Selected Topics on Open Charm Physics at CLEOc

1
Selected Topics on Open Charm Physics at CLEO-c

• Main topics
• Overview the CLEO-c experiment and its physics
  program
• Absolute Hadronic D0 and D Branching Fractions
• Preliminary Results for Absolute Branching
  Fractions and Form Factor Measurements in
  and

Batbold Sanghi Purdue University (CLEO
Collaboration)
2
CLEO-c and the CKM Matrix

• The CKM matrix provides the only mechanism for CP
  violation in the SM
• An important goal of flavor physics is to measure
  and (over)constrain the parameters in the CKM
  matrix (4 parameters) to test the SM
• Non-perturbative hadronic effects limit our
  ability to extract fundamental parameters from
  experimental measurements
• CLEO-c provides unique measurements in the charm
  sector that test theory and help reduce hadronic
  uncertainties
• CLEO-c tested theory can then be applied to B
  decay processes to extract
• CKM matrix elements (especially Vub and Vtd)

Recent status
Status with theory errors reduced)
3
An example of a test of Lattice QCD
Theories of Strong Interactions (LQCD)

• validate LQCD calculations for form factors

• use LQCD to extract ?Vub? from B??l?

• Measure form factors in D ?? l? at CLEO-c

4
An example of a test of Lattice QCD

• ?m is well measured

• But Vtd from ?m has a large uncertainties from
  fB

Theories of Strong Interactions (LQCD)

• validate theoretical calculations
• fB fB (LQCD)/ fD (LQCD) fD

• Use fB to extract Vtd

• measure fD in D ? l?

5
CLEO-c impact

• I will focus on two CLEO-c analyses that have
  impact on Vcd, Vcs, Vub and Vcd

D hadronic branching fractions (Analysis by
Cornell, Purdue and CMU) Including
and
D semileptonic Bs and form factors in (Analysis
by Purdue and SMU, my main thesis topic)
D and Ds leptonic branching fraction
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The CLEO-c detector
?P/P 0.6 at 1GeV ?E/E 2 at 1GeV
5 at 100MeV Excelent electron and hadron ID

• The main components of the CLEO-c detector were
  developed for B physics at the Y(4S).

• Minor modifications
• Replaced silicon with 6 layer inner drift chamber
• B field 1.5 T ?1.0 T

• Advantages at ?(3770)
• Pure DD, no additional particle
• Low multiplicity
• High tagging efficiency

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CLEO-c data samples

• Three generations of CLEO-c analyses at the
  ?(3770)
• Oct-03 through Jan-04 Luminosity 56 pb ?1
• all results are published(D hadronic
  branching fraction)
• Sep-04 through Apr-05 Luminosity 225 pb?1
• most analyses are on-going(D semileptonic
  Bs and form factors)
• Future running projected total Luminosity
  750 pb?1
• CLEO-c is also collecting data above the DsDsbar
  production
• threshold (goal 750 pb?1) and lower energies at
  the ?(2S).

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Absolute Hadronic D0 and D Branching Fractions

• Introduction and Overview of the Analysis
• Measurements of Absolute Hadronic Branching
  Fractions
• Summary

9
Overview of Technique
Double tagged D
Single tagged D

• Use 3 D0 modes and 6 D modes
• K-?, K-?,?0, K-? ,? ?-
• K-? ?, K-? ??0, Ks? , Ks? ?0, Ks? ?0,
  Ks?? ? , K-K ?
• Reference modes D " K-p and K-pp normalize
  many B measurements from other experiments.

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Overview of Technique

• Determine separately the and yields
• 182?(36) single tags(ST) and 45(32 62)
  double tag yields(DT)
• In a combined ?2 fitter (physics/0503050), we
  extract 9 branching ratios and and
  yields
• Include both statistical and systematic errors
  (with correlations)
• All experimental inputs treated consistently.
• Efficiency, cross-feed, background corrections
  performed directly in fit.
• Some systematic errors for and
  completely cancelled
• Branching fractions are independent of L and
  cross-sections.
• The main variables used in the reconstruction are

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Yield Fits

• Unbinned ML fits to MBC (1D for ST, 2D for DT)
• Signal function includes ISR, y(3770) line shape,
  beam energy smearing, and detector resolution.
• Signal parameters from DT fits, then apply to ST.
• Background phase space (ARGUS function).
• D and D yields and efficiencies separated.c

• Two dimensional fit allows to separate
• ISR and beam energy spread (causes correlated
  shifts in the mass of the two Ds)
• Detector resolution (uncorrelated among these Ds
  )

MBC (log scale) for ST modes
All D0 DT 248451
All D DT 165042
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Systematic uncertainties

• Dominant error MC simulation of tracking, K0S,
  and p0 finding efficiencies
• Correlated errors among all particles of a given
  type add up quickly.
• Missing mass technique measure syst errors by
  comparing data and MC
• Fully reconstruct entire event, but deliberately
  leave out one particle.
• Fraction of MM peak where the last particle is
  found efficiency.

