CKM 2006 Workshop, Nagoya, Japan, Dec. 12-16, 2006

Leptonic & Semi-Leptonic Charm Decays

Sheldon Stone,

Syracuse University

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 2

What We Hope to Learn Purely Leptonic Charm Decays D→+

Check QCD calculations including Lattice (LQCD) Look for New Physics

Semileptonic decay rates & form-factors QCD checks Use QCD to extract Vcq (See talk of M. Artuso) Use d/dq2 in conjunction with B decay rates to extract Vub.

Use Dto get form-factor for B, at same v•v point using HQET (&

Use BBK*+-, along with DDK*at the appropriate q2

Due to lack of time, many interesting results are omitted

Need fBs/fB from theory.Measure fD+/fDs

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 3

Experimental methodsDD production at threshold: used by Mark III, and more recently by CLEO-c and BES-II.

Unique event propertiesOnly DD not DDx produced

Large cross sections at (3770):

(DoDo) = 3.720.09 nb (D+D-) = 2.820.09 nb

Ease of B measurements using "double tags:“ BA = # of A/# of D's

At (3770) CLEO-c uses beam constrained massAt 4170 MeV, invariant mass with energy cut

Wor

ld

Ave

*

SSD D

* *S SD D

S SD D

•At Y(4S) (charm) ~ 1 nb (DS) ~ 0.15 nb

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 4

Leptonic Decays: D(s) +

Introduction: Pseudoscalar decay constants

c and q can annihilate, probability is to wave function overlap

Example :

_

22+ 2 2 2

221

(P ) 1 | |8 F P P Q

Pq

mG m M Vf

M

In general for all pseudoscalars:

Calculate, or measure if VQq is known

(s)

or cs

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 5

New Physics Possibilities

Another Gauge Boson

could mediate decay Ratio of leptonic decays

could be modified (e.g.)

22 22+2 2

+ 2 2

(P )1 1

(P )/

P P

mmm m

M M

See Hewett [hep-ph/9505246] & Hou, PRD 48, 2342 (1993).

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 6

New Physics Possibilities II

Leptonic decay rate is modified by H+ Can calculate in MSSM. Is mq/mc, so negligible

for D+ but not for DS (mS/mc) Leptonic decay for

DS gets modified by factor of

or

where R=tan/mHSee Akeryod [hep-ph/0308260]

222 2 21 tan / /

qD q cHr m m m m

From Akeroyd

r

22221 /

qD q cRr m m m

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 7

Old CLEO Measurements of fDs

1. Detected & from DS*→ DS → decay

2. Used missing energy & momentum in half of the event, to estimate 4-vector. Event half determined using thrust axis

3. Correct 4-vector to get right DS mass value

4. Measured real background by doing same analysis on DS*→ DS → e

5. Used D*o → Do → K-(+) to measure efficiencies, etc…

6. Used 4.8 fb-1 at or near Y(4S) (M. Chadha et al. Phys. Rev. D58, 32002 (1998))

0.173 0.023 0.035S

S

D

D

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 8

New BABAR Measurements of fDs

Similar analysis to CLEO [1) detect & , 3) correct P4, 4) use e for backgrounds, 5) use D*o → K-

(+)], but much improved because they use only events: e+e-→“D” x DS*-, where the “D” is a fully reconstructed Do, D+ or D*+ (B. Aubert et al [hep-ex/0607094])

This gives much better S/B and also missing energy resolution

Use 230 fb-1

0.143 0.018 0.006

S

S

D

D

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 9

New CLEO-c Measurement of DS+→+

In this analysis CLEO uses DS*DS events where they detect the from the DS*→ DS decay

They see all the particles from e+e- → DS*DS, DS

(tag) + + except for the A kinematic fit is used to (a) improve the resolution

& (b) remove ambiguities Constraints include: total p & E, tag DS mass, m=M(DS)-M(DS) [or m= M()-M()] = 143.6 MeV, E of DS (or DS*) fixed

Lowest 2 solution in each event is kept No2 cut is applied

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 10

Invariant masses

K-K++ KsK+

Inv Mass (GeV)

+

K*K* from KsK-+

Total # of Tags = 19185±325 (stat)

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 11

Tag Sample using First define the tag

sample by computing the MM*2 off of a & DS tag

Total of 11880±399±504

tags, after the selection on MM*2

All 8 Modes Data

s

s

2*2CM D γ

2

CM D γ

MM = E -E -E

- p -p -p

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 12

The MM2 (From Simulation)

To find the signal events, compute

S S

2 2 2CM D γ μ CM D γ μMM =(E -E -E -E ) -(p -p -p -p )

Signal Signal →

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 13

MM2 Results from 200 pb-1

Clear DS

+→+signal for case (i)

Events <0.2 GeV2 are mostly DS→+, →+ in cases (i) & (ii)

No DS→e+ seen, case (iii)

6 DS→+, →+in case (i) + peak Electron Sample

DATA 200/pb<0.3GeV in CC

DATA 200/pb>0.3GeV in CC

64 events

24 events

12 events

Case (i)

Case (ii)

accepts 99% of+, 60% + & K+

accepts 1% of +, 40% + & K+

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 14

Sum of DS+→++, →+

Two sources of background A) Backgrounds under

invariant mass peaks – Use sidebands to estimate

In +signal region 2 background (64 signal)

Sideband bkgrnd 5.5±1.9 B) Backgrounds from real DS

decays, e.g. +oo, or DS→+, →+o< 0.2 GeV2, none in signal region. Total of 1.3 additional events.

