1

Jim WissUniversity of Illinois

FPCP06April 11,2006

Content

I: Charm Semileptonic decay motivation

II: Semileptonic BF results from CLEO-c

III: Fully leptonic results from BaBar/CLEO-c

IV: Form Factors for PseudoScalar l from FOCUS, BaBar &CLEO-c

V: Vector l Form Factors from CLEO-c

VI: Summary.

Recent Charm Semileptonic Decay Results

Representing:

2

K-D

c W l

q

scsV

Charm semileptonic decay as tests of LQCD

Charm SL decays provide a high quality lattice calibration, which is crucial in reducing systematic errors in the Unitarity Triangle. The techniques validated by charm decays can be applied to beauty decays. Improvement of CKM @ beauty sector.

The hadronic complications are contained in the form factors, which can be calculated via non-perturbative Lattice QCD,

BF provides a measurement of |VCq|2

3

Semileptonic reconstruction in Cleo-c

e

K e

0

0

0

0

(3770)

,

D

D

D

D K eK

K-

-

e+

K+

0Example: D e

CLEO BFRelative to PDG

(~117 events)

Ev

ents

/ 1

0 M

eV

U ( = Emiss – |Pmiss| )

4

Inclusive Semileptonic BF.

CLEO-c 281 pb-1

0

0 0

0.985 0.028 0.015SL SL

D D DSL SL

D D D

B

B

Inclusive BF vs sum of exclusive BF

Consistent with the known exclusive modes saturating the inclusive . Some room for new modes?

mode

D0Xe+ (6.46 ± 0.17 ± 0.13)%

i i (D0 Xe+ (6.1 ± 0.2 ± 0.2)%

D+ Xe+ (16.13 ± 0.20 ± 0.33)%

i i (D+ Xe+ (15.1 ± 0.5 ± 0.5)%

Consistent w/ SL isospin symmetry:

5

22

222

2 18

= great LQCD test( ) / DDF

cqD DD

mGB D M V

Mfmf

Fully leptonic decays: D+ +and DS +

/ 1.25 0.14

As expected from LQCD

s

BaBar CLEOD Df f

279 17 6 M19 eVsD

f

* at (4S)S sD D

0 09

2 8

41

4

0 2

3

4 40 0 66 10

201 3

222 6 1

17

6 7

Fnal/Mil

.

.

.

c

.

.

. .

MeV

. MeV

D

D

f

B

f

D

Tag D

Signal D+

0 D K

50 signal candidates

489 55 signal

m m m

6

D Pseudoscalar l form factors

22 3

2 3

22 2

2(

4( ) )

F cq P

lf q O mG V Pd D P

dq

What do we know about f+(q2) ?

This process can give a clean measurement of CKM angles and powerful tests of LQCD

2q 2q

22( )f q

Ra

te

P3

Unfortunately the rate vanishes at highest q2 where sensitivity to the form of f+(q2) is greatest. This is also the zero recoil limit where theory calculations are cleanest.

7

Pole Dominance in K*l

2 22 2

2 1

*

Im(

()

)

DDm K

f sds

s qm if q

q

R

22

2

2 2 2

2

2

22 2

2

0

1 1

eff *

* *

*

*

*

*

HQET&SCET

Becirevic & Kaidalov write as

effective pole with

( )

( )

integral

Res & Po

/

(/

le

)

D D

D

D

D D

D D

D

m m

f q

f

c c m

m q

m

f qq m q

m q

m

2Dm K Re s

Im s

2*Dm

Cauchy Theorem

0 5 0 04. .

(2004)

<Mpole> is 5.1 lower than Ds*

22 2

1

+Fits to f ( )pole

qm q

c Integral term is important

Ds*

BK expression is a good fit to recent lattice calculations

8

RS-WS

MC WS

12,840 K +

m K m K

m cut

FOCUS D0 K + analysis

0*

Select

decay chain

D D

Fixed Target Neutrino closure

• Jump to K rest frame

• The D and D* mass constraints the neutrino lies on a cone around the soft pion.

• Pick the that points the D closest to the primary vertex.

q2 re

con

st

q2 actual

Kframe

K

2min

2maxq

2minq

Lab frame

• A good muon candidate.

• Cerenkov ID for K/ candidates.

• L/ > 5 between two good vertices.

• D* tag required, and wrong sign soft subtraction

9

Correcting for charm backgrounds inD0 K +

The background only affects the highest q2 bins.

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2

after subtraction pole=1.9 before subtraction

2f q

2 2 4 (GeV / )q c

After subtracting known charm backgrounds, f+(q2) is an excellent match to a pole form withmpole= 1.91 0.04 0.05 GeV/c2 or = 0.32 (CL 87%, 82%).

10

Comparing to Lattice Gauge & prelim BaBar

2q (GeV )D 2

~100K

13K

Nearly identical q2 resolution!

