 10-3
y’: (9.74.43.1) x 10-3
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M(Kp), M Fits in Decay Time Bins
• Kinematic fit done independently in five decay time bins
• RWS independent of any assumptions on resolution model
BaBar Data
c2 for mixing fit is 1.5; for the no mixing fit (RWS = .353%) c2 is 24.0
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Time Dependence of Mixed Final States: CP Violation
• If CP is not conserved, the time distribution for D0 and D0 differ

WS
 t
 (t )
p
 RD   y cos   x sin  
e
q
1
RD (t ) 
p
q
2
AD , M 
• Direct CP violation in DCS Decay
RD  RD
• CP violation in interference
between decay and mixing:
q
p
2
2
RD , M  RD , M
• Define CP violating observables
• CP violation in mixing
x   y  
( t ) 2
4
RD , M  RD , M
1
 1  AM 
cos  1
• Rewrite time dependence to explictly include asymmetries

WS (t ) 1  AD
1  AD 1  AM 
1  AM x2  y2
2


4






R

R
y
cos


x
sin


t


t
D
D
1  AD 1  AM 
e t
1  AD
1  AM
4
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Final Results for Kp Analysis
Fit type
Parameter
No CP viol. or mixing
RD
Fit results (/103 )
3.53 ± 0.08 ± 0.04
No CP violation
RD
3.03 ± 0.16 ± 0.10
CP violation allowed
x2
y
RD
-0.22 ± 0.30 ± 0.21
9.7 ± 4.4 ± 3.1
3.03 ± 0.16 ± 0.10
AD
-21± 52 ± 15
x 2 
y 
x 2 
y 
-0.24 ± 0.43 ± 0.30
9.8 ± 6.4 ± 4.5
-0.20 ± 0.41 ± 0.29
9.6 ± 6.1 ± 4.3
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Conclusions
Assuming CP conservation and including systematic
effects, BaBar finds a mixing signal at the 3.9 sigma
confidence level in the Kp final state. The parameters
describing the WS/RS branching ratio and mixing are:
RD: (3.030.160.06) x 10-3
x’2: (-0.220.300.21) x 10-3
y’: (9.74.43.1) x 10-3
No evidence is seen for CP violation.
Analyses in progress, along with the results of other
experiments, should allow significant progress in
reducing the errors on the parameters describing mixing.
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