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BEACH 2006July 5, 2006

Content

I: Why We Study Charm Semileptonic Decays.

II: Recent Analyses on Semileptonic BF, from BES and CLEO-c.

III: Form Factors for PseudoScalar l from BaBar, Belle, CLEO-c, & FOCUS.

IV: Vector l Form Factors from CLEO-c.

Semileptonic Charm DecaysDoris Y Kim

University of Illinois

2

(*)KD

c W l

q

scsV

I. Charm Semileptonic Decays as Tests of QCD

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, HQET, quark models, etc.

BF (decay rate) study provides a measurement of |Vcq|2

, etc.

3

An Example of Semileptonic Decays: CLEO-c

e

K e

0

0

0

0

(3770)

,

D

D

D

D K eK

K-

-

e+

K+

0Example: D e

(~117 events)

Ev

ents

/ 1

0 M

eV

U ( = Emiss – |Pmiss| )

CLEO-c (56/pb) & BESBF relative to PDG 04

4

II. 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 with SL isospin symmetry:

Extrapolated below 0.2

5

LFR (90)

LAG

R (93)

WB

S (85)

SU

MR

(91)

MITB

AG

(94)

ISG

W2 (95)

QP

T (96)

RQ

M (96)

QM

(97)

LFM (97)

DIS

P (01)

QM

(00)

EFT (02)

PC

L (01)

CV

FLD (01)

SR

(97)

LAT (94)

LAT (92)

0

0.2

0.4

0.6

0.8

1

1.2

DA

TA

* )

)

D K

D K

Predictions

Data (2004)

V/PS Anomaly in (DK*l / ( K l

• Recent V/PS measurements are consistent: FOCUS (04) CLEO(05) two new BES(06).

The V/PS anomaly is rapidly fading away.

Plot courtesy of BES

• Early V/PS predictions were 1.5 – 2 larger than known data ( the A1 form factor problem ). • Since 1995 predictions have stabilized close to data.

6

III. 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 Parameterization: D K l l

2 22 2

2 1

*

Im(

()

)

DDm K

f sds

s qm if q

q

R

2

22

2

2 2 2**

* *

eff *

Becirevic & Kaidalov write as

effective pole with

( )

integral

D

D

D

D

D

D

Dc m

m

m

c

mq

mf q

q

m

2KDm m Re s

Im s

2*Dm

Dispersion

22 2

1

+Fits to f ( )pole

qm q

c

Ds*

But there is a less model dependent way of dealing with f+ singularities

2

2 2 2 2

0

1 1* *

HQET&SCET

( )( )

/

Res & P e

/

ol

D D

ff q

q m q m

<Mpole> is 5.1 lower than Ds* Integral term is important

8

For BThe cut is very close to the maximum q2 andf+ (q2 as q2q2

max

After z mapping, the physical and cut region are far apart. The f+ (zdata is well fit with just a straight line as a polynomial.

R.J. Hill’s† New Approach to f (q2)

Illustrate with Be data [Hill (06)]

f+ (q2

Pf+ (z

10x 2.5x

-z

0 1( ) ) f z aP at zt L

q2

q2 z

physical

cut

Hill makes a complex mapping that pushes the cut singularities far from maximum q2.

Charm data?? †R.J. Hill hep-ph/0606023 (FPCP06)

Form factors are given by a simple Taylor series for |z | << 1

9

FOCUS (2004) non-parametricD0 K + analysis

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

The New Results from Belle (2006)

D0 l D0 l

D0 lD0 l

pole mass (GeV)

Kl 1.82 ± 0.04stat ± 0.03syst

l 1.97 ± 0.08stat ± 0.04syst

Kl 0.52 ± 0.08stat ± 0.06syst

l 0.10 ± 0.21stat ± 0.10syst

modified pole

fit results

One “effective” pole

Plot courtesy of L. Widhalm

unquenched LQCDquenched LQCDsimple pole model

11

LQCD, FOCUS & BaBar: q2 and z-trans

~100K

13K

Hill transformation gives a nearly linear f(Z) for DK data. The expansion should converge very rapidly since |z| << 1 in this decay

BaBarFOCUS

From Hill (06)

-z

Plus some new results from CLEO-c

12

Preliminary Untagged DK/ e from CLEO-c

Slightly lower than previous measurements

Neutrinos are determined by energy-momentum balance AND the recoil D tagging method is not used.

CKM info Modified pole

charm vector semileptonic decays

13

IV. D Vector 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 (1990)

Present in K* l nu

14

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*

c qV where x

cA wh

Fajfer & Kamenik (20

ere

5

)

cA

0

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 be one effective 1+ pole

• A2(q2) has two effective 1+ poles

Versus

The traditional method.

But spectroscopic pole dominance should work poorly at high q2 Need for alternative…

K&S write H and H0 as linear combinations of two axial and one vector form factors.

Two approaches are used to parameterize them:

15

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 DV l Fits

D+ Kl+

2V 2

1 1

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

A (0) A (0)

The latest results FOCUS (2004) on Dsform factors are consistent with those for D+.

RV

time

Experimental results are very consistent with small errors. But must we trust/rely on spectroscopic pole dominance?

RV

R2

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A non-parametric Approach

7 8 9

4 5 6

1 2 3

cosV

co

sLD: 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

P

m

P

m

m m

00

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

ul

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

ts appear as just 4 weighted histograms.

)+ -

n

´2 2 2 2 2 2 20 0 0

17

Non-parametric D+ K+e+Form Factors (281 pb1)

2 2 2( )q H q

2 2 2( )q H q

2 2 20 ( )q H q

2 20 0( )q H h q

CL = 40%

CL = 24%

CL = 59%

CL = 0.2%

2 2 2q (GeV /c )

FOCUS model

Low q2 peaking of H0 and h0 is very apparent.

Apart from interference term the CL are rather good.

18

Pole Mass Sensitivity in Data

MV=2.1 MA=2.5

2 2 2( )q H q

Constant Ai & V

2 2 2( )q H q

2 2 2( )q H q

2 2 2( )q H q

Data fits spectroscopic poles and constant form factors equally well.

2 2 20 ( )q H q

2 2 20 ( )q H q

19

Preliminary Z transform of PS-V decay by Hill

CLEO data

D+ K +e+

PH

0(z

2q

-z

Analysis of CLEO non-parametric data by R.J. Hill (private communication)

The Hill- transformed CLEO non-parametric H0

data seems nearly

constant.

For DK* decays, the z range is 4 small than for DK. Hence, one expects that the H0 data is nearly constant after transformation, which is confirmed in data

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Confirming the s-wave in D+ K +e+

( 0.896m K ( 0.896m K

2 2 2 (GeV / )q c

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

The disappearance of the interference above the pole implies the above phase relationships between the BW and the s-wave amplitude.

FOCUS

CLEO-c

21

(1) Inclusive BF of semileptonic decays from CLEO-c.• From 281/pb at (3770), much better than the PDG 04.

SL(D0)/ SL(D+) = 1. Known decay modes almost saturating.

(2) Active Form factor analyses for D Pseudoscalar l by several experiments are compared to the latest unquenched light-flavor LQCD results, B&K model & Hill transformation.

(3) Form Factor measurements for D V l from CLEO-c 281/pb and

FOCUS.• H+, H, H0 appear consistent with the spectroscopic pole dominance

model and consistent with Hill.

(4) Not covered here & Coming soon: Exclusive BF decays, rare

decays, Ds semileptonic decays, more form factors, etc.

(5) Looking forward to new data from B factories, CLEO-c, BES III,

and next-next-generation charm experiments.

Summary

22

Question slides

23

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

24

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

25

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

26

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