Fully leptonic and semileptonic decay

BESIII-Cleo-c workshop J. Wiss 1

Fully leptonic and semileptonic decay

CLEO-c and BESIII

Joint workshop on charm, QCD and tau physics

Jan. 13-15, 2004 in Beijing, China

Acknowledgements and Full Disclosure

1. This talk is from the perspective of a brand new CLEO-c member

2. It borrows very heavily from an excellent longer talk of Ian Shipsey

3. I have worked on semileptonic decays from the Fermilab FOCUS (fixed target) experiment with vastly different systematics and very complementary techniques.

Allowed transition

Jim WissUniversity of Illinois


Hi impact leptonic and semileptonic physics

/td tsV V

/ub cbV V

The most uncertain CKM

elements are |Vtd|and |Vub|. Both

uncertainties are dominated by systematics on calculating hadronic effects that can be significantly reduced by calibrating LQCD on related charm decays.

D+ D0 l

An impressive check of the unitarity triangle.


B(D+l)/ D+ : fD+|Vcd|

B(DS l)/ Ds : fDs|Vcs|

* Charm meson lifetimes known 0.3-2%* 3 generation unitarityVcs, (Vcd) known to 0.1% (1.1%) fD+ fDs

D meson Decay Constants

In a pseudoscalar D meson decay:

c and q annihilate

222

222

81 ||)1()( cqD

DDFq Vf

M

mmMGD

q

|fD|2

|VCKM|2

M

BDD s ,,

Q

q

QqV

*W

Helicity suppression


Improving knowledge Vtd using D+

2

3

2

1

108.820050.0

tdBB

d

V

MeV

fBpsM dd

Lattice predicts fB/fD with small errorsprecision measurement of fD

precision estimates of fB precision determination of Vtd

d

d

BB

BB

d

d

Bf

Bf

M

M )()(5.0

)(

1.2% ~15% (LQCD)

%3.2D

D

f

f

(ICHEP02)

/td tsV V

/ub cbV V


D meson Decay Constants Current Status

Common systematic error from B(Ds)

Estimated BR usingfDs=260 fD=220 fB=200 MeV

14% relative error

fDs Values from Ds

fD+ < 290 MeV @ 90% CL (Mark III)

B(

D+ 4.210-4 1.110-3

DS+ 5.710-3 5.510-2

B+ 3.210-7 7.110-5


D+

MC

Huge improvement over existing knowledge!

UL

33%

17%

PDG

f D+

f Ds

f Ds

2.3%

1.6%

1.9%

3fb-1

fD+ from Absolute Br(D+

• Fully reconstruct one D (tag)

• Require one additional charged track and no additional photons


Probing the hadronic current

B

b

q

c

q

Wl

(*)D

D

c

q

c

q

(*)K

Wl

2f q

Wl

D

K

2 2 2

2 2 21 2

: and

* : , ,

lD Kl f q m f q

D K l A q A q V q

/td tsV V

/ub cbV V


D0 Modes (%) Detection

“efficiency”

N Detected

Xetagging

fraction

NDetected

Xe + Tag

CKM

K-e+ 3.47 46% 559,500

14%

77,670 Vcs

K*-e+ 2.02 12% 28,200 3,900 Vcs

-e+ 0.37 63% 81,000 11,190 Vcd

-e+ 0.20 23% 15,600 2,190 Vcd

D+ Modes

K0S e

+ 3.40 37% 219,000

7.5%

16,560 Vcs

K*0e+ 4.65 19% 151,500 11,250* Vcs

0e+ 0.31 44% 34,500 2,580 Vcd

0e+ 0.25 38% 24,000 1,770 Vcd

yields with 3 fb-1

Exclusive Charm Semileptonic Signal Yields in 3 fb-1

yellow book

The BESIII yields are likely to be 5 to 10 times larger!