B(DS →) < 1.1x10-3 & energy cut yields <0.1 evts Total background < 0.2 GeV2

is 6.8 events, out of the 100

100 events

Sum of case (i) & case (ii)

K0+

signal line shape

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 15

Branching Ratio & Decay Constant

DS+→+

64signal events, 2 background, use SM to calculate yield near 0 MM2 based on known ratio

B(DS+→+(0.657±0.090±0.028)%

DS+→++ →+

Sum case (i) 0.2 > MM2 > 0.05 GeV2 & case (ii) MM2 < 0.2 GeV2. Total of 36 signal and 4.8 bkgrnd

B(DS+→+(7.1±1.4±0.3)%

By summing both cases above, find

Beff(DS+→+(0.664±0.076±0.028)%

fDs=282 ± 16 ± 7 MeV B(DS

+→e+3.1x10-4

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 16

Measuring DS+→++→e+

B(DS+→+B+→e+1.3%is “large”

compared with expected B(DS+→Xe+

Technique is to find events with an e+ opposite DS

- tags & no other tracks, with calorimeter energy < 400 MeV No need to find from DS* B(DS

+→+ (6.29±0.78±0.52)% fDs=278 ± 17 ± 12 MeV

400 MeV

Xe+

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 17

&

Weighted Average: fDs=280.1±11.6±6.0 MeV, the

systematic error is mostly uncorrelated between the measurements (More data is on the way)

Previously CLEO-c measured

M. Artuso et al., Phys .Rev. Lett. 95 (2005) 251801

Thus fDs/fD+=1.26±0.11±0.03

++2.3 †-3.4D

f =(222.6±16.7 ) MeV D+→

K0+

†

sDf +sD Df / f

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 18

Comparisons with Theory We are

consistent with most models, more precision needed

Using Lattice ratio find |Vcd/Vcs|=

0.22±0.03 1993

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 19

Comparison with Previous Experiments

Difficult to average without a clear measurement of B(DS→+). In any case CLEO-c result dominates

?

?

280.1±11.6±6.0

3.6±0.9 248 ± 15 ± 6 ± 31

-2

-2

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 20

Limits on New Physics Lepton Universality

(DS+→+(DS

+→+= 9.9±1.7±0.7 SM = 9.72

(D+→+(D+→+< 4.77 (90% cl) SM = 2.65

Limits on charged Higgs According to Akeryod Unquenched Lattice: fDs=249±3±16 MeV Our result: 280.1±11.6±6.0 MeV Take ms/mc=0.076 (PDG) Then the ratio of our result/SM gives >1, NP<1

222 2 21 tan / /

qD q cHr m m m m

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 21

Limits on Charged Higgs Mass

Can set limits in the tan - mH± plane

Competitive with CDF

But depends on Lattice Model. Don’t take seriously yet

Summary of the 95% CL exclusions obtained by LEP & CDF. The full lines indicate the SM expectation (no H± signal) and the horizontal hatching represents the ±1 bands about the SM expectation.

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 22

Exclusive Semileptonic Decays Best way to determine magnitudes of CKM elements, in principle is to use semileptonic

decays. Decay rate |VQiQf|2

Kinematics: Matrix element in terms of form-factors (for

DPseudoscalar +

For = e, f(q2)0:

22 2 2 2D hadron D P P Dq p p m m E m

2 2( ) ( ) ( )( ) ( )( )P D D P D PP P J D P f q P P f q P P

VQiQf

2 2 3

222 3

( )24

cq F PV G Pd D Pef q

dq

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 23

Form-Factor Parameterizations

In general

Modified Pole

Series Expansion

2

22 2

2 2 2 2( )

(0) 1 1 Im( ( ' ))( ) '

1 1 'DM mpole

f f qf q dq

q m q q

2

2 2 2 2

(0)( )

1 1pole pole

ff q

q m q m

2 20 02 2

00

1( ) ( )[ ( , )]

( ) ( , )k

kk

f q a t z q tP q q t

2

2 02( ) 0 2

0

, ( , )D K

t q t tt M m z q t

t q t t

Hill & Becher, Phys. Lett. B 633, 61 (2006)

