Study of DK/ π e + and measurement of |V cs | and |V cd | at CLEO-c

Bo XinDK/π e+ and |Vcs| and |Vcd| at CLEO-c 105/02/2009

Study of Study of DK/πe+ and measurement of and measurement of |V|Vcscs| and |V| and |Vcdcd| at CLEO-c| at CLEO-c

Introduction Analysis technique Results: (CLEO-c final

tagged) branching fractions, form factors, |Vcs| and |Vcd|

Summary

Bo Xin

Purdue University

CLEO collaboration

APS April Meeting, May 2 - 5, 2009

K-

-

e+

K+


• Semileptonic decays are an excellent laboratory to study

)(,)(24

))(( 22223

3)(

2

)(2

2

eMqwhereqfPVG

dq

eKDd KcdcsF

IntroductionIntroduction

Weak PhysicsQCD Physics

* *

eDeDeKDeKD

00

00

,,

• Gold-plated modes are P P semileptonic transitions as they are the simplest modes for both theory and experiment:

– Cabibbo favored :– Cabibbo suppressed :

Assuming theoretical calculations of form factors, we can extract |Vcs| and |Vcd|

Since |Vcs| and |Vcd| are tightly constrained by unitarity, we can check theoretical calculations of the form factors

Tested theory can then be applied to B semileptonic decays to extract |Vub|.


The CLEO-c detector and data sampleThe CLEO-c detector and data sample

SVX

CLEO III

p/p = 0.6% at 800 MeV/cp/p = 0.6% at 800 MeV/c

E/E = 2% at 1 GeV, E/E = 2% at 1 GeV,

5% at 100 MeV5% at 100 MeV93% coverage (charged and neutral)93% coverage (charged and neutral)

Excellent electron and particle IDExcellent electron and particle ID

CLEO-c

• Advantages at (3770)– Pure , no additional

particles – Large branching fractions to

low multiplicity modes

→ High tagging efficiency

DD

CLEO has world’s largest data set at (3770)

Today’s results (818/pb)

86X MARK III

25X BES II


Analysis Technique (tagged)Analysis Technique (tagged) Candidate events are selected by reconstructing

a D, called a tag, in several hadronic modes

Then we reconstruct the semileptonic

decay in the system recoiling from the tag.

Two key variables in the reconstruction

of a tag:

For semileptonic D : The partial decay rates are:

Tagging creates a single D beam of known 4-momentum

0

0

0

0

(3770)

,

D

D

D

D K eK

22

42 /cp/cEM Dbeambc

beamD EEE

|| missmiss PEU

e+e- (3770)DD

1,

1j

ij tag SLjmeasured

i i DD tag

N

BN

from fits to U

from fits to Mbc

efficiency matrix inversedAn absolute measurement


Pure DD,zero additional

particles, ~5-6 charged

particles per event

~6.6x 105 D0 and~4.8 x 105 D+ tagsreconstructed from

~5.4 x 106 DD events

We tag ~20% of the events,

compared to ~0.1% of B’s at the

Y(4S)

D D tagging at CLEO-ctagging at CLEO-c2

242 /cp/cEM Dbeambc 818 pb-1 @3770World’s largest data

set at 3.770 GeV

We perform binned likelihood fits to U distributions in each q2 bin and tag mode

Signal shapes are taken from signal MC, smeared with double Gaussians

background shapes are taken from MC with all DD and non-DD decays


| |missmissU E c P 00000000000000

4 of 27 U fits

0eD K e

Yield

(all tags/q2 ):

14121±121

Fits to the U Distributions for DFits to the U Distributions for DKK--ee (818/pb) (818/pb)

Belle luminosity = 282/fb = 350xCLEO-c

S/N Signal events

CLEO-c ~300/1 ~14000

Belle ~20/1 ~2700

Phys.Rev.Lett.97:061804(2006)


0eD e

Fits to the U Distributions for DFits to the U Distributions for Dππ--//ππ0 0 /K/K0 0 ee (818/pb) (818/pb)

4 of 54 U fits

0eD e

0eD e 0

eD K e

S/N Signal events

CLEO-c ~40/1 ~1400

Belle ~4/1 ~220

4 of 42 U fits

4 of 21 U fits

Measurements for D+ modes have not been made at B factories!

Belle luminosity = 282/fb = 350xCLEO-c

Phys.Rev.Lett.97:061804(2006)


DDK/K/ππee++ : Fits to the d : Fits to the dΓΓ/dq/dq2 2 DistributionsDistributions

2 2

2 2

1( ,0)

,0k

kkf q za q

P q q

Fit to Becher-Hill Series

Experimentally measured

decay rates measuredi

2 2' 2 2 3 2

'3

Theoretically predicted decay rates

| || ( ) |

24F Qqpredicted

i P

i i

G Vd f q p dq

Other form factor parameterizations

exist,

but are only used as functional forms as

their physical pictures are not supported by

the data

2

3 par (a0 a1 a2)

2 par (a0 a1)

Simultaneous fits to isospin conjugate modes are also performed


DK/πe+ Branching fractions

Precision measurements from BABAR/Belle/CLEO-c.

CLEO-c most precise. Theoretical precision lags experiment.

