D0-D0 Mixing at BaBar

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

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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
Propagation parameters for the two states are
given by
With the observable oscillations determined by
the scaled parameters
.
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.
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• Assuming CP conservation, small mixing
  parameters, and an initial state tagged as a D0,
  we can write the time dependence to first order
• in x and y Projecting this onto a
  final state f gives to first order the amplitude
  for finding f
• 
  
• This leads to a number of ways to measure
  the effect of mixing, for example
• 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 KK- or pp-). In
this case tagging the initial state isnt
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
Kp-). 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 Here y
y cosd x sind, where d is a strong phase
difference between the Cabibbo favored and Doubly
suppressed amplitudes. For the Kp- 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 Kp-p0, with a mass cut that
selects mostly Kr- decays, the largest channel
for the Cabibbo allowed amplitude arising from
mixing. Based on 230 fb-1, BaBar measures
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 KSpp- 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 gt 0.001
• D0 selection
• CMS p gt 2.5 GeV/c
• K, p particle identification
• DCH hits gt 11
• 1.81 lt M(Kp) lt 1.92 GeV/c2
• decay time error lt 0.5 ps
• -2 lt decay time lt 4 ps
• ptag
• CMS p lt 0.45 GeV/c
• lab p gt 0.1 GeV/c
• SVT hits gt 5

y
beam spot
interaction point
x

• 0.14 lt DM lt 0.16 GeV/c2,
• where DM 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
BaBar Data
1,229,000 RS candidates
events/0.1 MeV/c2
events/1 MeV/c2
BaBar Data
BaBar Data
64,000 WS candidates
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Analysis Strategy

• Blind analysis of D ? D0(?Kp) ptag
• 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), DM
  M(Kpptag) M(Kp) distributions (two of the
  variables) to establish shapes for different
  components (signal and backgrounds) of the two
  dimensional distribution. High-statistics 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.

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RS/WS M(Kp), DM Distributions
BaBar Data

• Fit RS/WS M(Kp), DM 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), DM
• True D0 combined with random ptag peaks in M(Kp)
  only
• Misreconstructed D0 peaks in DM only
• Purely combinatoric non-peaking in either
  variable

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Simultaneous Fit to RS/WS Data
BaBar Data
RS signal 1,141,5001200 Events.
BaBar Data
BaBar Data
WS signal 403090 Events.
BaBar Data
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Proper Time Analysis

• Use M(Kp) and DM 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 (Gt) (x 2y
  2)(Gt)2/4) e-Gt ,
• 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 1.843ltmlt1.883 GeV/c2 0.1445lt?mlt
0.1465 GeV/c2
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WS Mixing Fit No CP Violation

• Varied fit parameters
• Mixing parameters
• Fit class normalizations
• Combinatoric shape

BaBar Data
Mixing minus No mixing PDF
Data minus No mixing PDF
BaBar Data
Plot selection 1.843ltmlt1.883 GeV/c2 0.1445lt?mlt
0.1465 GeV/c2
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Mixing Contours No CP Violation

• y, x2 contours computed by change in log
  likelihood
• Best-fit point is in non-physical region x2 lt
  0, but one-sigma contour is in physical region
• correlation -0.95

BaBar Data

• 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 x2
(-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), DM 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

• Define CP violating observables

• Direct CP violation in DCS Decay

• CP violation in mixing

• CP violation in interference between decay and
  mixing

• Rewrite time dependence to explictly include
  asymmetries

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Final Results for Kp Analysis
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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
• x2 (-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.