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) Anne Dabrowski Northwestern University Ph.D. Thesis Defence Presentation April 20th 2007

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 2 Ke3: Kμ3:Kμ3: Γ(Ke3) / Γ(π ± π 0 ) Γ(Kμ3 ) / Γ(π ± π 0 ) Γ(Kμ3) / Γ(Ke3) Measurements

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 3 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 ± π 0 ), Γ(Kμ3)/Γ(π ± π 0 ), Γ(Kμ3)/Γ(Ke3) Discussion –Extraction of Vus –Test of Lepton Universality

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 4 Extract V us Measure: Γ(K l3 ) / Γ(π ± π 0 ) Br(K l3 ) / Br(π ± π 0 ) Assume branching ratio (Br) for π ± π 0  extract Br( K l3 ) Measure Br( K l3 ) Extract

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 5 Test CKM Unitarity (2)

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 6 Lepton Universality; Check of form factor measurements 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 λ 0 and the ratio of partial widths  cross check of form factor measurements λ+λ+ λ0λ0 Test Universality

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 7 NA48 Experiments NA48 experiment Designed for understanding of systematic errors to level, to measure direct CP violation in neutral kaons, Re(ε’/ε) Similarly, NA48/2  Direct CP violation in charged Kaon decays

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 8 NA48/2 Beamline, Special Run K ± collected during 2003 special low intensity (1/8) minimum bias run K + flux 3.2x10 6 ; K + /K - ~ 1.78 (production rate at target)

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 9 Beam Beam Energy (60 ± 3) GeV Width ~ 5mm K+/K- ~ 1mm K+/K- Beam focused to DCH1 to within 1mm  plot using reconstructed π+π0π+π0 π-π0π-π0 K+K+ K-K- collimator DCH 1

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 10 NA48 Detector

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 11 Measurement ingredients and strategy Measured the ratios of the decay rates: Same event signature in the ratio: 1 charged track and 2 γ’s from a π 0 decay  Cancellation of uncertainties Differentiate signals  particle ID & kinematics

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

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 13 Beam and Spectrometer Settings Z X Y Jura Saleve Achromats: K + Up Achromats: K + Down B+ BB K+K-K+K-K+K-K+K-

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 14 Track Treatment Z X Y Jura Saleve Achromats: K + Up B+ K+K-K+K-K+K-K+K- 1 track after excluding Ghost-tracks –Hodoscope time window ( 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)

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 15 Treatment of Additional Photons in Event Make inclusive measurements, K e3(γ) K 2π(γ) and K μ3(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 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

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 16 |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±π0π±π0 Kμ3

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 17 Reconstructed γγ mass Another test of goodness of reconstruction, is the invariant γγ mass. Ke3 π±π0π±π0 Kμ3 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 Z ij and calculate the invariant γγ mass

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 18 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±π0π±π0 K l3 Rec. missing mass

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 19 Differentiating Kinematics (2) Take advantage of: 1.Missing energy (Semileptonic vs pipi0 event) 2.Two versus three body decay kinematics Transverse Momentum (PT) K e3 Kμ3Kμ3

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

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 21 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 Efficiency E/P < 0.95 Efficiency 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

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 22 Background Estimation Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) Background subtraction in both signal and normalisation

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 23 Background Estimation Low intensity running conditions, accidental activity  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

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 24 Background Estimation Ke3 Ke3 distributions  low level of background after the final cuts, particle ID applied. Background negligible  level. Simulation describes data. Charged vertex (cm) Transverse Momentum PT (GeV/c) Energy π 0 (GeV)

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 25 Background Estimation pipi0 pions that decay are contrained in pipi0 sample  largest background from Kmu3 events, where μ & π 0 contain most of visible energy  also contributions from Ke3 where E/P < 0.95 Charged vertex (cm) Transverse Momentum PT (GeV/c) Energy π 0 (GeV)

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

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 27 Background Estimation Kmu3 Charged vertex (cm) Transverse Momentum PT (GeV/c) Energy π 0 (GeV) Background at the 0.2% level, dominated by K ± → π ± π 0 π 0, where π± → μν

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 28 Comparison between Data and Simulation Ke3

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 29 Comparison between Data and Simulation Kmu3

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 30 Comparison between Data and Simulation pipi0

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 31 K l3 form factors 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 f 0 (t) is a combination of the two are the vector and scalar form factors are related to the angular momentum of the lepton pair

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 32 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~ 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

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 33 Kl3 event generator Events generated according to the Dalitz plot density distribution Put in plots for Ke3 and Kmu3

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

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

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 36 Result BR(K e3 ) & Br(K μ3 ) Systematics Detector Acceptance with radiative effects Trigger Efficiency Form Factors ( Input Value & Models) Error dominated by BR(K 2π ) uncertainty BNL-E865 result is confirmed Taking BR(K 2π ) from PDG 

A. Dabrowski, April 20th 2007 Ratio(Ke3/pipi0); Ratio(Kμ3/pipi0) 37 Theoretical Motivation, Vus (2)

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

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

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

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