1. Recent results on kaon rare decays from the NA48/2 experiment High Energy Physics in the LHC Era December 11-15 2006, Valparaiso – Chile Massimiliano Fiorini (Università degli Studi di Ferrara – INFN Ferrara) on behalf of the NA48/2 Collaboration: Cambridge, CERN, Chicago, Dubna, Edinburgh, Ferrara, Firenze, Mainz, Northwestern, Perugia, Pisa, Saclay, Siegen, Torino, Vienna

2. Outline The NA48/2 experiment at CERN SPS The K ±  π ± π 0 γ decay (K π2γ )  Matrix element contributions  Experimental status  NA48/2 preliminary measurement of Direct Emission and Interference Terms The K ±  π 0 π 0 e ± ν decay (K e4 00 )  Introduction and events selection  NA48/2 preliminary measurement of Branching Ratio and Form Factors Conclusions

3. The NA48/2 simultaneous beams K+K+ K−K− BM P K spectra, 60  3 GeV/c 54 60 66 Width ~ 5 mm K+/K- ~ 1.8  p/p ~ 1 %  x,y ~ 100  m SPS protons @ 400 GeV/c Simultaneus, unseparated, focused beams

4. NA48/2 detector Spectrometer: Spectrometer: LKR calorimeter LKR calorimeter Hodo Hodo, AKL MUV HAC MUV, HAC Kabes Kabes

5. NA48/2 data taking periods 2003 2003 run: ~ 50 days 2004 2004 run: ~ 60 days Total statistics in 2 years:  K   π + π - π ± : > 3·10 9  K   π 0 π 0 π ± : > 1·10 8 Rare K ± decays: BR’s down to 10 –9 can be measured >200 TB of data recorded A view of the NA48/2 beam line Primary goal: Search for CP-violating charge asymmetries in K ±  3  decays (see Dmitri Madigozhin talk on Friday Plenary Session)

6. K ± →π ± π 0 γ decay

7. Gamma production mechanism DEIB IB DE IBINT DE Γ ± depends on 2 variables (W e T * π ), reduced to only W by integration With this parametrization the ratio data/MC(IB) has the form 1+αW 2 +βW 4 P * K = 4-momentum of the K ± P * π = 4-momentum of the π ± P * γ = 4-momentum of the radiative γ Lorentz invariant variable:

8. W distributions for IB, DE, INT IB and DE are well separated in W Inner Bremsstrahlung(IB) : (2.75±0.15) × 10 -4 PDG 2006 (55<T * π <90 MeV) Direct Emission (DE) : (4.4±0.8) × 10 -6 PDG 2006 (55<T * π <90 MeV) Interference (INT) : not yet measured

9. K π2γ amplitudes Two amplitudes:  Inner Bremsstrahlung (IB) Calculable: QED corrections to K ±  π ± π 0 Suppressed by ΔI=1/2  Direct Emission (DE) Insight on weak vertex structure Electric contribution (E) comes from L 4 ChPT lagrangian and loops L 2 (non predictable) Magnetic contribution (M) has contributions from reducible chiral anomaly (WZW calculable) and also direct contributions (non predictable) Interference (INT) possible between IB and electric part of DE  Measuring at the same time DE and INT gives measurement of both M and E  In addition CPV could appear in INT Present experimental results seem to suggest a M dominated DE

10. Experimental measurements All the measurements have been performed: in the T* π region 55-90 MeV to avoid π ± π 0 π 0 and π ± π 0 BG assuming INT term = 0 BNL E787 KEK E470 Interference measurements: ExperimentYear# EventsBR(DE) × 10 6 E787 E470 E787 E470 ISTRA 2000 2003 2005 2006 19836 4434 20571 10154 930 4.7 ± 0.8 ± 0.3 3.2 ± 1.3 ± 1.0 3.5 ± 0.6 + 0.3 -0.4 3.8 ± 0.8 ± 0.7 3.7 ± 3.9 ± 1.0 History of DE Branching ratio NA48/2 has analyzed > 5 times more events

11. What’s new in NA48/2 measurement In-flight Kaon decays Both K + and K - in the beam (possibility to check CP violation) Very high statistics (220K π ± π 0 γ candidates of which 124K used in the fit ) Enlarged T* π region in the low energy part (0 < T* π < 80 MeV) Negligible background contribution < 1% of the DE component Good W resolution mainly in the high statistic region More bins in the fit to enhance sensitivity to INT Order ‰ γ mistagging probability for IB, DE and INT Fit with free interference term

12. Enlarged T *  region T * π (IB) T * π (DE) T * π (INT) Standard region Using standard region 55 < T* π < 90 MeV is a safe choice for background rejection (π ± π 0 π 0 and π ± π 0 ) But the region below 55 MeV is the most interesting for DE and INT measurements The presented measurement is performed in the region 0 < T* π < 80 MeV to improve statistics and sensitivity to DE