Example K- efficiency from D0 " K-p e 91 in
fiducial volume
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Fit Results (PRL 95,121801)

• Precision comparable to PDG-04.
• Statistical errors 2.0 neutral, 2.5 charged
  from total DT yields.
• s(systematic) s(statistical).
• Many systematic errors are measured in data and
  will be improved with time.
• Our MC simulation includes FSR
• Using efficiencies without FSR would lead to
  lower B.
• NDD includes continuum and resonant production.

The CLEO-c measurement is the single most precise
measurement for every mode
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Comparisons with other measurements

• Reasonable agreement with PDG for all modes
• Measurements and errors normalized to PDG.
• PDG numbers are correlated among modes
• PDG global fit includes ratios to K-p or K-pp.
• No FSR corrections in PDG measurements
• Our measurements are also correlated (through
  statistics and efficiency systematics).

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Results for D cross sections

• Using a measurement of the luminosity of the data
  sample (55.8/pb), we obtain

• Our cross sections are in good agreement with BES
  Phys.Lett. B 241, 278(1990) and higher than
  those of MARKIII Phys.Rev.Lett. 60, 89 (1988)

• CLEO-c inclusive

PRL 96, 092002
16
Absolute Branching Fractions and Form Factor
Measurements in and

• Introduction and Overview of the Analysis
• Measurements of Absolute Branching Fractions
• Measurements of Form Factors
• Summary

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Introduction

• Semileptonic decays are an excellent laboratory
  to study
• Weak physics
• QCD physics
• Gold-plated modes are P ? P semileptonic
  transitions as they are the simplest modes for
  both theory and experiment
• Cabibbo favored
• Cabibbo suppressed
• Main goals of the analysis
• Measure efficiency-corrected absolutely-normalized
  decay rate distributions and form factors
• Measure form factor parameters to test LQCD and
  model predictions
• We analyze both D0 and D decays. By isospin
  invariance
• 
  
  .
• 
  
  .
• This is a nice cross check and adds statistics
  to improve statistical precision.

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Overview of the analysis
?(3770)?D0 D0 D0?K?-, D0?K-e?

• Reconstruct one of the two Ds in a hadronic
  decay channel. It is called a tagging D or a tag.
  Two key variables in the tagging D reconstruction
  are
• Reconstruct from the remaining tracks and showers
  the observable particles in the final state of a
  semileptonic decay.
• Define an observable that can be used to separate
  signal and background as
• where Emiss and Pmiss are the missing energy
  and momentum in the event, approximating the
  neutrino E and P. The signal peaks at zero in U.
• Branching fractions are obtained as

Obtained from Fits to U
Obtained from Fits to Mbc
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D0 and D tag yields in 281/pb of DATA
Examples of Mbc for tag modes in the data
30 event tagging efficiency
20 event tagging efficiency
Tagging provides a beam of D mesons allowing
semileptonic decays to be reconstructed with no
kinematic ambiguity
20

• Measurements of
• Absolute Semileptonic Branching Fractions

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Fits to U in 281 pb-1 of Data for
N7000

• Main backgrounds for
• Main backgrounds for
• Electron fakes from kaons

N700
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Fits to U in 281 pb-1 of Data for

• Main backgrounds for
• Main Backgrounds for

N2900
N290
23
Preliminary Results for BFs
24
Comparisons with other experiments and
projections for 750 pb-1
Systematically limited
Statistically limited
Reasonable agreement
25

• Measurements of
• Semileptonic Form Factors

26
Two Fitting Methods Fit A and Fit B

• The observed decay rate is related to the true
  decay rate in the following way
• in terms of Acceptance and Smearing
  functions. The fit has to take into account both
  effects. We have developed and tested two types
  of fits.

