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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
2
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
4
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.
5
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
7
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
8
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!
9
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
12
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.
13
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
14
(D+K* / K) circa 1993
circa 1993
15
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.
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