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Doris Y. Kim, University of Illinois Urbana-Champaign

Content

• Part I: Theories of Charm Semileptonic decays

• Part II: q2 dependence in Pseudo-scalar l decays

• Part III: Vector l decays

D+ K*0 analysis (not so simple!)

Form factors ofDs

• Part V: Future of Semileptonic decays.

Semileptonic Charm Decays and QCD

ISMD Sonoma July 27, 2004

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I: Charm semileptonic decay as tests of LQCDThe decay rates are computed from first principles (Feynman diagrams) using CKM matrix elements.

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

(*)KD

c W l

q

scsV

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.

etc.

3

II: Pseudoscalar l decays

22 3

2 3

22 2

2(

4( ) )

F cq P

lf q O mG V Pd D P

dq

But a major disconnection exists between experiment and theory. In the past, theories worked best where experiments worked worst.

0 0.5 1 1.5 2 2.5 3

3P

2q

cleanest theory

highest rate

D l

is the easiest point for LQCD calculation.

c

q

2max

2 qq

s

q

l

lattice daughtera P at rest in D frame

Simple kinematics Easy to extract form factors.

The lattice community is actively fixing the situation and calculating f+ as a function of q2.

hep-lat/0309107 preliminary

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Comparing Pole versus ISGW forms in Dl

2q

22f q

The difference between these forms can be quite dramatic in

decays. Especially since decay gets quite close to the D* pole.

2 2pole

1f

q m

2expf q ISGW1

f+(q2) parameterization

pole

Until quite recently one required a specific parameterized form to bridge the gap between a theory and an experiment, since neither an experiment nor a theory had clean f+(q2) information.

ISGW2 Updated one.

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Brand new q2 information in Dl/KlPreliminary Cleo 2004 epole mass is

e

Ke It disfavors ISGW2 form by ~4.2

form factor f+(q²)

single-pole model

single-pole model

Based on 820 events

q² / GeV²

Kl

l0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

q² / GeV²

Preliminary K

6

Fo

cus 04

MK

3

E691

Cleo

91

Cleo

93

E687 tag

E687 in

c

Cleo

04

1.4

1.6

1.8

2.0

2.2

2.4

2.6

po

le m

ass

Summary of Dl/KlResultsClearly the data does not favor the simple Ds* pole

1.91 0.03

(0)0.86 0.07 0.05

(00.01

)K

f

f

Consistent w/ SU(3) breaking

0.082 .006 0.005 CLEOe

Ke

A big advance in precision!

Kl

2

2

22 3

2 3(

4)

2

F cq PG V Pd D P

dqf q

BR

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III: Dvector decays

H0(q2), H+(q2), H-(q2) are helicity-basis form factors computable by LQCD

A

22

22 2 2

2

00

sin sin(1 cos )sin

sin sin1( ) (1 cos )sin

8 2cos cos2sin cos

2cos

ii l V

l V ii l V

l l V

l Vl V

V t

e He H

m e Hq m e H

q HH

H

right-handed + left-handed +Two amplitudes get sumed over W polarization using D-matrices

22 2

(0)( )

1i

iA

AA q

q M

22 2

(0)( )

1 V

VV q

q M

Helicity FF are combinations of one vector and two axial form factors.

v 1(0) (0)r V A

2 2 1(0) (0)r A A

Two observables parameterize the decay

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Interference in D+ K*

Yield 31,254

DataMC

K* interferes with S- wave K and creates a forward-backward asymmetry in the K* decay angle with a mass variation due to the varying BW phase.

(2002)

F-B

asy

mm

etry

(m K

The S-wave amplitude is about 7% of the (H0) K* BW with a 45o relative phase

Focus “K*” signal

It’s the same relative phase as the LASS (1988)

matches model

-15% F-B asymmetry!

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K*form factors

Results are getting very precise and unquenched calculations for incisive tests of the theory would be very desirable.

1 cos 0.5V

0.5 cos 1V

0.5 cos 0.5V

acoplanarity

Precision tests of the model.

Due to interference

Direct measurement of (D+K* / K)

*0

00.594 0.043 0.033

D K

D K

Use upstream Ks (~10%) so that both the numerator (K) and denominator (Ks ) leave 3 tracks in FOCUS -strip

0

0( ) ( ) (11 11) /K K

D D ns

0

0( ) ( ) ( 25 9.7) /K e K e

D D ns

sK

0CLEO(02) partially reflects an inconsistency in ( )D K e

0using (D K

*0 0D K l K l Theory

S-wave corrected

Old

qu

ark

mo

del

11

0

0.5

1

1.5

2

2.5

3

R2

E7

91

CL

EO

E6

53

E6

87

BK

S

LM

MS

ISG

W2

0

0.5

1

1.5

2

2.5

3R

V

The Ds form factor enigma

Theoretically, the Dslform factors should be within 10% of D+ K*l The rV values were consistent, but r2 for Dslwas 2 higher than D+ K*l

ISG

W2

Fo

cus

E79

1

CL

EO

E65

3

E68

7 BK

S

LM

MS

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 1 2 3 4 5 6 7 8 9

RV

But the (2004) FOCUS measurement obtained a consistent r2 value as well!

Ds versus D+ K*l

circa 1999 circa 2004

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The future of charm SL physics

Precision neutrino closure in D e.

Cleo-c and Bes III: Run at (3770) with high luminosity and modern detectors.

DoDo, DoK-+

K-

K+

+

Extremely clean events!

CLEO-c yellow book:1 fb-1 MC

U = Emiss - Pmiss U = Emiss - Pmiss

Prelim. data (60 pb-1)

Pavlunin

APS(2004)

dp

d

P (GeV/c)

dp

d

P (GeV/c)

Yellow book1 fb-1 (MC)

The q2 impasse afflicting SL data for the last 20 years shall be solved, finally.

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Summary

Consistent FF for D+ K* & Ds

+

(m K

s-wave interferencein D+ K*

F-B

asy

mm

etry

V(q20) problem D+ K*

q2< 0.2

cos

New CLEO 2004 De/Keresult

0.082 .006 0.005 e

Ke

*( )sm D

(0)0.86 0.07 0.05

(0)K

f

f

*0

0

)

)

D K

D K

V/PS

ratio

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(D+K* / K) circa 1993

circa 1993

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Some more tests of the K*model

Vcos

cos

Vcos

cos

Generally the model tracks the data rather well…

cos

A dramatic mismatch is seen at very low q2

suggesting a V(q20) problem

Focus has a preliminary analysis of the K*0 line shape. K*0)is seen as less than PDG by~1.6 MeV.