Precision study of charged kaon decays to three pions by the NA48/2 experiment at CERN

1. Precision study of charged kaon decays to three pions by the NA48/2 experiment at CERN Evgueni Goudzovski (Scuola Normale Superiore, Pisa) on behalf of the NA48/2 Collaboration: Cambridge, CERN, Chicago, Dubna, Edinburgh, Ferrara, Firenze, Mainz, Northwestern, Perugia, Pisa, Saclay,Siegen, Torino, Vienna SPP/Dapnia June 4th, 2007

2. Overview • The NA48/2 experiment at CERN SPS:history, physics programme, setup and data taking; • K3 processes: primary physics motivations; • Recent NA48/2 results on K3: • Limit on DCPV charge asymmetry in K+– decays; • Limit on DCPV charge asymmetry K00 decays; • Discovery of an anomaly in K00 spectrum allowing a measurement of  scattering lengths; • Study of K+– Dalitz plot distribution; • Conclusions and outlook. E. Goudzovski / Saclay, June 4th, 2007

3. NA48/2 experimentat the CERN SPS E. Goudzovski / Saclay, June 4th, 2007

4. NA48/2 experiment • A fixed target experiment at the CERN SPS • A multipurpose K decay in flight experiment; • Record flux of K decays (18109 triggers collected); • Specifically designed for precision measurement K3 of charge asymmetries; • Other goals: CKM unitarity,  scattering, lepton universality, ChPT studies. Jura mountains France NA48/2 SPS LHC Switzerland Geneva airport N E. Goudzovski / Saclay, June 4th, 2007

5. NA48 history and future NA48: a series of experiments= the modern CERN kaon physics programme 1997-2001:NA48  simultaneous KL and KS beams, discovery of direct CPV in K02 decays! 2002:NA48/1 high intensity KS and neutral hyperon beam, discovery of KS0e+e–, KS0+– decays (BR~10–9) 2003-2004:NA48/2 simultaneous K+ and K– beams, search for DCPV and a multipurpose K decay study 2007: (now!)NA48/3 (P326) phase I Precise test of lepton universality with Kl decays 2011-2013:NA48/3 (P326) phase II SM test by measurement of BR(K)~10–10 >2015: SM test with BR(KL0)~10–11 ??? The NA48 series is producing more physics output than expected! Primary goals: SM tests complementary to those at the high energy frontier E. Goudzovski / Saclay, June 4th, 2007

6. PK spectra, 603GeV/c BM z 10 cm Kaon momentumspectrum NA48/2: kaon beam line Simultaneous K+ and K beams: large charge symmetrization of experimental conditions 2-3M K/spill (/K~10), decay products stay in pipe. Flux ratio: K+/K–  1.8 magnet 54 60 66 K+ K+ beam pipe Be target focusing beams K ~71011ppp, 400 GeV K Second achromat • Cleaning • Beam spectrometer (momentum resolution ~0.7%) Front-end achromat Quadrupole quadruplet Beams coincide within ~1mm all along 114m decay volume • Momentum • selection • Focusing •  sweeping vacuum tank He tank + spectrometer 1cm not to scale 200 250 m 50 100 E. Goudzovski / Saclay, June 4th, 2007

7. The NA48 detector • Main detector components: • Magnetic spectrometer (4 DCHs): • 4 views/DCH: redundancy efficiency; • used in trigger logic; • Δp/p = 1.0% + 0.044%*p [GeV/c]. • Hodoscope • fast trigger; • precise time measurement (150ps). • Liquid Krypton EM calorimeter (LKr) • High granularity, quasi-homogenious; • E/E = 3.2%/E1/2 + 9%/E + 0.42% [GeV];x=y=0.42/E1/2 + 0.6mm (1.5mm@10GeV). • Hadron calorimeter, muon veto counters, photon vetoes. Drift chambers,related L2 trigger: Saclay responsibility Vacuum beam pipe Kbeams E. Goudzovski / Saclay, June 4th, 2007

