1
A. Dabrowski, April 20th 2007 Γ(Ke3/pipi0); Γ(Kμ3/pipi0)
Kaon Semileptonic Decays Measurements
Γ(Ke3) / Γ(π±π0) Γ(Kμ3) / Γ(π±π0)Γ(Kμ3) / Γ(Ke3)
Anne DabrowskiNorthwestern University
Ph.D. Thesis Defence PresentationApril 20th 2007
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Ke3: eK eK 0
Kμ3: 0K
Γ(Ke3) / Γ(π±π0) Γ(Kμ3 ) / Γ(π±π0)Γ(Kμ3) / Γ(Ke3)
Measurements
3 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)
Outline
• Theoretical Motivation for Measurements– Extract CKM Matrix Element Vus; Br(Ke3),Br(Kmu3)– Test Lepton Universality; Γ(Kμ3)/Γ(Ke3)
• Experimental Setup– K+/K- Beamline– NA48 Detector
• Event Selection– Trigger– Fiducial volume & Kinematics– Particle Identification Requirements– Background Estimation
• Result– Γ(Ke3)/Γ(π±π0), Γ(Kμ3)/Γ(π±π0), Γ(Kμ3)/Γ(Ke3)
• Discussion– Extraction of Vus– Test of Lepton Universality
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Extract Vus
Measure: Γ(Kl3) / Γ(π±π0)
Br(Kl3) / Br(π±π0)
Assume branching ratio (Br) for π±π0 extract Br(Kl3)
Measure Br(Kl3)
Extract
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Lepton Universality; Check of form factor measurements
)1(/)1()(/)(
)]0(/)0([ 332eK
eKKK
eee II
KKfgfg
)1(/)1()]0(/)0([)(/)( 233
eK
eKKK
eee IIfgfgKK
Measure ratio
phase space integrals based on form factors
radiative corrections
Assuming mu-e universality & linear approximation for the form factors:
Relationship between the form factors λ+ and λ0 and the ratio of partial widths cross check of form factor measurements
λ+λ0
Test Universality
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NA48 Experiments
NA48 experiment
Designed for understanding of systematic errors to 10-4 level, to measure direct CP violation in neutral kaons, Re(ε’/ε)
Similarly, NA48/2 Direct CP violation in charged Kaon decays
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NA48/2 Beamline, Special Run
K± collected during 2003 special low intensity (1/8) minimum bias run
K+ flux 3.2x106; K+/K- ~ 1.78 (production rate at target)
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Beam
Beam Energy (60±3) GeV
Width ~ 5mm
K+/K- ~ 1mm
K+/K- Beam focused to DCH1 to within 1mm plot using reconstructed
π+π0
π-π0
K+ K- collimator
collimator
DCH 1
DCH 1
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Measurement ingredients and strategy
Measured the ratios of the decay rates:
Same event signature in the ratio: 1 charged track and 2γ’s from a π0 decay Cancellation of uncertainties
Differentiate signals particle ID & kinematics
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Trigger
Special low intensity run Minimum bias triggers
Main trigger “Q1”/4
Based on hit in the charge hodoscope in each of two planes, within the same geometric quadrant
Trigger efficiency calculation “1-Trackloose”/100
(based on Hits in the DCH)
Trigger efficiency high, and independent of track type
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Beam and Spectrometer Settings
ZZ
XXYY
JuraJura
SaleveSaleve
Achromats: KAchromats: K+ + UpUp
Achromats: KAchromats: K++ DownDown
B+
BKK++KK--
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Track Treatment
ZZ
XXYY
JuraJura
SaleveSaleve
Achromats: KAchromats: K+ + UpUpB+
KK++KK--
1 track after excluding Ghost-tracks
–Hodoscope time window (-17. 20. ns)
–Diff DCH time, hodoscope time ±6ns
–Track quality > 0.8
–Beta, alpha corrections from database
–z charge vertex (-500,7000) cm
–Blue Field correction applied
Event time window (ns)
(HOD – DCH) time (ns)
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Treatment of Additional Photons in Event
Make inclusive measurements, Ke3(γ) K2π(γ) and Kμ3(γ) additional photons in the event are kept
Photon candidates (3 < Eg < 65) GeV
Difference between 2 γ candidates < 2ns
Separation of 2 γ candidates > 10 cm Ke3/Kmu3 events > 35 cm for pipi0 events
2
0
1ijjiij DEE
mZ
among all the possible γ pairings, the couple for which |Δz| is smallest is selected
|Δz| difference neutral and charge vertex
No cut on |Δz| is applied
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|Δz| difference neutral and charge vertex
Resolution depends on Charge Vertex (average z position) and Neutral Vertex (average energy pi0)
Monte Carlo Simulation describes data
Ke3
π±π0
Kμ3
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Reconstructed γγ mass
Another test of goodness of reconstruction, is the invariant γγ mass.
