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1 A. Dabrowski, April 20th 2007 Γ(Ke3/pipi0); Γ(Kμ3/pipi0) Kaon Semileptonic Decays Measurements Γ(Ke3) / Γ(π ± π 0 ) Γ(Kμ3) / Γ(π ± π 0 ) Γ(Kμ3) / Γ(Ke3) Anne Dabrowski Northwestern University Ph.D. Thesis Defence Presentation April 20th 2007

A. Dabrowski, April 20th 2007 Γ(Ke3/pipi0); Γ(Kμ3/pipi0) 1 Kaon Semileptonic Decays Measurements Γ(Ke3) / Γ(π ± π 0 ) Γ(Kμ3) / Γ(π ± π 0 ) Γ(Kμ3) / Γ(Ke3)

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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

2 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

4 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

5 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

Test CKM Unitarity (2)

6 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

7 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

8 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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)

9 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

10 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

NA48 Detector

11 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

12 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

13 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

Beam and Spectrometer Settings

ZZ

XXYY

JuraJura

SaleveSaleve

Achromats: KAchromats: K+ + UpUp

Achromats: KAchromats: K++ DownDown

B+

BKK++KK--

14 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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)

15 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

16 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

|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

17 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

18 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

19 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

20 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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)%

21 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

22 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

Background Estimation

Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

Background subtraction in both signal and normalisation

23 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

24 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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)

26 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

28 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

Comparison between Data and Simulation Ke3

29 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

Comparison between Data and Simulation Kmu3

30 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

Comparison between Data and Simulation pipi0

31 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

33 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

Kl3 event generator

Events generated according to the Dalitz plot density distribution

Put in plots for Ke3 and Kmu3

34 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

35 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

36 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

37 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

Theoretical Motivation, Vus (2)

38 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

Extraction of Vus

39 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

40 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

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

41 A. Dabrowski, April 20th 2007Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0)

Appendix Data/ MC comparison

)1)(()0(192

)( )2(0

22

3

522

3lEM

lSU

lKusEW

KFK IfVSmGC

Kl