8. NA48/2 data taking: completed 2003run: ~ 50 days 2004run: ~ 60 days K3 statistics in 2 years: K  +: ~4·109 K  00: ~1·108 Rare K± decays: BR’s down to 10–9can be measured >200 TB of data recorded A view of the NA48/2 beam line E. Goudzovski / Saclay, June 4th, 2007

9. The K3 decays:physics motivation E. Goudzovski / Saclay, June 4th, 2007

10. Kinematics of K3 decays Two decay modes: BR(K±±+)=5.57%; BR(K±±00)=1.73%. “charged” “neutral” Matrix element: |M(u,v)|2 ~ 1 + gu + hu2 + kv2 Kinematics: si = (PKPi)2, i=1,2,3 (3=odd ); s0 = (s1+s2+s3)/3; u = (s3-s0)/m2; v = (s2-s1)/m2. V “Charged” mode g = 0.2154±0.0035 |h|, |k| ~ 10-2 Kaon rest frame: u = 2mK∙(mK/3Eodd)/m2; v = 2mK∙(E1E2)/m2. U Direct CP-violating quantity: the slope asymmetry Ag = (g+g)/(g++g)  0 E. Goudzovski / Saclay, June 4th, 2007

11. Primary interest: search for DCPV Experimental precisions before NA48/2: E. Gámiz et al., JHEP 10 (2003) 42 [Ag~10-3, dominated by systematics] SM estimate (NLO ChPT):Agc = (–1.41.2)10–5; Agn = (1.10.7)10–5. Smith et al. (1975) “neutral” 10-2 Ford et al. (1970) |Ag| HyperCP prelim. (2000) TNF (2005) “neutral” 10-3 NA48/2 proposal G. D’Ambrosio et al., PLB480 (2000) 164 Models beyond the SM predict substantial enhancement partially within the reach of NA48/2. “neutral” 10-4 “charged” SUSY& 10-5 Asymmetry of integrateddecay widths is stronglysuppressed. SM New physics 10-6 E. Goudzovski / Saclay, June 4th, 2007

12. DCPV: description in the SM Present observations (K,B) are phenomenologicallyaccommodated in the SM via the CKM quark mixing c12c13 s12c13 s12e-i VCKM = –s12c23–c12s23s13ei s12c23–s12s23s13ei s23c13 s12s23–c12c23s13ei –c12s23–s12c23s13ei c23c13 sij = sinij, cij = cosij 4 observable parameters 3 quark generations33unitary matrix 3 angles ij, 1 complex phase  CPV possible only due to the complex phase! (phases appear for Ngenations3) Small number of observations,yet large theoretical uncertainties Searches for CPV give a unique window beyond the SM Enhancements of CPV effects in many extensions of the SM E. Goudzovski / Saclay, June 4th, 2007

13. DCPV: rôle in astrophysics Baryogenesis (A.Sakharov, 1967):DCPV is a necessary condition for dynamical generation of the observed matter-antimatter asymmetry of the Universe. Despite its phenomenological success, CKM mechanismfails to accommodate the observed matter asymmetry. • Strong suggestion for non-CKM mechanisms of CPV • Motivation for rigorous precise search for CPV: tests of the SM and constraints on new physics; • Large-scale programs for CPV search in kaon, B-meson,-, t-physics, recently also in lepton sector ( mixing). E. Goudzovski / Saclay, June 4th, 2007

14. CPV charge asymmetryin K3 decays •  Partial 2003 result: PLB634 (2006) 474 • Final result: to be published soon E. Goudzovski / Saclay, June 4th, 2007

15. K3event selection Time differencefor pairs of tracks Main requirements:simplicity, charge symmetry • Identification of the best 3-track vertex; • Track times: |ti–tj|<10ns probability of event pile-up~10–4; • Zvertex>–18m (downstream the last collimator); • PT<0,3 GeV/c – suppression of background decays; • |M3–MK|<9 MeV/c2 – 5 times the resolution. Z-coordinateof the decay vertex Data MC K3 MC K3 +  decay MC K3 Ke4 background E. Goudzovski / Saclay, June 4th, 2007

16. Selected statistics M=1.7 MeV/c2 The final 2003+2004 data sample:3.11x109 events selected Events even pion in beam pipe  K+ : 2.00x109 events odd pion in beam pipe  K: 1.11x109 events E. Goudzovski / Saclay, June 4th, 2007