*Focus K* FF sample


List of Modes

PDG(2000)

(%)

PDG(2000)

/ (%)

(3fb-1)

/ (%)

D0K-e+ 3.47 0.17 4.9 0.36

D0K*-e+ 2.02 0.33 16.3 1.60

D0-e+ 0.37 0.06 16.2 0.95

D0-e+ - - 2.14

D+K0e+ 6.7 0.9 13.4 0.63

D+K*0e+ 4.7 0.4 9.4 0.94

D+0e+ 0.31 0.15 48.4 1.97

D+0e+ 0.22 0.08 36.4 2.38

Improvements in charm semileptonic branching ratiosfrom 3 fb-1

Threshold running can dramatically improve on the PDG value of dB/B for every D+ and D0 semileptonic branching ratio.


|f(q2)|2

|VCKM|2

I. Absolute magnitude & shape of form factors are a stringent test of theory. II. Absolute charm semileptonic rate gives direct measurements of V cd and Vcs. III Key input to precise Vub vital CKM cross check of sin2

b

c

u

d

l

l

1) Measure D form factor in Dl. Calibrate LQCD uncertainties .2) Extract Vub at BaBar/Belle using calibrated LQCD calc. of B form factor.3) But: need absolute Br(D l) and high quality f(q2) data and neither exist

2

2 3 2 2 2FQq2 3

G|V | p |f (q )|

q 24 daughter l

dm

d

B

D

Importance of absolute charm semileptonic decay rates..

~ 25%B

B


f(q2) models of the past

32

2

2

2

2 324( )

F cq PG V Pd D P

dqf q

0 0.5 1 1.5 2 2.5 3

3P

2q

cleanest theory

highest rate

2 2pole

1f

q m

2expf q ISGW

A major disconnect between experiment and theory afflicts published data

An incisive test of LQCD requires one to measure f(q2) where there is still rate and compare in a theoretically controlled q2 region

Previous data had low rates and terrible q2 resolution which required a parametric form for meaningful measurement

is easiest for LQCD

c

q

2max

2 qq

s

q

l

lattice daughtera

D l


Measuring q2 evolution

At present, K*l data fits to the pole form return poles slightly lower than Ds*. But past studies were compromised by poor q2 resolution and control of backgrounds at low visible mass and K*l is not an optimal state...

l probe q2 dependence nearly up to the spectroscopic pole!

DK*l

“yellow

book”1 fb-1

MC

Signals at the (3770) will be clean , copious, and well resolved in q2


Pole versus ISGW form in De

22f q

2 2 (GeV/c)q

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

dp

d

P (GeV/c)

dp

d

yellow book1 fb-1

MC

The lattice can now calculate f+ as a function of q2. De provides a powerful test of the lattice predictions. Once validated, the lattice can be used with confidence in the extraction of CKM matrix. for both B’s and D’s

dp

dLattice

hep-ph/0101023

better sys


Dvector l decays

MK MW2 q2

A 4-body decay requires 5 kinematic variables: Three angles and two masses.

H0(q2), H+(q2), H-(q2) are helicity-basis form factors computable by LQCDThese evolve according to vector and axial pole forms

A

22

22 2 2

20

0

sin sin(1 cos )sin

sin sin1( ) (1 cos )sin

8 2cos cos2sin cos

2cos

il Vi

l V il Vi

l l Vl V

l VV t

e He H

e Hmq m e H

q HH

H

c

c

cmc

q qq q

q qq q

q qq q

q

+

+ ---

-

ì üï ïï ïï ï+ï ïï ï+ï ïï ï= - - - +í ýï ï+ï ïï ï-ï ïï ï+ï ïï ïî þ

right-handed + left-handed +

(“mass terms”)Wigner D-matrices

Two amplitude sums over W polarization


*0( )D K Form Factor Ratios The H+ , H- , and H0 form factors are various combinations of vector and axial pole forms which are parameterized as spectroscopic poles.

22 2

(0)( )

1i

iA

AA q

q M

22 2

(0)( )

1 V

VV q

q M

2.5

2.1A

V

M

M

Nominal spectroscopicpole masses

The intensity is then described by

just 2 numbers

v 1(0) (0)r V A2 2 1(0) (0)r A A

2/GeV c2/GeV c

rv/ rv= 4.6% r2/ r2 = 9.2%

YB 1 fb-1 stat

2 2

/ 2%

/ 3%V Vr r

r r

E69

1

E65

3

E79

1

FO

CU

S

BE

AT

E68

7

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

E68

7E79

1

FOC

US

BE

AT

E69

1

E65

3

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Focus sys+statr2

rV1.66 0.060

0.827 0.055time

Latest LGT: Becirevic (ICHEP02) RV = 1.55 0.11

Although ratios of form factors are known precisely, A1(0) , A2(0) and V(0) measurement requires knowledge of (1) absolute BR (2) charm lifetimes (3) reliance on q2 model


Hadronic complications in K*l

Yield 31,254

21 cosV

dd

a qG

µ +W

DataMC

constant s-wave

The Kl process consists of both K* l and an interfering, s-wave component which creates a forward-backward asymmetry in the K* decay angle with a distinctive mass variation.


