1. Charged Kaon Semileptonic Decays: K±  π0μ±ν and K±  π0e±ν and their Ratio at the NA48/2 experiment K0μ3 form factors at NA48 experiment
Anne Dabrowski
Northwestern University
On behalf of the NA48 and NA48/2 Collaborations

2. Outline: NA48 Measurements presented
NA  Kmu3 form factors λ+ , λ0
KL collected during 1999 ε’/ε data taking
Special minimum bias run, KL beam only
Physics Letters B 647 (2007) 341–350
NA48/2  Br (Ke3), Br(Kmu3)
K+/K- Decays
Special low intensity minimum bias data taking (2003)
J. R. Batley et al., hep-ex/ v2
Eur. Phys. J C 50 2, (2007) erratum

3. Vus and Kl3
Kl3 decays  the most accurate and theoretically cleanest way to extract |Vus|
NA48/2  Br (Ke3), Br(Kmu3)
NA  Kmu3 form factors λ+λ0
The formula is proportional to matrix element squared
In the Isospin limit. The full form factor for the neutral and the charged kaon are equal.
Extract
Slide from:
Michele Veltri CKM 2006

4. Lepton Universality & cross-check of Form Factor measurements
phase space integrals based on form factors
radiative corrections
Measure ratio
Test Universality
Assuming μ-e universality & linear approximation (order λ+2 and λ02 ) for the form factors*: λ+ λ0
Relationship between the form factors λ+ and λ0 and the ratio of partial widths  cross-check of form factor measurements
* JB, GC, GE and JG (1994) hep-ph/

5. NA48/2 Beamline
K± collected during 2003 special low intensity (1/8) minimum bias run
K+ flux ~3.2x106; K+/K- ~ 1.78 (production rate at target)
(Trigger efficiency > 99.8% and independent of decay type)
10cm
1cm
Mention the purpose of the copper collimators, the middle section to stop neutral particles, and the size of the slit to make the momentum selection
The opening of the TAX can be controlled to modify the intensity
100 m
50 m

6. NA48 Detector Muon Scintillation Counters
Put in the resolution for the spectrometer for K_L
Muon Scintillation Counters
3 planes, oriented alternately vertically and horizontally in 25 cm strips
.σt350 ps

7. Analysis Strategy
K+/K- Semileptonic Decay Branching Fractions

8. Analysis 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
Common Selection:
Tracks
Photons
Differentiate signals
 Kinematics & Particle Identification (e±/μ±/π±)
Decay Specific Selection:
Kinematics
Particle ID

9. Common Track SelectionY X
Achromats: K+ Up B+
K+K- Z
Event time window (ns)
(Event – DCH) time (ns)
1 track required in fiducial region
Hodoscope defines event time window
Difference (Event – DCH) time ±6 ns
Use position and slopes (dx/dz and dy/dz) measured in spectrometer, to extrapolate back to Kaon decay vertex (-500,7000) cm
Correct tracks due to residual magnetic fields in decay volume and small time dependent changes in spectrometer magnet
Vertex region is
13 m from the final collimator
25 meters From the DCH
Avoid regions of conversions and multiple scattering that are difficult to simulate in the MC

10. Common Selection of photons that originate from π0 decay
Make inclusive branching ratio measurements:
Ke3(γ) K2π(γ) and Kμ3(γ)  additional photons in the event are kept.
Label 2γ’s that originate from a π0 decay:
Exploit two methods for calculating Kaon decay vertex
Track extrapolation (already discussed)
Kinematics of π0 decay
γ-pairing corresponding to smallest |Δz| is selected
|Δz| difference neutral and charge vertex
No cut on |Δz| is applied

11. Differentiating Kinematics (1)
Take advantage of:
Missing energy (Semileptonic vs pipi0 event)
Two vs three body decay kinematics
Take advantage of:
Missing energy (Semileptonic vs pipi0 event)
Two vs three body decay kinematics
Reconstruct Kaon Mass under π± mass assumption for the track
π±π0
π±π0
Kl3
Kl3
Kl3 or

12. Differentiating Kinematics (2)
Take advantage of:
Missing energy (Semileptonic vs pipi0 event)
Two vs three body decay kinematics
Assumption of Track Mass
Reconstruct Missing Mass Squared
(under differing mass assumptions for the track) π± e± μ±
π±π0 MC
Ke3 MC
Kμ3 MC

13. Differentiating Kinematics(3)
Take advantage of:
Missing energy (Semileptonic vs pipi0 event)
Two v.s. three body decay kinematics
Transverse Momentum (PT)
Ke3
Kμ3
Events (log scale)
Equivalently, reconstructing energy in the rest frame of the kaon also powerful