17. 1 + (g+g)u + hu2+ kv2 f(u,v) = n 1 + gu + hu2+ kv2 g measurement: fitting method analysis of 1-dimensional U spectra If K+ and K acceptances are made sufficiently similar, in general case g can be extracted fitting the 2D-ratioR2(u,v) with a non-linear function: R2(u,v)=N+(u,v)/N(u,v) (normalization is a free parameter) However, in view of “smallness” of the quadratic slopes, 1-dimensional analysis R1(u) sufficient approximations: R1(u)=N+(u)/N(u) The “charged” mode: g = 0.21134 |h|, |k| ~ 10–2 f(u) =n∙(1+gu/(1+gu+hu2)) E. Goudzovski / Saclay, June 4th, 2007

18. Addressing the acceptance • Magnetic fields present in both beam line and spectrometer: • Lead to residual charge asymmetry of the setup; • Supersample data taking strategy: • Beam line (achromat) polarity (A) reversed on weekly basis; • Spectrometer magnet polarity (B) reversed on a morefrequent basis (~daily in 2003, ~3 hours in 2004) Example: Data taking from August 6 to September 7, 2003 Achromat – B+ B– B+ B– B+ B– Week 1 Supersample 1 12 subsamples B+ Achromat + B+ B– B+ B– B– Week 2 Achromat – B+ B– B+ B– B+ B– Week 3 Supersample 2 12 subsamples Achromat + B+ B+ B– B+ B– B– Week 4 B– Achromat – B+ Supersample 3 Week 5 4 subsamples Achromat + B+ B– E. Goudzovski / Saclay, June 4th, 2007

19. N(A+B+K+) RUS(u)= N(A+B-K-) N(A+B-K+) RUJ(u)= N(A+B+K-) N(A-B+K+) RDS(u)= N(A-B-K-) N(A-B-K+) RDJ(u)= N(A-B+K-) Acceptance cancellation within supersample Detector left-right asymmetry cancels in 4 ratios of K+ over K–U-spectra: • same deviation direction by spectrometer magnet in numerator and denominator; • data from 2 different time periods used at this stage. Y X Achromats: K+ Up Jura(left) B+ Z B– Salève(right) Achromats: K+Down • Indices of R’s correspond to • beam line polarity (U/D); • direction of kaon deviation in spectrometer magnet field (S/J). E. Goudzovski / Saclay, June 4th, 2007

20. More cancellations (1) Double ratio: cancellation ofglobal time instabilities(rate effects, analyzing magnet polarity inversion):[IMPORTANT: SIMULTANEOUS BEAMS] f2(u)=n∙(1+ΔgUu/(1+gu+hu2))2 RU = RUS × RUJ RD = RDS× RDJ f2(u)=n∙(1+ΔgDu/(1+gu+hu2))2 (2) Double ratio: cancellation oflocal beam line biaseseffects (slight differences in beam shapes and momentum spectra): f2(u)=n∙(1+ΔgSu/(1+gu+hu2))2 RS = RUS × RDS RJ = RUJ × RDJ f2(u)=n∙(1+ΔgJu/(1+gu+hu2))2 (3) Quadruple ratio: maximum cancellation R = RUS×RUJ×RDS×RDJ f4(u)=n∙(1+gu/(1+gu+hu2))4 The method is independent ofK+/K– flux ratio andrelative sizes of the samples collected Normalization Slope difference Δg = 2gAg ≈ −0.43Ag E. Goudzovski / Saclay, June 4th, 2007

21. Beam spectra difference (an example of cancellation) Beam line polarity reversal almost reverses K+ and K– beam spectra K+ Systematic differences of K+ and K–acceptance due to beam spectra mostly cancel in RU×RD Systematic check: Reweighting K+events so as to equalize momentum spectra leads to a negligible effect (Δg)=0.0310-4 K– Supersample 2 SS 3 Supersample 1 E. Goudzovski / Saclay, June 4th, 2007