Both good news and bad news

const ampLASS ampev

ents

Cos

V

M(K)

Pha

se (

deg)

|am

p|2

Adds additional complications such as amplitude and phase variation, an additional helicity form factor etc.

But allows additional handles on the relevant hadronic physics such as:

1. Studies of the I=1/2 s-wave phase variation

2. Detailed studies of the K* line shape

Estimated errors for a 31 000 event sample

A very naive calculation


Great to extend data to D lKinematic projections from 1 fb-1

1 Very clean2 Great resolution3 Good efficiency

l

K*l

It would very interesting to compare form factors in l to K*l and search for s-wave interference in l

MC MC

MCMC

BESIII could study S-wave interference in l interference with half the (tagged) statistics as used in the Focus K* study

e *K e


Enigma #1: (DK*lK

*l /K

E691

E653

Focus

Argus

Omega

Cleo 1

Cleo 2

Cleo 2

E687

0.3

0.4

0.5

0.6

0.7

0.8

0.9

muons electrons

0.620.02

2*1

Quark models predicted a

(0)

as oldtwice as hig er a dh a .t

oD K A

A1 follows from (K*) measured from K*lK using the K BF and D+ lifetime. This can then be compared with LGT prediction

The 2002 CLEO result tended to resolve this discrepancy.

The 2002 FOCUS result tended to reinstated it.

circa 1993Form factor ratios were well predicted but the scales were not.


Enigma #2: Dslform factors

ISG

W2

Fo

cu

s

E7

91

CL

EO

E6

53

E6

87 B

KS

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

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

ISG

W2

LM

MS

BK

S

E6

87E6

53

CL

EO

E7

91

0

0.5

1

1.5

2

2.5

3

R2 CL (rV) = 44.3% CL(r2) = 21.5%circa 1999

It was anticipated that the form factor ratios for Dslshould be within 10% of those for D K*lUntil just recently, it looked like rV values were consistent but r2 for Dslwas a factor of two higher than that for D K*lThe new Focus data (hep-ex/0401001) challenges this.


Determining Vcs and Vcd

If theory passes the test…..

combine semileptonic and leptonic decays eliminating V CKM

(D+ l(D+ lindependent of VcdTest rate predictions at ~4%

Test amplitudes at 2%Stringent test of theory!

(Dsl(Dslindependent of VcsTest rate predictions at ~ 4.5%

Use CLEO-c validated lattice to calc. B semileptonic form factor, then B factories can use Blv for precise Vub

Vcs /Vcs = 1.6% (now: 11%) Vcd /Vcd = 1.7% (now: 7%)

eKD0

eD0I

II


Improving unconstrained CKM elements

Vcd Vcs Vcb Vub Vtd Vts

7% 11% 5% 25% 36% 39%

1.7% 1.6% 3% 5% 5% 5% B Factory/Tevatron

Data & CLEO-c

Lattice Validation

(Snowmass E2 WG)

CLEO-cdata andLQCD

PDGPDG

|Vcd|2 + |Vcs|2 + |Vcb|2 = 1 ??CLEO –c: test to ~3% (if theory D K/lgood to few %)

Without invoking powerful unitarity constraints, many CKM elements are relatively poorly known.

With lattice validation from threshold e+e- running allows for much better unitarity tests


Summary

• Leptonic Decay– Dramatic improvements in fDs and first measurements of fD+ at 2%

• Plays a crucial role in Vtd when combined with mixing

• Pseudoscalar semileptonic decay– Unparalleled cleanliness in f+ form factor measurement in D l

• Remove reliance of f(q2) models to bridge theory and experiment

• Pole dominance and ISGW forms can be easily distinguished

• Provide clean calibration of f+ : Both value and q2 evolution predicted by LQCD

– Provides crucial calibration f+ to use B lto measure Vub

• Vector semileptonic decay– Improvement in rV and r2 parameters– Unique advantages in determining A1(q2), A2(q2) , V(q2)

• q2 dependence for the first time

– Hadronic complications / opportunities due to s-wave interference– Settle two long term experimental enigmas

• The K*l/Kl problem

• The Ds l versus D+ K*lr2 inconsistency

• Direct measurements of Vcs , Vcd and incisive unitarity tests


• Crucial Validation of Lattice QCD: Lattice QCD will be able to calculate with accuracies of 1-2%. The CLEO-c decay constant and semileptonic data will provide a “golden,” & timely test.