13. K ± →π ± π 0 γ selection Track Selection # tracks = 1. P π+ > 10 GeV E/p < 0.85 No muon hits 0 MeV < T * π+ < 80 MeV Gamma selection N γ = 3. (well separated in time LKr clusters) Minimum γ energy > 3 GeV (>5 for the fit) Gamma tagging optimization CHA and NEU vertex compatibility Only one compatible NEU vertex BG rejection cuts COG < 2 cm Overlapping γ cuts |M K -M KPDG | < 10 MeV 200K events

14. Reconstruction strategy Z V (CHA) γ1γ1 γ3γ3 γ2γ2 Z V (2-3) Z V (1-3) Z V (NEU) LKr We can get two independent determination of the K decay vertex: - The charged vertex Z V (CHA) using the K and π flight directions (DCH) - The neutral vertex Z V (NEU) imposing π 0 mass to gamma couples (LKr) For the neutral vertex we have 3 values: Z V (12), Z V (23), Z V (13) We evaluate the kaon mass for all of them and then choose the vertex giving the best kaon mass. Once the neutral vertex has been chosen we also know what the radiated γ is.

15. Main BG sources Physical BG rejection:  For π ± π 0 we can rely on the cut in T * π < 80 MeV, M K and COG cuts  For π ± π 0 π 0 we have released the T * π cut, but we can anyway reach required rejection with kaon mass cut (missing γ) and overlapping γ cut (fused γ) Accidental BG rejection: mainly π ± π 0, K e3 (π 0 e ± ν) and K μ3 (π 0 μ ± ν)  Clean beam, very good time, space, and mass resolutions. DecayBRBackground mechanism K±→π±π0K±→π±π0 (21.13±0.14)%+1 accidental or hadronic extra cluster K±→ π±π0π0K±→ π±π0π0 (1.76±0.04)%-1 missing or 2 overlapped gammas K±→π0e±νK±→π0e±ν (4.87±0.06)%+1 accidental γ and e misidentified as a π K±→ π0μ±νK±→ π0μ±ν (3.27±0.06)%+1 accidental γ and μ misidentified as a π K ± → π 0 e ± ν (γ)(2.66±0.2)·10 −4 e misidentified as a π K±→ π0μ±ν(γ)K±→ π0μ±ν(γ)(2.4±0.85)·10 −5 μ misidentified as a π

16. Fused  rejection:overlapping  cut Split 1 out of the 3 clusters in two γ of energies: εγ 1 =xE CL εγ 2 =(1-x)E CL now we got 4 γ’s and we start reconstructing the event as a π ± π 0 π 0. Evaluate the Z V (x) pairing the gammas and extract x imposing that: Zv(π 0 1 )= Zv(π 0 2 ) same K decay vertex: the 2π 0 came from the same K! Zv(π 0 2 ) Zv(π 0 1 ) Put x back in the Zv(π 0 2 ) to get the real Z V (neu) If the |Zv(CHA)-ZV(neu)| < 400 cm the γ are really fused and so we discard the event Fused gamma events are very dangerous BG source: - M K and COG cuts automatically satisfied! - Releasing the T * π cut they can give sizable contribution NA48 LKr is very good to reject them: - very high granularity (2×2 cm) cells - very good resolution in Z vertex Multi step algorithm looped over clusters:

17. BG rejection performance Source%IB%DE π ± π 0 π 0 ~1·10 -4 ~0.61·10 -2 Accidentals<0.5·10 -4 ~0.3·10 -2 total background < 1% DE component Selected region 220K events K±  π±π0π0K±  π±π0π0 K±  π±π0γK±  π±π0γ All physical background can be explained in terms of the π ± π 0 π 0 events only. Very small contribution from accidentals

18. ■ DE ▼ IB The mistagged  events: a self BG The mistagging probability has been evaluated in MC as a function of the mistagging cut to be 1.2‰ at 400 cm Mistagging problem:  mistagged gamma events behave like BG because they can induce fake shapes in the W distribution  they tend to populate the region of high W simulating DE events  must keep mistagging probability as small as possible Simply demanding compatibility between zvc and best zvn gives 2.5% mistagging probability Solution: Reject events with a second solution for neutral vertex close to best one Require |zvn (second)-zvn (best)| D zvn > xx cm

19. The K ±  π ± π 0  decay. Trigger L1 trigger  Require one track and LKr information (peaks) compatible with at least 3 clusters  This introduces an energy dependence  distortion of W distribution  Correction found using all 3  events ( K ±  π ± π 0 π 0 with  lost) and applied to Monte Carlo L2 trigger (rejects K ±  π ± π 0 )  Using DCH information and assuming 60 GeV kaon along z axis on-line processors compute a sort of missing mass of the K-π system  Cut events whose missing mass is compatible with π 0. Equivalent to T* π < 90 MeV cut  To avoid edge resolution effects require T* π < 80 MeV in analysis L1 requires n x >2 or n y >2

20. Data MC comparison Data MC for E γ (W<0.5) W(Data)/W (IB MC ) Fitting region IB dominated region The IB dominated part of the data W spectrum is very well reproduced by MC The radiated γ energy (for the IB part of the spectrum) is very well reproduced E γmin cut

