Selected Topics
on Open Charm Physics at CLEO-c
Main topics:
 Overview the CLEO-c experiment and its
physics program
(3770)D0 D0
D0K+-, D0K-e+
 Absolute Hadronic D0 and D+ Branching
Fractions
 Preliminary Results for Absolute Branching
Fractions and Form Factor Measurements
0

0

0

 
in D  K /  e  and D  K /  e 
Batbold Sanghi

K-
K+
-
Purdue University
e+
(CLEO Collaboration)
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
1
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)
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
Recent
status
Status
with
theory
errors
reduced)
2
An example of a test of Lattice QCD
d( D  l )
~ Vcd
2
dq
2
2
f  (q )
2
d( B  l )
2
2 2
~ Vub f  (q )
2
dq
Theories of Strong
Interactions (LQCD)

Measure form
factors in D  l
at CLEO-c
July, 2006

validate LQCD
calculations for form
factors

use LQCD to
extract Vub from
Bl
Selected Topics on Open Charm Physics from CLEO-c
3
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)

measure fD in D  l

validate theoretical
calculations

Use fB to extract |Vtd|
fB ~fB (LQCD)/ fD (LQCD) fD
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
4
CLEO-c impact

I will focus on two CLEO-c analyses that have impact on Vcd, Vcs, Vub and Vcd:
D semileptonic B’s and form factors in
D hadronic branching fractions
D  K /  e 
(Analysis by Cornell, Purdue and CMU)

 
Including: D 0  K   and D  K  
(Analysis by Purdue and SMU, my main thesis topic)
Vud/Vud 0.1%
e
n

p
Vcd/Vcd 7%
D
CLEO-c
l

K
l



l
D

K
Vts/Vts 39%
Bd Bs
Bs
CLEO-c + Lattice
QCD +B factories
Vub/Vub 15%
l
B
Vcs/Vcs =16%
Vtd/Vtd =36%
Bd
Vus/Vus =1%



Vcb/Vcb 5%
l
B

D
Vtb/Vtb 29%
t
W
b
CLEO-c + Lattice QCD
+B factories + ppbar
D and Ds leptonic branching fraction
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
5
The CLEO-c detector

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
Over 20 years of
data taking at Y(4S)
An event taken
at (4S)
Note: Log Scale


P/P = 0.6% at 1GeV
E/E = 2% at 1GeV
= 5% at 100MeV
Excelent electron and hadron ID
Started data taking
in the fall of 2003
 (3770)
e  e    (3770)  D  D  ,
D   K    , D   K   

Advantages at (3770)



July, 2006
Pure DD, no additional particle
Low multiplicity
High tagging efficiency
Selected Topics on Open Charm Physics from CLEO-c
6
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 B’s 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).
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
7
Absolute Hadronic D0 and D+
Branching Fractions
 Introduction and Overview of the Analysis
 Measurements of Absolute Hadronic Branching Fractions
 Summary
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
8
Overview of Technique
Single
tagged D
Double
tagged D
X
D0
e+
e
D0
K+
e+
D
K+
K+
N DD 
Si S j  ij
e
0


Si  2 N DD Bi i
D0
Dij  N DD Bi B j  ij
S  ii
 i
4 Dii  i 2
2
or N DD
2 Dij  i j
Dij  j
D 
Bi 
or Bi  2 ii i
S j  ij
S i  ii
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+ and K++ normalize many B measurements from other
experiments.
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
9
Overview of Technique

Determine separately the


D and D yields
18=2(3+6) single tags(ST) and 45(=32 + 62) double tag yields(DT)
In a combined 2 fitter (physics/0503050), we extract 9 branching ratios and N D 0 D 0
and N D  D  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 N D 0 D 0 and N D  D  completely cancelled
 ij /  i j  1
N DD ~ S i S j / Dij

Branching fractions are independent of L and cross-sections.

The main variables used in the reconstruction are:
 E  Ebeam  Ecandidate
July, 2006
2
2
M bc  Ebeam
 Pcandidate
Selected Topics on Open Charm Physics from CLEO-c
10
Yield Fits

Unbinned ML fits to MBC (1D for ST, 2D for DT) 
Two dimensional fit allows to separate





Signal function includes ISR, (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
MBC (log scale) for ST modes:

ISR and beam energy spread (causes
correlated shifts in the mass of the two
D’s)
Detector resolution (uncorrelated among
these D’s )
DT signal shape
Detector
resolution
All D0 DT
2484±51
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
All D+ DT
1650±42
11
Systematic uncertainties