Interplay between semileptonic , leptonic charm and improved beauty data and LQCD

Imagine a world Where we have theoreticalmastery of non-perturbative QCDat the 2% level

B Factories only ~2005

Theoryerrors = 2%


Question slides

??


Currently SL of all D mesons are consistent with being equal:

Threshold: the best place to measure inclusive semileptonic branching ratios

Hadronic tag

30 improvement !

HQE predicts the near equality of SL for D+, D0 and Ds but large 1/mc corrections and duality violations are a concern. CLEO-c inclusive rate and spectral shape provide precision test of 1/mc expansion

Mode

(10-2ps-1) / (%) / (%)

CLEO-c (3fb-1)

D0e+X 16.40.7 4.4 1.4

D+e+X 16.41.8 11.0 1.1

DSe+X 16.110.1 62.7 2.8

Mode B %

PDG2000

B /B %

PDG2000

B / B(%)

CLEO-c (3fb-1)

D0e+X 6.80.3 4.4 0.8

D+e+X 17.21.9 11.0 0.8

DSe+X 8 5 63 1.7

e

Inclusive Semileptonic Decays


CLEO-c Yellow Book Run Plan

Year 1 (3770) – 3 fb-1

30 million DD events, 6 million tagged D decays (310 times MARK III)

Year 2 MeV – 3 fb-1

1.5 million DsDs events, 0.3 million tagged Ds decays (480 times MARK III, 130 times BES)

Year 3 (3100), 1 fb-1 –1 Billion J/ decays (170 times MARK III, 20 times BES II)

CLEO-c

A 3 yearprogram

4140~S

…and about to begin the year 1 program with 50 pb-1

@ (3770) X5 Mark III with a state of the art detector that isunderstood at a precision level, and has proven itself withpioneering measurements of Vub, Vcb, & radiative penguins, discovery of the YD states and DsJ(2463) and many more.


Unique Opportunities at Charm Thresholds

(DoDo) = 5.8 nb

(D+D-) = 4.2 nb

(Ds Ds) = 0.5 nb

R (units of (+))

(+)= 5.4 nb at 4 GeV

(3770) DD s ~4140 DsDs


b c

u u

u

dW

fb

d b

dt

tW WBf Bf

u

,d sW

Mf

v

Mf

q

q

M e

e

Decay constants are important in many processes

M

BDD s ,,

Q

q

QqV

*W

b t s

W


CKM Facts

sin 2 0.78 0.08

0.489 0.008 psDM


Vub/Vub 25%lB

l

D

Vcd/Vcd 7%lD

Vcs/Vcs =16%l

B D

Vcb/Vcb 5%

Bd Bd

Vtd/Vtd =36%

Bs Bs

Vts/Vts 39% Vtb/Vtb 29%

Vus/Vus =1%

l Vud/Vud 0.1%

e

pn

t

b

W

Goal for the decade: high precision measurements of Vub, Vcb, Vts, Vtd, Vcs, Vcd, & associated phases. Over-constrain the “Unitarity Triangles”- Inconsistencies New physics !

Many experiments will contribute. Measurement of absolute charm branching ratiosAt CLEO-c will enable precise new measurements at Bfactories/Tevatron to be translated into greatly improved CKM precision.

Precision Quark Flavor Physics

CKMMatrixCurrentStatus:

Nc Wcs


Experiment Current Full K-+

BABAR 91 fb-1 500 fb-1 6.6 x 106

Belle 46.2 fb –1 500 fb-1 6.6 x 106

CDF(Run II-a) 65 pb –1 2 fb-1 14 x 106

CLEO-c - 3 fb-1 5.5 x 105

BESIII - 30 fb-1 5.5 x 106

Super Charm - 500 fb-1 9.2 x 108/ 107s

SuperKEKB - 2 ab-1 2.5 x 107/ 107s

SuperBABAR - 10 ab-1 1.3x 108/ 107s

BTeV - ~6 x 108/ 107s

Charm Facilities

Future charm data sets

Documents

Fully leptonic and semileptonic decay