0 2B( ) 10D K e 0 3B( ) 10D e

( ( )) / ( ) ~ 1.4%

( ( )) / ( ) ~ 3.0%

B Ke B Ke

B e B e

1

3.50(3)(4)%

(CLEO-c 818 pb ) 1

0.288(8)(3)%

(CLEO-c 818 pb )

The branching fractions are extracted from the form factor fits

tagtag NEWNEW


D K e+ Form Factor: Test of LQCD

1 σ bands (stat and syst) by FNAL-MILC-HPQCD

2

2 2 2 2

(0)( )

1 1pole pole

f qq m

f

q m

Modified pole model used to compare with LQCD

Shape: ( )Ke

K+Normalization: f (0)

0

(BABAR measures

relative to )D K

K fast

Form factor measures probability hadron will be formed

0.39(2)

my average

(CLEO, Belle

& BaBar)

K

Assuming |Vcs |= 0.973340.00023 (CKM unitarity)

1/2

32( )2( ) ( )

( ( ) )~ /i

K ii

cs cd

D K ef q P

qV

α : CLEO-c prefers smaller value for shape parameter than others

f+ (0): experiments (1.2%) consistent with LQCD (10%).

CLEO-c is most precise. Theoretical precision lags.

tag

tag

NEW

NEW

K at rest


Dπe+ Form Factor: Test of LQCDshape: ( )e

+Normalization: f (0)

0.22(4)

my average

(CLEO & Belle)

α : CLEO-c measurements are compatible with LQCD

f+ (0): experiments (2.9%) consistent with LQCD (10%).

CLEO-c is most precise. Theoretical precision lags.

2

2 2 2 2

(0)( )

1 1pole pole

f qq m

f

q m

Modified pole model used to compare with LQCD

fast at rest

Form factor measures probability hadron will be formed

Assuming |Vcd |= 0.22560.0010 (CKM unitarity)

1/2

32( )2( ) ( )

( ( ) )~ /i

K ii

cs cd

D K ef q P

qV

tag

tag

NEW

NEW

1 σ bands (stat and syst) by FNAL-MILC-HPQCD


SummarySummary

Most precise B(D K e+) and B(D e+).

Most precise measurements of f+(0) and shape for D K/ e+ .

Very stringent tests of unquenched LQCD.

Best direct measurement of |Vcs|.

Most precise determination of |Vcd| from semileptonic decays.

The work uses the entire CLEO-c sample at Ψ(3770).

The results are about to be submitted to Phys. Rev. D.

These will remain the best results before BESIII do the same measurements.

We are eagerly awaiting more precise LQCD calculations of semileptonic form factors.


Backup slidesBackup slides

2 2

( )

( )

ˆ where ( / ) ( )

miss beam h e brem

miss tag h e brem

tag beam D tag

E E E E E

p p p p p

p E c cm p

Vub0.63 3

0.41(3.62 0.22 ) 10

exp LQCDubV

( ) ~ 6% precision

BABAR/Belle/CLEO(HFAG)

Br B l

11- 17% e.g. HPQCD &FNALExpt. 5%

q2>16 GeV

(summer 2008)


Backup slidesBackup slidesTheory + Experiment = Precision Flavor PhysicsTheory + Experiment = Precision Flavor Physics

(ρ, η)

~|Vub|

Δmd,s

Now

l

B

2 2 2[ ( )] | |Bubrate f q V

l

D2

)(22)( ||)]([ scd

KD Vqfrate

HQS

One of the most important goals of B physics

Measured

experimentally

Tightly constrained by CKM unitarity

Suffer from large theory uncertainty

The discovery potential of B physics is limited by systematic errors from QCD:


Form Factor: D→ P Form Factor: D→ P e e , , which parameterization to choose?which parameterization to choose?

When the shape parameters are not fixed, each parameterization is able to describe the data with a comparable χ2 probability.As data do not support physical basis for the pole & modified pole models, the model independent Becher-Hill series parameterization is used for |Vcx|.

PRELIMINARY


The Global Branching FractionsThe Global Branching Fractions

• The tag yield can be expressed as

• The yield of tags with a semileptonic decay can be expressed as

• The branching fraction of the semileptonic decay

• The branching fraction determined by tagging is an absolute measurement, independent of the integrated luminosity and number of D mesons in the data sample.

2tag tag tagDDN N B

, ,2tag SL tag SL tag SLDDN N B B

, ,,

,

/, where /tag SL tag tag SL

SL tag SL tagtag tag SL tag

N NB

N N

from fits to U

from fits to Mbc


Fits to the Partial RatesFits to the Partial Rates• Define q2 (the invariant mass of the e+νe pair):

• The method described above can also be used to obtain partial branching fractions, or equivalently, partial rates in q2 bins.

• The theoretically predicted partial rates

• Use the least squares method to fit to the partial rates

2 2' 2 2 3 2

'3

| || ( ) |

24F Qqpredicted

i P

i i

G Vd f q p dq

1,

1j

ij tag SLjmeasured

i i DD tag

N

BN

from fits to U

from fits to Mbc

efficiency matrix inversed

2 1

,

( )[cov( , )] ( )measured predicted measured predictedi i i j j j

i j

2 24 2

1 1ˆ( ) | | , where miss

miss e e miss

Eq E E p p p p

c c c

Study of DK/ π e + and measurement of |V cs | and |V cd | at CLEO-c

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