14. Additional selection Ke3 & pipi0
Use E/p to distinguish electrons from pions
Illustration from Data
Choose Electrons E/p > 0.95
Efficiency (98.59±0.09)%
Momentum region:
5 GeV/c < p < 35 GeV/c
Choose Pions E/p < 0.95
Efficiency (99.524±0.009)%
Momentum region:
10 GeV/c < p < 50 GeV/c
Efficiency for measuring & used in analysis as a function of momentum

15. Additional selection Kμ3
Difference: (event time-Muon Detector time) ns
Use muon counters for muon identification
Require hits in both of the first two planes of the muon counters within 2ns
Low accidental activity
10 GeV/c < p < 40 GeV/c
Average efficiency, above 10 GeV/c
Measured with sample of K±→μ±ν decays

16. Reconstructed γγ mass Test of “quality” of reconstruction.
Given reconstructed charge vertex (Ztrack)  calculate the invariant γγ mass
Plotted Data  invariant γγ mass from events with 1-track and 2γ’s
Non Gaussian tails same order for each of the three channels
Do not apply a cut on pi0 mass
Low accidental activity
Mass centered on π0 mass

17. Final Data Samples After all the selection criteria: Channel K+ K- Ke3
56 195
30 898
Kμ3
49 364
27 525
Pipi0
 Extract Ratio’s
Require:
Acceptance, Particle ID Efficiency, Trigger Efficiency and Background estimation
Require:
Acceptance, Particle ID Efficiency, Trigger Efficiency and Background estimation

18. Background Estimation Ke3
Low intensity  accidental activity << 10-4
 Simulation of the beam, detector response and kaon decay amplitudes sufficient to describe signal and background
Arrows indicate signal region
Background to Ke3:
 pions with E/P > 0.95
Release Missing-Mass cut to illustrate background
MC Simulation describes data including the tails
Background  negligible (10-4 level) after Cuts & particle ID

19. Background Estimation Kμ3
Arrows indicate signal region
Select muons with muon counters
pions that decay & detected in muon counters are background to Kμ3.
MC simulation describes DATA
including the tail that is dominated by background containing π±
sensitive to understanding π± decay probability
Background ~ 0.2% level

20. Background Estimation pipi0
Allow μ± in pipi0 sample (i.e. π± μ± ν)
Background from Kμ3 events, where μ± & π0 contain most of visible energy
Small contributions from Ke3 where E/P < 0.95
Total Background level ~ 0.3%

21. Acceptance Calculation

22. Semileptonic Decay Event Simulation
Events generated according to the Dalitz plot density distribution
A, B and C are kinematic terms, and t is the transferred 4-momentum to the lepton pair (q2)
Use PDG 2006 form factors for Charge Kaon decays
Quadratic
Local creation of the lepton pairs requires that they be functions of the square of the four momentum transfer to the leptons.
Configuration of the lepton system
(PDG 2006)
Linear
(PDG 2006)
Other models considered - Pole

23. Modify Dalitz plot density with Radiative corrections
Radiative corrections are added to the Dalitz plot density:
prescription by Ginsberg (real and virtual corrections)
real bremmstrahlung photons added with PHOTOs program
Acceptance sensitive to inclusion of real gammas
Ke3
Local creation of the lepton pairs requires that they be functions of the square of the four momentum transfer to the leptons.
Kμ3
Simulation described the data
Acceptance (Ke3) checked by MC program of C. Gatti

24. Inputs to Final results
Total Number of events K+/(K-)
Ke3: 56k (31k)
Kμ3: 49k (28k)
π±π0 : 462k(257k)
Background < 1 %
Trigger efficiency > 99.8 %
Acceptance * Particle ID K+(K-)
Ke3: ± (6.94 ± 0.01)%
Kμ3: ± (9.25 ± 0.01)%
Pipi0: ± (14.12 ± 0.01)%
Local creation of the lepton pairs requires that they be functions of the square of the four momentum transfer to the leptons.

25. Systematic due to form factor parameters
Reference form factors:
Quadratic
(PDG 2006)
Linear
(PDG 2006)
Effect on final measurements based on variation of Form factor parameters
 assigned as a systematic error corresponding to the change in acceptance due to varying form factor parameters above by one σ ~ 5x10-4 effect 
Change in result owing to using Pole Model:
Mv = 0.887±0.005 GeV/c2; Ms = 1.187±0.050 GeV/c2 (PDG 2006 K0)
 Full difference in result assigned as a systematic error ~ 5x10-4

26. Result: Γ(Ke3/pipi0); Γ(Kμ3/pipi0)
Systematics
Detector Acceptance with radiative effects
Particle ID efficiency
Trigger Efficiency
Form Factors (Input Value & Models)
No systematic effect was found related to the detector or kinematics

27. Result: Γ(Ke3/pipi0); Γ(Kμ3/pipi0)
Both measurements higher than PDG 2006 average by 3.1%(Ke3/pipi0) and 2.8%(Kμ3/pipi0)
Assuming Br(pipi0) from PDG 
Error dominated by BR(K2π) uncertainty
BNL-E865 result is confirmed