11

Preliminary untagged DK/ e from CLEO-c

Slightly lower than previous measurements

Neutrinos are closed by energy-momentum balance but no recoil D tag

q2 resolution still about 10x better than FOCUS/BaBar

q2

CKM info Modified pole

12

DVector l Decay

H0(q2), H+(q2), H-(q2) are helicity-basis form factors computable by LQCD A new factor h0 (q2) is needed to describe s-wave interference piece.

2 22 2

2 22 2

22 222 20

2 2 20

2

(1 cos )sin ( )

(1 cos )sin ( )

1A 2sin cos ( )

8 sin cos ( ) ( ) e8

R

( )

l V

l V

l V

V

o

l

iH q h q

H q BW

H q BW

d q H q B

O

W

A

Ae BW

Korner+Schuler form from 1990

S-wave interfere asymmetry

cosV

Present in K* l nu

13

KS / GS model for H and H0

2V 2

1 1

Only 2 shape parameters needed

in spectroscopic pole

A (0)V(0) R = R =

A (0

dominance

) A

fit

(0)

2.1 2.5V A1 A2M GeV M M GeV

Spectroscopic pole dominance

22

2

2

*

* * "2

*

(1 )

(1 )(1 )

(1 )

1 '

'(1 ) 2 (1 ')

(1 ' )(1 '' )

2H'

H'1

H2

Ds*

Fajfer & Kamenik (

c qV where x

c A w

2005

here

)

cA

D

D K

D K K H

D K

aq

x ax m

a mq

b x m m

m m a m c aq

m m b x b x

B&K style “effective” poles

•V(q2) essentially same as B&K with one physical and one effective 1- poles.

•A1(q2) forced to one effective 1+ pole

•A2(q2) has two effective 1+ poles

Versus

This is traditional method

But S-pole dominance should work poorly at low q2 Need for alternative…

14

E6

87

E7

91

FO

CU

S

BE

AT

E6

91

E6

53

0.0

0.5

1.0

1.5

2.0

2.5

3.0 1.66 0.060

0.827 0.055R2

Spectroscopic pole dominance DVl fits

Ds D+ K

2V 2

1 1

A (0)V(0)R = R =

A (0) A (0)

The latest (FOCUS) data on Dsis consistent with D+ K

theory

theory

RV

R2

RV

15

A non-parametric approach

7 8 9

4 5 6

1 2 3

cosV

cosL

D: M+ M- M0

m vectors (angular bin)��������������

0

0

0 0 0 00

The projection weights can be computed directly

from the MC bin populations using linear algebra

I

I

I

P m m m m m m

P m m

m m

m m m m

m m m m m mP

m m

P

0

0

0

1

I

II I I I I

m m

m m m m m m m

m

m m

m

m

Disentangle helicity form factors based on their different angular bin populations.

Each Kπe candidate is given four weights based on its decay angles.

These weights project

Re

o

s

ut

ults appear as just 4 weighted histogram

H (q ) , H (q ) , H (q ) & H h (q )

s.

-+

n

´2 2 2 2 2 2 20 00

16

CL = 40%CL = 24%

CL = 59%CL = 0.2%

Preliminary CLEO D+ Kefrom 281/pb

20 0( )H h q

2 2( )H q

2 2( )H q

2 2( )oH q

FOCUS model

2 2 2 2

The CL are to the Focus model

Normalized so that

as 0 , ( ) 1 oq q H q

2 2q (GeV )

Low q2 peaking of Ho and ho is very apparent. Apart from interference term the CL are rather good.

17

Intensity contributions q2 H2(q2)

2 2q (GeV )

2 2 2( )q H q

2 2 2( )q H q

2 2 2

0( )q H q

2 20 0( )q H h q

H+ contribution vanishes at 0.

H- contribution vanishes at 0.

Subtle deviation of H0 from pure 1/q .

Confirms KS expected forms

18

Pole mass sensitivity

MV=2.1 MA=2.5

2 2 2( )q H q

q H (q )2 2 20

MV= MA=

2 2 2( )q H q

2 2 2( )q H q

2 2 2( )q H q

2 2 20q H (q )

Data fits spectroscopic poles and constant form factors equally well

19

Confirming the s-wave phase

( 0.896m K ( 0.896m K

2 2 (GeV )q

V

V saw cos

asym for m(K K

t

Focus

erm :

* pol

Re co

e fro

(20 )

m

02

siAe BW

20 0 Re{ exp( }H h q A i BW BW

Re

Im

BW

A

For 40 the high mass BW is nearly to s-wave amp and interference nearly vanishes.

Our interference “Ho (q2) ho

(q2)” should also vanish above pole if 40 and it does!

Focus

CLEO-c

20

Search for D-wave K

2 2D F2 2

1 1No evidence for h ( ) or h ( ) q q

q q

20 ( )DH h q

*m K *m KGuard against “phase cancellation” by showing above and below the K*

Add a D-wave projector

q2 GeV2

21

(1) New result on BF D+ and fD

from CLEO-c 281/pb and preliminary fDs from BaBar

(2) Exclusive BF of semileptonic decays from CLEO-c.• With just 56 pb-1, many CLEO SL BF are already the world best.