Dominant error: MC simulation of tracking,
K0S, and 0 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+
 ≈ 91% in fiducial volume
K found
(MC)
K not found
(MC)

July, 2006
Source
Uncertainty (%)
Tracking/K0s/0
0.7/3.0/2.0
Particle ID
0.3 /1.3 K
Trigger 
< 0.2
E cut
1.0—2.5 per D
FSR
0.5 ST / 1.0 DT
(3770) width
0.6
Resonant
substructure
0.4—1.5
Event environment
0.0—1.3
Yield fit functions
0.5
Data processing
0.3
Double DCSD
0.8
K-+0,
etc.
Selected Topics on Open Charm Physics from CLEO-c
12
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


The CLEO-c measurement is the single most
precise measurement for every mode
Using efficiencies without FSR
would lead to lower B.
NDD includes continuum and
resonant production.
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
13
Comparisons with other measurements

Reasonable agreement with PDG for all modes

PDG numbers are correlated among modes



Other direct meas.
PDG global fit includes ratios to K-+ or K-++.
No FSR corrections in PDG measurements
Our measurements are also correlated (through
statistics and efficiency systematics).
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
B(D+ " K- ++)
Overall
C.L
25.9%
B(D0 " K-+)

Measurements and errors normalized to PDG.
14
Results for D cross sections

Using a measurement of the luminosity of the data sample (55.8/pb), we obtain


s e e  D D  (3.60  0.07  0.07)nb s e e  D  D    (2.79  0.07  0.10)nb
 
0
0


s e e  D D  (6.39  0.1000..17
08 )nb

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: s e  e    (3770)  hadron  (6.38  0.0800..41
30 )nb


s e  e   D  D  

s ee  D0 D
July, 2006
0

PRL 96, 092002
014
 (0.776  0.02400..006
)
Selected Topics on Open Charm Physics from CLEO-c
15
Absolute Branching Fractions and Form Factor
Measurements in
0
0

 

0 
and
D  K / e 
D  K / e 




July, 2006
Introduction and Overview of the Analysis
Measurements of Absolute Branching Fractions
Measurements of Form Factors
Summary
Selected Topics on Open Charm Physics from CLEO-c
16
Introduction
 Semileptonic decays are an excellent laboratory to study2
GF2 Vcs ( cd ) PK3( )
d( D  K ( )e
2 2

f  (q ) ,
2
2
 Weak physics
dq
24
 QCD physics
where
q 2  M 2 (e )
 Gold-plated modes are P  P semileptonic transitions as they are the
simplest modes for both theory and experiment:
D0  K e ,
D   K 0e
 Cabibbo favored :
0
 
 Cabibbo suppressed : D   e  ,
D    0e
 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


D0  K e   D   K 0e 
D0   e   2  D    0e 
.
.
This is a nice cross check and adds statistics to improve statistical precision.
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
17
Overview of the analysis

(3770)D0 D0
K+-, D0K-e+
Reconstruct one of the two D’s in a hadronic
decay channel. It is called a tagging D or a tag.
Two key variables in the tagging D reconstruction D0
are:
2
2
M bc  Ebeam
 Pcandidate

 E  Ebeam  Ecandidate




Define an observable that can be used to
separate signal and background
 as
U  Emiss  Pmiss
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
B
semilep
July, 2006

NUsemilep /  signal
N Mtagb c /  tag
NUsemilep

  semilep  N Mtagb c

K-
Reconstruct from the remaining tracks and
showers the observable particles in the final state
of a semileptonic decay.
K+
e+
Obtained from Fits to U
Obtained from Fits to Mbc
Selected Topics on Open Charm Physics from CLEO-c
18
D0 and D+ tag yields in 281/pb of DATA
Examples of Mbc for tag
modes in the data
D 0  K  
D 0  K   0
~ 51K events
All D 0 tags :
All D  tags :
~ 308K / (281 pb 1 )
~ 163K / (281 pb 1 )
~30% event
tagging efficiency
~20% event
tagging efficiency
~ 98 K events
D   K   
~ 80 K events
D 0  K   0 0
~ 23K events
D   K    0
~ 24K events
D   K    
0
~ 16 K events
Tagging provides a beam of D mesons
allowing semileptonic decays to be
reconstructed with no kinematic ambiguity
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
19
Measurements of
Absolute Semileptonic Branching Fractions
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
20
Fits to U in 281 pb-1 of Data for D 0  K  /   e
D 0  K  e
N~7000

