1 BEACH 2006 July 5, 2006 Content I: Why We Study Charm Semileptonic Decays. II: Recent Analyses on...
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Transcript of 1 BEACH 2006 July 5, 2006 Content I: Why We Study Charm Semileptonic Decays. II: Recent Analyses on...
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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
16
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
20
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
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