• Fit A is a fit to efficiency-corrected and
  absolutely-normalized d?/dq2 distributions. This
  fit is a good match for CLEO-c data as the q2
  resolution is excellent. Fit A is our primary fit
  as the main goal of our analysis is to obtain
  d?/dq2 and f(q2).
• Fit B is a fit to the observed decay rate
  according to a procedure described in
  D.M.Schmidt, R.J.Morrison and M.S.Witherell in
  Nucl. Instr. and Meth. A328 547(1993). The
  technique makes possible a (multidimensional) fit
  to variables modified by experimental acceptance
  and resolution. This method has been used by CLEO
  several times before, for example, to measure
  form factor ratios in ??c??e? and B?Dl?.
• Both fitting methods were tested using large
  Monte Carlo samples. Two fits provide
  cross-checks.

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q2 resolutions and Raw q2 distributions
Raw q2 distribution
q2 resolution
?q2 0.012GeV2
D0?K-e?
D0?K-e?
7000 events S/B gt 300/1
CLEOIII(Y(4S) ?q2 0.4 GeV2 CLEO-c(?(3770))
?q2 0.012GeV2
Note the background in blue
?q2 0.011GeV2
D0?p-e?
D0?p-e?
700 events S/B 40/1
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Efficiency corrected and absolutely normalized
decay rates (DATA)
Subtracting background and applying efficiency
corrections (matrices) we find absolute decay
rates in bins of q2 (The bin width is equal
q2max/10, the last bins for D0???e? and D??0
e? are 2 and 3 times wider)
D0?K-e?
D?Kse?
D0?p-e?
D?p0e?
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Efficiency corrected and absolutely normalized
decay rates (DATA)
The spectra on the last slide are tabulated here
These rates can be fit to any form factor model
w/o knowing CLEO acceptance and resolution
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Form Factor Models

• Simple pole model
• Modified pole model (BK) Phys.Lett.B 52,
  478,417(2000)
• Series parameterization .Becher and R.Hill,
  hep-ph/0509090
• ISGW2 Phys.Rev.D 52,2783,(1985)

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Tests of Fit A and B

• The fitting techniques were tested by making
  ensembles of fits to mock data samples with the
  number of signal events equal to the expected
  number of events in the data. We have tested
• Fits for all 4 form factor models
• simultaneous fits to isospin conjugate modes
• fit with two free parameters f(0)Vcs and
• a form factor shape parameter

Example
The fitter is consistent with being unbiased.

• The efficiency of fits is tested using the
  Cramer-Rao inequality

The fitter is consistent with being fully
efficient.
Mpole (GeV)
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Example of a fit (DATA)
Modified Pole (BK) Model
D0?K-e?
D?Kse?
D0?p-e?
D?p0e?
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DATA Cross Check 1
By isospin invariance





The plots show
The q2 spectra for isospin conjugate modes are
consistent.
34

Cross check 2 Hadron Electron Spectra W
Helicity

• Quantities that are not constrained in the fit
  are well described

D?Kse?
D0?p-e?
D?p0e?
D0?K-e?
Hadron Momentum
Electron Momentum
35
Systematic Uncertainties for Form Factor Shape
Parameters

• Systematic uncertainties that are independent of
  q2 (ex tag Mbc fit function) do not change the
  decay rate shape and hence have a negligible
  contribution to the shape parameter uncertainty

• Systematic effects correlated with the hadron
  (K/KS/?/?0) momentum, change the decay rate
  distribution and lead to modest systematic
  uncertainties

Kaon momentum vs q2
PK(GeV)
eff
Kaon ID efficiency
q2 (GeV)
PK 100MeV Few events
Lepton momentum vs q2
Our studies indicate that the total systematic
uncertainty is much smaller than the statistical
uncertainty for each semileptonic mode
Pe(GeV)
This correlation is not as strong as the hadron
momentum correlation
q2 (GeV)
36
Fit results with two parameters

• The shape parameters for modified pole, simple
  pole model and series parameterization with two
  parameters

• The normalization parameter for modified pole
  model and series parameterization with two
  parameters

37
Comparison with Other Measurements

• First measurements of form factors for the D
  modes
• CLEO-c is the most precise for D?pe?

38
Comparison with Other Measurements

• First measurements of form factors for the D
  modes
• CLEO-c is the most precise for D?pe?

39
Confidence levels for fits results with 2
parameters

• The confidence levels for fits with 2 parameters

• Which parameterization does the data prefer? The
  confidence levels for all parameterizations are
  comparable, as the functional forms for the
  parameterization are similar and the shape
  parameters are not fixed. However, the CLEO-c
  data exclude the ISGW2 (K/?) , pole (K) and
  modified pole (K) parameterizations when the
  shape parameters are fixed to the physical
  values.