21. Fitting algorithm To get the fractions of IB(α), DE(β), INT(γ), from data we use an extended maximum likelihood approach: The fit has been performed in 14 bins in W, between 0.2-0.9, with a minimum γ energy of 5 GeV, using a data sample of 124K events. To get the fractions of DE and INT the raw parameter are corrected for different acceptances

22. Systematic uncertainties EffectSyst. DESyst. INT Energy scale+0.09-0.21 Fitting procedure0.020.19 L1 trigger±0.17±0.43 Mistagging_±0.2 L2 Trigger±0.17±0.52 Resolutions difference<0.05<0.1 LKr non linearity<0.05 BG contributions<0.05 TOTAL±0.25±0.73 Many systematic checks have been performed using both data and MC Trigger efficiency dominates In 2004 both L1 and L2 triggers have been modified in order to reduce systematics

23. Fit results First measurement in the region 0 < T * π < 80 MeV of the DE term with free INT term. First evidence of a non zero INT term NA48/2 Preliminary The error on the results is still dominated by statistics and we could profit of 2004 data (and the remaining fraction of 2003 data) to reduce statistical uncertainties. High correlation (ρ=-0.92)

24. INT=0 fit: just for comparison For comparison with other experiments, we have also extracted the fraction of DE, with the INT term fixed to 0 in the region 55-90 MeV. A likelihood fit using IB and DE MC only has been performed in the region 0 < T * π < 80 MeV. Extrapolating to the 55-90 MeV region using MC we get: The analysis of fit residuals shows a bad χ 2 Description in term of IB+DE only is unable to reproduce W data spectrum.

25. K ± → π 0 π 0 e ± ν decay

26. Introduction to Ke 4 00 Ke4 decays  form factors are good constraints on ChPT Lagrangian parameters  clean sources of π-π pairs at low energy (extraction of scattering lengths)  theoretically related to each other by isospin arguments Ke 4 00 is the simplest because decay kinematics is described by only one form factor (2 identical π 0 ’s in final state  no P wave) Best measurement so far by KEK-E470 (stopped kaon decays) based on 216 events  Measured branching ratio (2.29  0.33) × 10 -5

27. Signal selection Ke 4 00 Signal Topology:  1 charged track  2 π 0 ’s (reconstructed from 4γ’s in LKr)  1 electron  some missing energy and p T (neutrino) Analysis cuts:  ≥ 4 good γ clusters in LKr  2 good π 0 ’s with similar vertex positions  Cut on E/p > 0.95 and on shower width for e/π separation  Assume 60 GeV/c Kaon momentum traveling on z axis for neutrino reconstruction  Elliptical cut in plane m K (hypothetical π ± π 0 π 0 mass) and p T in order to eliminate K ±  π ± π 0 π 0 decays

28. Background estimate Background: main sources  π  π 0 π 0 decay + π misidentified as e (dominant)  π 0 e  νγ (K e3γ ) decay + accidental γ In total 9642 selected events (2003 data only) with the following BG:  260 ± 94 from K ± → π ± π 0 π 0  16 ± 2 accidental BG form Ke3(γ) Total contamination: 3%

29. Branching Ratio Measurement The statistical error can be further reduced using the 2004 data set (28K events) Using only a fraction of 2003 data ( 9642 signal events with 276  94 background events) and π  π 0 π 0 as normalization channel, the Branching Ratio of the K e4 00 decay has been measured: The result has been crosschecked using also Ke3 as normalization channel leading to consistent result. NA48/2 Preliminary

30. The K e4 00 form factors In this case we have only 1 form factor F (2 identical  0 ): The fit has been performed using both 2003 and 2004 data (~38K events) No sensitivity to f e reached → f e set to 0. Under this assumption we get: Those values are consistent with the ones measured by NA48/2 in “charged” K e4  see detailed presentation by Dmitri Madigozhin NA48/2 Preliminary

31. Conclusions NA48/2 has performed the first measurement of the DE and INT terms in the region 0 < T * π < 80 MeV for the decay K ± → π ± π 0 γ: The results seem to indicate the presence of a negative, non vanishing, interference and therefore a non negligible contribution of E terms to the DE An improved measurement of the K e4 00 BR has been achieved, to be compared with recent published value: In addition Form Factors are measured, consistent with the charged K e4 measurement The results can be further improved using the remaining fraction of 2003 data and the full 2004 statistics NA48/2 Preliminary NA48/2 Preliminary

32. SPARE SLIDES

33. Aim to reject K ± → π ± π 0 events and get K ± → π ± π 0 π 0. It’s based on the online computation of Mfake: Only events with M FAKE < 475 MeV, are collected by the trigger MBX1TR-P LVL2 trigger

34. Ke4 neutral decays : formalism Branching fraction and Form factors measurements: Two identical π 0 (no P wave)  only ONE form factor F s S e /4m 2 π0 S π /4m 2 π0 background