Results on 281 pb-1 coming soon!.• Inclusive BF of D Xepreliminary from 281/pb. Consistent with

SL(D0)/ SL(D+) = 1. The sum of exclusive BF almost saturates

the inclusive BF

(3) Non-parametric form factor measurement from FOCUS

for D K l , in comparison with the latest unquenched light-

flavor LQCD results and preliminary BaBar results

Summary

22

Summary Continues…

(4) Preliminary non-parametric Form Factor measurements for D V l from CLEO-c 281/pb

a. H+, H-, H0 appear very consistent with expected K&S shapes.

b. Data fits constant A1(q2), A2 (q2), V (q2) as well as it fits spectroscopic pole dominance no sensitivity to q2 dependence

c. Statistically significant Ho (q2) ho (q2) interference term ho (q2) 1/q confirming s-wave interference effect.

d. The effective “Ho (q2) ho (q2) ” vanishes above the K* pole, suggesting an s-wave amplitude phase near 40 which is consistent with the Focus phase.

e. No evidence for a K non-resonant d-wave or f-wave contribution.

23

Question slides

24

More semileptonic signals

U ( = Emiss – |Pmiss| ) plots

(~1311 events) (~545 events)

The first 56pb-1

0 D K e

Ev

ents

/ 1

0 M

eV

0;D e

(~8 events) First Observ.

(~422 events)

0 0* *,D K e K K

0D K e

25

Vcd (1.1%) from 3 generation unitarity

D+ (0.3%) well-measured

fD from Absolute Br(D+ +)|fD|2

|VCKM|2

2222 2

21

8( ) / ( )F

cdD D DD

mGB D f m M V

M

• Based on 281 pb–1,158,354 tags and 50 signal events.• Background ~ three events.

0.09 40.12

2.83.4

5

4.40 0.66 10

222.6 16.7 MeV

2.4 10 @90%

D

B D

f

B D e CL

2+1 flavorPRL 95, 122002

26

Summary of CLEO-c (56 pb-1) Exclusive BF

Phys. Lett. B608, 24 (2005)

Phys. Lett. B 597, 39 (2004)

References: PRL 95 181801 and PRL 95 181802

(2005)

2 2 2

| | 0.957 0.017(exp) 0.093( )

| | 0.213 0.008(exp) 0.021( )

1 | | | | | | 0.037 0.181( )

cs

cd

cs cd cb

th

th

tot

Using the lastest LQCD (PRL 94, 011601),

V

V

V V V

27

Expected q2 Dependence of Helicity FF

Only 0 helicity components can survive at q2 0because of V-A helicity laws.

22 2

V

2 2 20 0 2

2Since A ( ) ( , )

c0 constant or H 0 , 0

q

d H q f

H q q h q

q l

2

c

q

28

q2 dependence: Deconvolution

2genq2

genq2genq

2genq 2

genq

2recq 2

recq2recq

2recq

2recq

1 2 2 2 3 21 1 1 2 1 3

1

2 21

122 2 2 3 2

2 1 2 2 2 3

1 2 2 2 3 23 1 3 2

22

33 3

2

2 23

1/ / /

/ / /

/ / /

G G GM M M

G G GM M M

G G GM M M

N f N f N f f qM

M f qN f N f N f

N f N f N f M f q

We actually use a 10 10 matrix

A deconvolution matrix is constructed from the number of events generated in thei-th q2 bin that end up reconstructed in the j-th q2 bin. This matrix is then used to correct data for resolution and efficiency.

29

Information on vector-axial pole masses

V

H--H

+

A1

H

++

H-

q2 q2

Difference and sum of non-parametric H+ and H- data

A1 and V are very consistent with spectroscopic pole forms and measured rV.

But the slopes are only a few sigma from 0, so no useful pole mass information can be obtained with present statistics.

30

M K

Preliminary CLEO D+ Ke FOCUS D+ K

Comparing CLEO-c & FOCUS Results

2 2q (GeV )

2 2+H (q ) 2 2H (q )-

2 20H (q )

20 0h H (q )´

Data 11397

2 2q (GeV )

Data 2472

M K

2 2+H (q )

2 20H (q ) 2

0 0h H (q )´

2 2H (q )-

2 2meas trueq -q

2 0.2 GeVs=

2 2meas trueq -q

20.02 GeVs=q2 res

q2 res

31

IV. c. Isospin Conjugation Test.0

0 0

( ( ) ) ( ( ) ),

( ) / ( ) 1.35 0.19 !D K e D K

D qd l D qu

e

l

We expect iso-spin conjugati

However, PDG04,

on

0

0 0( ) / ( ) 0.87

( )

0.11

D

D K D

K

K

From FOCUS (04) BR measurement,

From CLEO-c (56pb-1) measurements,

0

0

( )1.00 0.05 0.04

( )

D K e

D K e

0

0.140.110

( )0.75 0.04

2 ( )

D e

D e

0 *

*0

( )0.98 0.08 0.04

( )

D K e

D K e

ii

B