22. Monte-Carlo simulation Due to acceptance cancellations, the analysis does not rely on Monte-Carlo to calculate acceptance Example of data/MC agreement: mean beam positions @DCH1 K+ data K data K+ MC K MC Still Monte-Carlo is used to study systematic effects. • Based on GEANT; • Full detector geometry and material description; • Local DCH inefficiencies simulated; • Variations of beam geometry and DCH alignment are followed; • Simulated statistics similar to experimental one (~1010 events). K+ K E. Goudzovski / Saclay, June 4th, 2007

23. Systematics: spectrometer Transverse alignment Time variations of spectrometer geometry: do not cancel in the result.Alignment is fine-tuned by scaling pion momenta (charge-asymmetrically)to equalize the reconstructed average K+,K− masses M3 Sensitivity to DCH4 horizontal shift: |M/x|  1.5 keV/m Maximum equivalent transverse shift: ~200m @DCH1 or ~120m @DCH2 or ~280m @DCH4 Magnetic field The effect of imperfect inversion of spectrometer field cancels in double ratio [due to simultaneous beams] Effects of permanent fieldsin the spectrometer region remain,systematic uncertainty computedbased on expected stray field magnitude:(g)=0.310–4 Max. effect in 2004 Subsample  Much more stable alignment in 2004 E. Goudzovski / Saclay, June 4th, 2007

24. Systematics: beam geometry • Geometric acceptance mainly determined by the beam pipe (R10cm); • Geometry variations, non-perfect superposition: asymmetric acceptance. • Additional acceptance cut defined by a “virtual pipe” (R=11.5cm) centered on averaged reconstructed beam position as a function ofcharge, time and K momentum Statistics loss: 12% [Special treatment of permanent magnetic fields effect on measured beam positions] Beam width: ~ 1 cm Position stability:~ 2 mm Sample beam profile at DCH1 0.8 Y, cm Y, cm 2mm 0.4 “Virtual pipe” also corrects the differences between the upper and lower beam paths 0 -0.4 Uncertainty due to effectsof permanent fields: (g)=0.210–4 -0.8 -0.8 -0.4 0.8 0.4 0 X, cm X, cm E. Goudzovski / Saclay, June 4th, 2007

25. Only charge-asymmetrictrigger inefficiency dependent on u can bias the result Systematics: trigger Trigger efficiencies measured using control data samplestriggered by downscaled low bias triggers L2 trigger[online vertex reconstruction, DCH data]time-varying inefficiency (local DCH inefficiencies, tuning)1–= 0.06% to 1.5% u-dependent correction applied L1 trigger [2 hodoscope hits]small and stable inefficiency1–≈ 0.910-3(no correction) Statistical errors due to limited sizesof the control samplesare propagated into the result Inefficiency, % L2 inefficiencyvs time (2003 data) 1.6 1.4 1.6 L2 inefficiency vs u(normal conditions) Beginning of 2003 run: L2 algorithm tuning 1.2 1.4 1.0 1.2 Inefficiency x103 1.0 0.8 0.8 0.6 0.6 Max. inefficiency in 2004 0.4 0.4 0.2 0.2 -1.5 -0.5 0.0 0.5 1.5 -1.0 1.0 U E. Goudzovski / Saclay, June 4th, 2007

26. Other systematic effects Field map in decay volume: Y projection [Gauss] 0.4 Residual effects of stray magnetic fields (magnetized vacuum tank, earth field) minimized by explicit field map correction 0 -0.4 -0.8 -1.2 Decay volume: Z coordinate • Further systematic effects studied: • Accuracy of beam tracking, variations of beam widths; • Bias due to resolution in u; • Sensitivity to fitting interval and method; • Coupling of  decays to other effects; • Effects due to event pile-up; • +/– hadronic interactions with setup material. No magnetic field correction Magnetic field corrected for 0.5MeV/c2 E. Goudzovski / Saclay, June 4th, 2007

27. Supersamples collected Supersample: a minimal independentself-consistent set of data (including all magnetic field polarities) E. Goudzovski / Saclay, June 4th, 2007