Ke3
π±π0
Kμ3
21ijjiij DEE
mZ
•Plotted , events from Data with 1 track and 2 γ’s, log scale:
•Non Gaussian tails same order for each of the three channels
•Do not apply a cut on pi0 mass
•Low accidental activity
% of tot events with 2 gammas
90%
97.7%
99.7%
Assume “charge” vertex for Zij and calculate the invariant γγ mass
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Differentiating Kinematics
Take advantage of:
1. Missing energy (Semileptonic vs pipi0 event)
2. Two vs three body decay kinematics
Rec. Kaon Mass under π± assumption
π±π0
Kl3Kl3
Rec. missing mass
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Differentiating Kinematics(2)
Take advantage of:
1. Missing energy (Semileptonic vs pipi0 event)
2. Two versus three body decay kinematics
Transverse Momentum (PT)
Ke3
Kμ3
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Particle ID Muons
Use sample of K±→μν (Br(63.44±0.14)%)to calculate muon ID efficiency:
• hit in planes 1 and 2 of the muon counters
• within 2 ns of hodoscope time K±→μν signal
Momentum (GeV/c)
PT
(GeV
/c)
Momentum (GeV/c)
Average efficiency, above 10 GeV/c
μν
Background (0.012+-0.001)%
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Particle ID Electrons & Pions
Constrained sub-sample of electrons with background level at (0.07±0.01)x10-4
Average efficiency E/P > 0.95: (98.59±0.09)%
Timing and fiducial requirements applied as in analysis
E/P > 0.95
Effi
ciency
E/P < 0.95
Effi
cien
cy
Track momentum measurement from spectrometer (P) & energy in deposited in LKr (E)
Constrained sub-sample of pions with background level at (0.1±0.01)x10-3
Average efficiency E/P < 0.95: (99.54±0.01)%
Timing and fiducial requirements applied as in analysis
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Background Estimation
Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)
Background subtraction in both signal and normalisation
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Background Estimation
Low intensity running conditions, accidental activity 10-4 Simulation of the beam, detector response and kaon decay amplitudes sufficient to describe signal and background
Sources of Background Ke3:
pions with E/P > 0.95
Missing mass squared distribution before missing mass cut is applied
Arrows indicate signal region
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Background Estimation Ke3
Ke3 distributions low level of background after the final cuts, particle ID applied. Background negligible 10-
4 level. Simulation describes data.
Charged vertex (cm) Transverse Momentum PT (GeV/c)
Energy π0 (GeV)
25 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)
Background Estimation pipi0
pions that decay are contrained in pipi0 sample largest background from Kmu3 events, where μ & π0 contain most of visible energy
also contributions from Ke3 where E/P < 0.95
Charged vertex (cm) Transverse Momentum PT (GeV/c)
Energy π0 (GeV)
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Background Estimation Kmu3
Recall: MUC used to select muons pions that decay & detected in MUC are background to Kmu3.
Correction is at xxx level?
Monte Carlo decays pions before LKr small correction from data needed to estimate pions decay between LKr and MUC (not simulated by MC)
MC simulation describes DATA well, even in tail that is dominated by π background sensitive to π decay probability
27 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)
Background Estimation Kmu3
Charged vertex (cm) Transverse Momentum PT (GeV/c)
Energy π0 (GeV)
Background at the 0.2% level, dominated by K±→π±π0π0, where π±→μν
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Comparison between Data and Simulation Ke3
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Comparison between Data and Simulation Kmu3
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Comparison between Data and Simulation pipi0
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Kl3 form factors
))(),(( 0 tftfI lK
22 /)( Kl Mmtf
is needed to extract Vus
Standard Model, Born level Matrix element for K/3 decays
t is the square of the four-momentum transfer to the lepton system
this part of the matrix is only relevant for Kμ3 decays
)()(
)()(220 tfmm
ttftf
K
f0(t) is a combination of the two
)(0, tf are the vector and scalar form factors are related to the angular momentum of the lepton pair
32 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)
Form Factor Parameterization used
PDG 2006 measurements for Charged Kaons,
Pole parameterization:
Quadratic
Linear
If the f.f acquire a physical meaning, they are related to the exchange of K* resonances with spin-parity 1-/0+ and masses mv/ms
Change in acceptance due to varying form factor parameters above by one sigma taking into account in systematic estimation~ 10-4 effect
Systematic assigned also due to alternative form factor models, for example the pole model. Full difference in acceptance assigned as systematic error ~ 10-4 effect
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Kl3 event generator
Events generated according to the Dalitz plot density distribution
Put in plots for Ke3 and Kmu3
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Radiative corrections
Radiative corrections are added to the Dalitz plot density:
•use prescription by Ginsberg (real and virtual corrections)
•real bremmstrahlung photons added using the PHOTOs program
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Sensitivity of acceptance to radiative corrections
Reconstruction sensitive to inclusion of real photons
Energy of leptons in Rest frame of Kaon well described by simulation, despite sensitive to radiative corrections
Ke3
Kμ3
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Result BR(Ke3) & Br(Kμ3)
SystematicsSystematics
•Detector Acceptance
with radiative effects
•Trigger Efficiency
•Form Factors (Input Value & Models)
Error dominated by BR(K2π) uncertainty
BNL-E865 result is confirmed
Taking BR(K2π) from PDG
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Result: Γ(Kμ3) / Γ(Ke3)
Consistent with KEK-E246 & PDG 2006
=
Comparing to semi-empirical prediction & assume linear f.f. model;
Extract
(PDG)
Verification of μ-e universality
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Conclusion
Measured ratio of three charged kaon decay modes
Br(Ke3) and Br(Kmu3) better than previous PDG averages for charged kaon decays
Confirm BNL-E865 measurement
•Extraction of Vus consistent with CKM unitarity, and most accurate for charged kaons, and in agreement with CKM unitarity
Verification of μ-e universality
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