4/17/2005 FOCUS / Doris Kim 1
Doris Y. KimUniversity of IllinoisUrbana-Champaign
Content ( hep-ex/0410037,
PLB 607 (2005) 233 )
• Part I: Theories of charm semileptonic decays.
• Part II: Reconstructing D0 K + and +
• Part III: q2 dependence, f+(q2)
a. Deconvolution approach: Non-parametric analysis.
b. Parametric fit.
• Part VII: Summary
Measurements of q2 Dependence of D0 K + and + Form Factors.
APS Meeting April 17, 2005
Tampa, FL
4/17/2005 FOCUS / Doris Kim 2
I: Charm semileptonic decay as tests of LQCDThe decay rates are computed from first principles (Feynman diagrams) using CKM matrix elements.
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.
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
qcqV
etc.
4/17/2005 FOCUS / Doris Kim 3
The lattice community is actively fixing the situation and calculating f+ as a function of q2.
hep-ph/0408306PRL 94 (2005) 011601
Theories of D 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.
4/17/2005 FOCUS / Doris Kim 4
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. Now we have enough data, hence,
What do we measure?
2 2pole
1
1 /f
q m
2expf q (old) ISGW1
• Method I: f+(q2) shape obtained non-parametrically by deconvolution.
• Method II: Or fit f+(q2) using specific forms.
(old) pole
* *
2 2 2 2
D D
1
(1 / )(1 / )f
q m q m
modified pole
f+(q2) parameterization
ISGW2 Updated version.
Spin 1 D*S
4/17/2005 FOCUS / Doris Kim 5
• A good muon candidate.
• Cerenkov ID for K/ candidates.
• Good CL’s for D production/decay vertices, and L/ > 5 between two vertices.
• D* tag required, and wrong sign soft subtraction
II. Reconstructing D0 K + and +Selection
~
cutrs-ws
MC ws
12,840 K +
Neutrino Reconstruction
• 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.
* 0D D
K
m K m K
/GeV
/c2
4/17/2005 FOCUS / Doris Kim 6
III.a q2 dependence: Deconvolution approach.
2genq2
genq2genq
2genq 2
genq
2recq 2
recq2recq
2recq
2recq
1 2 2 2 3 21 1 1 2 1 3
1
2 21
122 2 2 3 2
2 1 2 2 2 3
1 2 2 2 3 23 1 3 2
22
33 3
2
2 23
1/ / /
/ / /
/ / /
G G GM M M
G G GM M M
G G GM M M
N f N f N f f qM
M f qN f N f N f
N f N f N f M f q
We actually use a 10 10 matrix
A deconvolution matrix is constructed from the number of events generated in the i-th q2 bin that end up reconstructed in the j-th q2 bin. This matrix is then used to correct data for resolution and efficiency.
4/17/2005 FOCUS / Doris Kim 7
Correcting for charm backgrounds inD0 K +
The background only affects the highest q2 bins.
After subtracting known charm backgrounds, f+(q2) is an excellent match to a pole form with mpole= 1.91 0.04 0.05 GeV/c2 or = 0.32 (CL 87%, 82%).
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
4/17/2005 FOCUS / Doris Kim 8
III.b Parameterized f+(q2) for D0 K + / +
6574 K + events
288 + events
• 2-dim fit: cos l, q2
• Signal ~ MC with reweighted intensity.
• Backgrounds are floated within known uncertainties.
D0W
rest frame
l
4/17/2005 FOCUS / Doris Kim 9
Comparing to Lattice Gauge Result
2f q
K +
21.93 0.05 0.0: 3 / ,poleK m GeV c 0.28 0.08 0.07 1.51.41.(0) / 7 0.3(0)f f
0.30 20.15: 1.91 0.07 /pole GeV cm
4/17/2005 FOCUS / Doris Kim 10
Other q2 information in D0 K l /l
lpole mass is l
Kl
It disfavors ISGW2 form by ~4.2form factor f+(q²)
single-pole model
single-pole model
Based on 820 events
q² / GeV²
Kl
l
Cleo 2004 lpole mass is
Preliminary study
4/17/2005 FOCUS / Doris Kim 11
Fo
cus 05
MK
3
E691
Cleo
91
Cleo
93
E687 tag
E687 in
c
Cleo
041.4
1.6
1.8
2.0
2.2
2.4
2.6
po
le m
ass
Summary of D0 K l l Results
Clearly the data does not favor the simple Ds* pole
2
1.91 0.04
/GeV c
Kl
32
2
2
2
2 324( )
F cq PG V Pd D P
dqf q
New world average for K l
2 2pole
(0)
1 /
ff
q m
New world average for l 0.10 20.071.88 /GeV c
4/17/2005 FOCUS / Doris Kim 12
Question slides