U  Emiss
Main backgrounds for D0  K e


D 0    e

N~700
D0  K * ( K  0 )e
D0   e
Main backgrounds for D   e 
0



July, 2006

 Pmiss
 
D0  K e
D0    (  0 )e
Electron fakes from kaons
Selected Topics on Open Charm Physics from CLEO-c
21
Fits to U in 281
pb-1 of
Data for D  K /  e 

D  K 0 e

N~2900
D   0 e
N~290

0 
Main backgrounds for D   K 0e 


D  K *0 ( K 0 0 )e
D  K *0 ( K   )e
Main Backgrounds for D    0e 


July, 2006
0
D   K 0e 
D  K *0 ( K 0 0 )e
Selected Topics on Open Charm Physics from CLEO-c
22
Preliminary Results for BFs
D 0  K  e
D  K 0 e
D 0    e
D   0 e
( D 0  K e  )
( D 0    e  )
 1.024  0.024(stat )
 0.975  0.075(stat )

0 

0 
( D  K e  )
2( D   e  )
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
23
Comparisons with other experiments and
projections for 750 pb-1
D 0    e
Statistically limited
D 0  K  e
Systematically limited
Reasonable agreement
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
24
Measurements of
Semileptonic Form Factors
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
25
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D*l.
 Both fitting methods were tested using large Monte Carlo samples. Two fits provide
cross-checks.
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
26
q2 resolutions and Raw q2 distributions
q2 resolution
D0→K-e+ν
Raw q2 distribution
D0→K-e+ν
sq2 ~
0.012GeV2
d
dq 2
7000 events
S/B > 300/1
CLEOIII(Y(4S): q2 ~ 0.4 GeV2
CLEO-c((3770)): q2 ~ 0.012GeV2
Note the background in blue
D0→π-e+ν
sq2 ~
0.011GeV2
July, 2006
D0→π-e+ν
d
dq 2
700 events
S/B ~40/1
Selected Topics on Open Charm Physics from CLEO-c
27
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):
July, 2006
D0→K-e+ν
D+→Kse+ν
D0→π-e+ν
D+→π0e+ν
Selected Topics on Open Charm Physics from CLEO-c
28
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
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
29
Form Factor Models
  1  q f /0M

Simple pole model :

Modified pole model (BK) [Phys.Lett.B 52, 478,417(2000) ] :
f 0
f q 2  
f q2 
1  q

2
/M
2
D*( s )
2
pole

;
1
;
1  q / M D2 *(s )
 
2

Series parameterization [.Becher and R.Hill, hep-ph/0509090]
f  q 2  


ak z k ( q 2 ,0) 


P q  q ,0   k

1
2
2
11/    

2
mD2  mK2 ( ) df  (q 2 )
f  (0)
dq 2
 F ( ak )
q 0
2
ISGW2 [Phys.Rev.D 52,2783,(1985) ] :
 
f q
July, 2006
2

r2 2
  1 
qmax  q 2
12






2
Selected Topics on Open Charm Physics from CLEO-c
30
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:
Example:



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]
data
1.0  s stat
The fitter is consistent with being unbiased.

The efficiency of fits is tested using the
Cramer-Rao inequality:
1
s M pole  
, where
I N
2
 F q 2 , M pole  
 F q 2 , M pole 1 dq 2 and
I  
 M

pole


The fitter is consistent with being fully efficient.
July, 2006
D0  - e+ 
700 events
C-R Prediction
Our Fits
D0  K- e+ 
7000 events
Mpole (GeV)
Selected Topics on Open Charm Physics from CLEO-c
31
Example of a fit (DATA)
Modified Pole (BK) Model:
July, 2006
D0→K-e+ν
D+→Kse+ν
D0→π-e+ν
D+→π0e+ν
Selected Topics on Open Charm Physics from CLEO-c
32
DATA Cross Check 1
By isospin invariance:
D  K e   D  K e 
D0   e   2  D    0e 
0

f D 

f D  K
0

e
(q 2 )  f D
e
(q 2 )  f D


 K 0 e
 0 e
D0→Ke+ν
0
f+(q2)Vcs

0
(q 2 )
(q 2 )
D+→KSe+ν
q2 (GeV2)
The plots show:
  ( D  K ( )e ) 3 
Vcs ( cd ) f  (q 2 ) ~  i
/ PK ( )i 
2

q
i


f+(q2)Vcd
1/ 2
D0→πe+ν
D+→π0e+ν
The q2 spectra for isospin
conjugate modes are consistent.
July, 2006
q2 (GeV2)
Selected Topics on Open Charm Physics from CLEO-c
33
Cross check 2: Hadron & Electron Spectra & W Helicity

