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

Outline: NA48 Measurements presented NA48  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/0702015v2 Eur. Phys. J C 50 2, (2007) 329-340 + erratum

Vus and Kl3 Kl3 decays  the most accurate and theoretically cleanest way to extract |Vus| NA48/2  Br (Ke3), Br(Kmu3) NA48  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

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/9411311

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

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

Analysis Strategy K+/K- Semileptonic Decay Branching Fractions

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

Common Track Selection Y 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

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

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

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

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

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

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

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

Final Data Samples After all the selection criteria: Channel K+ K- Ke3 56 195 30 898 Kμ3 49 364 27 525 Pipi0 461 837 256 619  Extract Ratio’s Require: Acceptance, Particle ID Efficiency, Trigger Efficiency and Background estimation Require: Acceptance, Particle ID Efficiency, Trigger Efficiency and Background estimation

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

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

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%

Acceptance Calculation

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

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

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: 6.98 ± 0.01 (6.94 ± 0.01)% Kμ3: 9.27 ± 0.01 (9.25 ± 0.01)% Pipi0: 14.18 ± 0.01 (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.

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

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

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

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

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/9411311

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

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

Results: Form Factor Analysis

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

Extra Slides

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 (0.012+-0.001)%

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

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)

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)

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

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%

Comparison between Data and Simulation Ke3

Comparison between Data and Simulation Kmu3

Comparison between Data and Simulation pipi0

|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

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

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