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 24

Beam Constrained mass usingEmiss & Pmiss to find

CLEO-c Exclusive Decays (281 pb-1)

Both Tagged results & untagged using reconstruction

reconstruction has larger statistics but larger systematic errors

U = Emiss– |Pmiss| (GeV)

29520

69928

291055

679684 14397132134749

58468845029

Samplesoverlap, so chooseonly oneresult

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 25

Exclusive Branching Ratio Summary

Theory needs to catch up

preliminary

preliminary

preliminary

preliminary

Do → K- e+

νDo → π- e+

ν(2006)(2006)

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 26

CLEO-c Form-Factors Compared to Lattice

Lattice predictions*DKef+(0)=0.73±0.03±0.07 =0.50±0.04±0.07Def+(0)=0.64±0.03±0.06 =0.44±0.04±0.07*C. Aubin et al., PRL 94 011601

(2005)

DATA FIT(tagged)

LQCD

0D e

DATA FIT(tagged)

LQCD

0D K e

Assume Vcd = 0.2238

Assume Vcs = 0.9745

Belle

.

Belle

.

CLEO-c

CLEO-c

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 27

Other Form-Factor Measurements

CLEO-c & Belle somewhat disagree with LQCD, Belle 2 28/18 (K) & 9.8/5 ()

DoKℓ

& FOCUS

LQCD: Aubin et al., PRL94, 011601(2005)

~2.5k signal events

232 signal events

Unquenched LQCDQuenched LQCDSimple pole model

Kℓ

ℓ

Belle

Belle

q2 (GeV2)

(hep-ex/0607077)

BELLE: PRL 97, 061804 (2006) [hep-ex/0604049]

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 28

Pseudoscalar Form Factors

D→K e+ D→ e+

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 29

D Form Factors (CLEO-c)

Can be used to detemine Vub along with BDK*& BK*+- (See Grinstein & Pirjol [hep-ph/0404250]) D+-

Do-

q2

cos

cos e

Line is projection for fitted RV, R2

Rv = 1.40 0.25 0.03,

R2 = 0.57 0.18 0.06B(D0 -e+)=(1.560.160.09)10-3

B(D+ 0e+)= (2.320.200.12)10-3

U = Emiss– |Pmiss| (GeV)

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 30

CLEO-c Discovery of Do→K e+

B(Do→K1(1270)e+)*B(K1(1270) →K-) = consistent with ISGW2 prediction

1.4 41.0(2.2 0.2)x10

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 31

Conclusions not preliminary

fDs=280.1±11.6±6.0 MeV preliminary

fDs/fD+=1.26±0.11±0.03 preliminary

No violation of Lepton Universality observed

Accurate semi-leptonic form-factors confronting LQCD & perhaps indicating deviations

Much much more to do

++2.3-3.4D

f =(222.6±16.7 ) MeV

CKM 2006 Workshop, Nagoya, Japan, Dec. 12-16, 2006

The End

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 33

Simp. Pole

Mod. Pole

Untagged: Form-Factor Results

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 34

D /Ke: Which Form Factor Parameterization?

CLEO preliminary

All these models describe the data pretty well (except when forcing pole mass to nominal value in pole model).

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 35

Compare with Limits from Belle

Belle: assumes fB and |Vub | are known, take the ratio to the SM BF.

rB=1.130.51

22

21 tanB

BH

mr

m

Excluded byCLEO-c95% CL

But taking no theoretical erroris abhorrent

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 36

Goals in Leptonic Decays

fB & fBs/fB needed to

improve constraints from

md & mS/md. Hard to measure directly (i.e. B measures VubfB but we can determine fD+

& fDs using D and use them to test theoretical models (i.e. Lattice QCD)

Constraints from Vub, md,ms & B

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 37

New CLEO-c Measurements of fDs

Two separate techniques (1) Measure DS

+→+ along with DS→+, →+. This requires finding a DS

- tag, a from either Ds*-→Ds

- or Ds*+→+. Then finding the muon or pion using kinematical constraints

(2) Find DS+→+ →e+opposite a Ds

- tag

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 38

Comparisons with Theory

We are consistent with most models, more precision needed

280.1±11.6±6.0 222.6±16.7 +2.8-3.4CLEO-c 1.26±0.11±0.03

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 39

CLEO-c Untagged DK(or ) e

S. Stone (Syracuse) CKM 2006 Workshop, Dec. 12-16, 2006 40

Define Three Classes Class (i), single track deposits < 300 MeV in

calorimeter (consistent with ) & no other > 300 MeV. (accepts 99% of muons and 60% of kaons & pions)

Class (ii), single track deposits > 300 MeV in calorimeter & no other > 300 MeV (accepts 1% of muons and 40% of kaons & pions)

Class (iii) single track consistent with electron & no other > 300 MeV