Quantities that are not constrained in the fit are well described
D0→K-e+ν
D+→Kse+ν
D0→π-e+ν
D+→π0e+ν
Hadron
Momentum
Electron
Momentum
cosW
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
34
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
eff
PK(GeV)
Kaon momentum vs q2
Kaon ID efficiency
Pe(GeV)
q2 (GeV)
Lepton momentum vs q2
PK ~ 100MeV
Few events
This correlation is not
as strong as the hadron
momentum correlation
Our studies indicate that the total
systematic uncertainty is much smaller
than the statistical uncertainty for each
semileptonic mode
q2 (GeV)
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
35
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 :
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
36
Comparison with Other Measurements
M D*  2.010GeV
M D*  2.112GeV
s
D→K


e+
ν
D → π e+ ν
First measurements of form factors for the
D+ modes;
CLEO-c is the most precise for D→πe+
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
37
Comparison with Other Measurements
D → π e+ ν
D → K e+
ν


First measurements of form factors for the
D+ modes;
CLEO-c is the most precise for D→πe+
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
38
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.
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
39
Data vs. physical basis for shape parameters

#1: ISGW2
Form factor shape
parameters in the data for
ISGW2 are inconsistent
with the model predictions

Output
Physical value for
ISGW2
D0  K- e+ 
1.567 ± 0.045
1.131
D0  - e+ 
1.997 ± 0.114
1.410
D+  K0 e+ 
1.476 ± 0.070
1.131
D+  -0e+ 
1.806 ± 0.209
1.410
#2: Pole
D0  K- e+ 

#3: Modified Pole
D0  K- e+ 
Output
Physical value for pole
1.94 ± 0.04
2.112
Output
Physical Value for
effective pole
0.26 ± 0.06
~1.75
Because the data do not support the physical interpretation of these three parameterizations we use the
series parameterization
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
40
Fit results with 3 parameters

Our main form factor shape and intercept results are for the series
parameterization :
 
f q2 

1  b z (q
Pq  q ,0
b0
2
2
1
2
,0)  b2 z 2 (q 2 ,0)

The series is expected to converge rapidly, so only the 1st few terms are
expected to be measurable: we test for three
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
41
Interpretation

The fit results for 2 and 3 parameters are consistent with each other;

Noticeable improvement for 2 for D→Ke+ν 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+ν 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.
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
42
Comparison Between Parameterizations
 Data
--- Simple pole
D0→K-e+ν
D0→π-e+ν

--- Modified Pole --- Series with 2 par
 Series with 3 par
D+→Kse+ν
D+→π0e+ν
Data and Fit results are normalized to the fit results for the series parameterization
with 3 parameters.
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
43
Form Factors as a Stringent Test of LQCD
 Plotted LQCD results
(blue) are recent
results of FNAL+MILC
unquenched three
flavor LQCD [C. Aubin et
al., PRL 94 011601 (2005)]
Vcd = 0.22380.0029(CKM unitarity, i.e Vcd = Vus)
LQCD
D 0   e 
 Lattice systematic
uncertainties
dominate:
 LQCD ( D  e ) :
f  (0)  0.64  0.03  0.06;
  0.44  0.04  0.07.
 LQCD ( D  Ke ) :
f  (0)  0.73  0.03  0.07;
  0.50  0.04  0.07.
 The green lines are
our fits to CLEO-c data
 The dashed lines show
1s (stat+syst) regions
July, 2006
DATA FIT
Vcs = 0.97450.0008(CKM unitarity)
D0  K e
LQCD
Selected Topics on Open Charm Physics from CLEO-c
DATA FIT
44
Projections for  and f+(0)
D0→π-e+ν
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
D0→K-e+ν
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
45
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)]:
D0  K e
D0   e
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
46
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
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
47
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
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
48
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 absolutelynormalized d/dq2 (or the form factor)
We make fits for form factor parameters to efficiency-corrected and absolutelynormalized 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.
i
i
1
j
j


 2   N eff

N

V

N

N
corr
est
ij
eff corr
est 
ij
j
N eff
corr-

the decay rate
- the decay rate estimated
from a form factor
j
N est
Vij -
the correlation
matrix
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 [~0.10s(stat. data) ]
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
49
Efficiency Matrices
0



0

 We use 10 q2 bins for D  K e  and D  K e  . For D0    e
and D    0 e  we use 9 and 8 bins, respectively. The last bin for these two
modes are two or three times wider than other bins.
D0  K  e
10 bins
Full efficiency matrix for
Efficiency matrices in
a truncated form for
10 bins
D  K 0 e
D0    e
9 bins
D    0 e 
8 bins
July, 2006
Selected Topics on Open Charm Physics from CLEO-c
50