40
Data vs. physical basis for shape parameters

• 1 ISGW2

Form factor shape parameters in the data for
ISGW2 are inconsistent with the model predictions

• 2 Pole

• 3 Modified Pole

Because the data do not support the physical
interpretation of these three parameterizations
we use the series parameterization
41
Fit results with 3 parameters

• Our main form factor shape and intercept results
  are for the series parameterization

• The series is expected to converge rapidly, so
  only the 1st few terms are expected to be
  measurable we test for three

42
Interpretation

• The fit results for 2 and 3 parameters are
  consistent with each other
• Noticeable improvement for ?2 for D?Ke? with 3
  parameters
• The ? modes do not show this trend as they lack
  the statistics to probe the third term in the
  expansion
• For D ? Ke? the 3rd term b2 is a order of
  magnitude larger than b1. This cannot be
  interpreted as a lack of convergence if the
  series because both are consistent with zero
  indicating that the data does not yet have the
  sensitivity to determine three parameters
  simultaneously.

43
Comparison Between Parameterizations
--- Simple pole
--- Modified Pole
--- Series with 2 par
? Data
? Series with 3 par
D?Kse?
D0?K-e?
D0?p-e?
D?p0e?

• Data and Fit results are normalized to the fit
  results for the series parameterization with 3
  parameters.

44
Form Factors as a Stringent Test of LQCD

• Plotted LQCD results (blue) are recent results of
  FNALMILC unquenched three flavor LQCD C. Aubin
  et al., PRL 94 011601 (2005)
• Lattice systematic uncertainties dominate
• The green lines are our fits to CLEO-c data
• The dashed lines show 1? (statsyst) regions

Vcd 0.2238?0.0029(CKM unitarity, i.e Vcd Vus)
LQCD
DATA FIT
Vcs 0.9745?0.0008(CKM unitarity)
LQCD
DATA FIT
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Projections for ? and f(0)
The anticipated precision for a larger 750 pb?1
data sample to be collected in the future

• In these plots, the central values for our
  projections are equal to the central values from
  the LQCD results

46
Vcs(d) and f(0) determination

• Using

• Vcd 0.2238?0.0029 (CKM unitarity, i.e Vcd Vus)

Vcs 0.9745?0.0008 (CKM unitarity)

• Using LQCD results C. Aubin et al., PRL 94
  011601 (2005)

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Summary for D semileptonic studies

• I have shown preliminary results for D?K/? e?
  branching fractions and form factor measurements
  from the 280/pb data sample collected at ?(3770).
  Results of this analysis include
• the most precise branching fraction measurements
  for these decays
• the most precise or first measurements of form
  factors for these modes
• the most precise or first measurements of the
  efficiency corrected and absolutely normalized
  decay rates
• a stringent test of LQCD calculations of
  semileptonic form factors

48

In summary, CLEO-c provides

• unique input to test LQCD, the theory capable of
  solving strongly couple field theory
  equations, and
• input to other experiments that help improve
  their measurements

• Thank you

49
Fit A a ?2 fit to efficiency corrected d?/dq2

• A brief description of the procedure for making
  Fit A
• Create an N x N efficiency matrix, where N is the
  number of q2 bins
• Invert the efficiency matrix
• Measure raw background subtracted q2
  distributions
• Use the inverted efficiency matrix to obtain
  efficiency-corrected and absolutely-normalized
  d?/dq2 (or the form factor)
• We make fits for form factor parameters to
  efficiency-corrected and absolutely-normalized
  d?/dq2 (or the form factor), using the ?2 fitter
  which includes both statistical and systematic
  errors (with correlations)
• bin migrations, background uncertainty, and
  efficiency corrections.

- the decay rate estimated from a form factor
- the correlation matrix
- the decay rate

• The low number of events in the high q2 bins can
  lead to biases in ?2 fits, we find that the

Bias, if any, is SMALL 0.10?(stat. data)
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Efficiency Matrices

• We use 10 q2 bins for
  and . For
  and we use
  9 and 8 bins, respectively. The last bin for
  these two modes are two or three times wider than
  other bins.

10 bins
Full efficiency matrix for
Do not need to read these tables
Efficiency matrices in a truncated form for
10 bins
9 bins
8 bins