28. Extraction of |Vus|f+(0)
Given Br(Ke3) and Br(Kmu3)
HL & MR (1984)
In Good agreement with CKM unitarity

29. Result: Γ(Kμ3) / Γ(Ke3)
Consistent with KEK-E246 & PDG 2006 * =
Comparing to semi-empirical prediction & assume linear f.f. model;
Extract 
(PDG)
% Test of μ-e universality
* JB, GC, GE and JG (1994) hep-ph/

30. KL--> π±μmpνμ Form Factor Analysis
To extract the form factors, fit the Dalitz Plot Density
Well known parameterizations of the form factors are Linear, Quadratic, Pole
In the pole model the f.f. acquire a physical meaning: exchange of K* resonances with spin-parity 1-/0+ and mass mv/ms

31. KL--> π±μmpνμ Form Factor Analysis
Recently new parameterization of the Kmu3 form factors have been proposed [VB, MO, EP & JS Phys. Lett. B 638(2006) 480]
Based on dispersive techniques
Describes simultaneously the slope and the curvature of the f.f.
H(t) and G(t) (Dispersive integrals) have accurate polynomial approximations
Key parameter is ln C = ln [fo(mK2-mπ2)] the value of the scalar f.f. at the Callen-Treiman point
The value of ln C can provide a test of Right Handed quark Currents coupled to the standard W boson
Δ(ε) is the RHC contribution and ΔCT ~10-3 is the Callan-Trieman discrepancy
More information, see Talks E. Passemar & J. Stern after coffee break

32. Results: Form Factor Analysis

33. Conclusion
Measured ratio of three charged kaon decay modes, with better precision than current PDG 2006 measurements
Br(Ke3) and Br(Kμ3) higher than previous PDG averages for charged kaon decays
Confirm BNL-E865 measurement
CKM unitarity OK
Verification of μ-e universality at % level
Measured Kmu3 Form Factors with KL decays:
important for phase space integral evaluation in Vus extraction & for tests of New physics
Observe a quadratic term in expansion of f+(t)
λ0 smaller than what recently reported

34. Extra Slides

35. 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
Average efficiency, above 10 GeV/c
K±→μν signal
Momentum (GeV/c)
PT (GeV/c) μν
Background ( )%

36. E/p Efficiency for electron/pion ID
Track momentum measurement from spectrometer (P) & energy in deposited in LKr (E)
Efficiency measured using DATA
E/P < 0.95
Efficiency
Constrained sub-sample of pions
Average efficiency E/P < 0.95: (99.54±0.01)%
Timing and fiducial requirements applied as in analysis
Efficiency
E/P > 0.95
Constrained sub-sample of electrons
Average efficiency E/P > 0.95: (98.59±0.09)%
Timing and fiducial requirements applied as in analysis

37. Background Estimation Ke3
Energy π0 (GeV)
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)

38. Background Estimation Kμ3
Energy π0 (GeV)
Background at the 0.2% level, dominated by K±→π±π0π0, where π±→μν
Charged vertex (cm)
Transverse Momentum PT (GeV/c)

39. Modify Dalitz plot density with 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
Ke3
Ke3
Corrections Ke3 ~5%
Corrections Kμ3 ~0.5%
Kμ3
Local creation of the lepton pairs requires that they be functions of the square of the four momentum transfer to the leptons.
Kμ3
Generate radiative events outside Dalitz plot

40. Reconstructed γγ mass Test of “quality” of reconstruction.
Take advantage of reconstructed charge decay vertex, to calculate the invariant γγ mass
% of tot events with 2 gammas
π±π0
90%
Ke3
Assume “charge” vertex for Zij and calculate the invariant γγ mass
97.7%
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
Kμ3
99.7%

41. Comparison between Data and Simulation Ke3

42. Comparison between Data and Simulation Kmu3

43. Comparison between Data and Simulation pipi0

44. |Δz| difference neutral and charge vertex
Kμ3
Ke3
π±π0
Resolution of |Δz| is a function of the average z position, and the average energy pi0
Monte Carlo Simulation describes data well including the tails
No cut requirement is made

45. Beam properties
Width ~ 5mm
K+/K- ~ 1mm
Y (cm)
K+/K- Beam focused to First drift chamber (DCH1) (beginning of detector) to within 1mm
 Measured using reconstructed
X (cm)
Beam Energy ~ (60±3) GeV
π+π0 K+
π-π0 K-
GeV
GeV

46. Special Low Intensity run  Minimum Bias Trigger
No cuts on kinematics at the trigger level!
Main Trigger
Hit in the charge scintillating hodoscope in each of two planes, within the same geometric quadrant
Pre-scaling factor of 4 optimize readout bandwidth restrictions
Trigger efficiency calculation
Hits in 3 planes of DCH1
Pre-scaled by factor of 100
Trigger efficiency > 99.8% & independent of track type