28. Fit of the K+/K– ratio R4(u) R4(u) averaged over supersamples bin-by-bin f(u)=n(1+gu/(1+gu+hu2))4 E. Goudzovski / Saclay, June 4th, 2007

29. Time-stability & control quantities Control quantities cancelling in the result quadruple ratio components rearranged (smallness demonstrates: second order effects are negligible) Physics asymmetry RLR(u)=RS/RJ RUD(u)=RU/RD 2003 2004 Control of setuptime-variable biases Control of differencesof the two beam paths Monte-Carlo (reproduces apparatus asymmetries) (results consistent) E. Goudzovski / Saclay, June 4th, 2007

30. Systematic effects: summary E. Goudzovski / Saclay, June 4th, 2007

31. The result g = (0.6 ± 0.7stat ± 0.4trig ± 0.5syst)  10-4 g = (0.6 ± 0.9)  10-4 Ag = (1.5 ± 1.5stat ± 0.9trig ± 1.1syst)  10-4 Ag = (1.5 ± 2.1)  10-4 FINAL RESULT based on the full statisticsaccumulated in2003 and 2004 runs Measurements of Ag • A factor ~20 better precision than the previous measurements; • Uncertainties dominated by those of statistical nature; • Result compatible with the Standard Model predictions, no evidences for New Physics; • NA48/2 design goal reached! Ag 104 preliminary 2003 final 2003+2004 final 2003 HyperCP (2000) Ford et al. (1970) NA48/2 (results supersedingeach other) E. Goudzovski / Saclay, June 4th, 2007

32. CPV charge asymmetryin K00 decays • Partial 2003 result: PLB638 (2006) 22 • Final result: to be published soon E. Goudzovski / Saclay, June 4th, 2007

33. (Dik)2 m02 = 2EiEk(1–cosa) ≈ EiEka2 = EiEk (zik)2 K00selection principle For each photon pair (i,k) a decay vertex reconstructed along beam axis under the assumption of 0 decay m0 – mass of p0 Ei, Ek – energy of gi, gk Dik – distance between gi and gk on LKr zik – distance from p0gg decay vertex to LKr accidental photon Ek LKr Dik Em z K-decay vertex zlm zik Ei El Dz selected photon 3 mass resolution , MeV/c2 … excellent at low M00! 0 0.09 0.12 0.10 0.08 0.11 M2(00), (GeV/c2)2 E. Goudzovski / Saclay, June 4th, 2007

34. K00 asymmetry analysis M=1.1 MeV/c2 Events M(3), GeV/c2 |V| Statistical precision in Ag0 similar to “charged” mode: • Ratio of “neutral” to “charged” statistics: N0/N±~1/30; • Ratio of slopes: |g0/g±|3/1; • A favourable Dalitz-plot distribution (gain factor f~1.5). Final result with 2003+2004 sample (based on 91106 events) Ag0 = (1.8±1.8)10-4 U E. Goudzovski / Saclay, June 4th, 2007

35. Fit of the K+/K– ratio R4(u) R4(u) averaged over supersamples bin-by-bin f(u)=n(1+gu/(1+gu+hu2))4 E. Goudzovski / Saclay, June 4th, 2007

36. K00Dalitz plotdistribution: effectsof  scattering • Partial 2003 result: PLB633 (2006) 173 • Updated result: to be published soon E. Goudzovski / Saclay, June 4th, 2007

37. Observation of the “cusp” 2003 data: 16.0 mln events 2004 data: 43.6 mln events Events 80k 200k 60k 160k 120k 40k 80k 20k 40k A sudden change of slopenear 2m threshold:anomaly never observed before. 0 M2(00), (GeV/c2)2 M2(00), (GeV/c2)2 45k 120k 110k 40k 100k Realized to be due tofinal-state interactions( rescattering) 35k 90k 30k 80k +– threshold +– threshold 25k 70k 0.079 0.080 0.080 0.078 0.078 0.076 0.077 0.076 0.077 0.079 M2(00), (GeV/c2)2 M2(00), (GeV/c2)2 E. Goudzovski / Saclay, June 4th, 2007

38. + K+ 0 0 Theory: final state rescattering N. Cabibbo, PRL 93 (2004) 121801 M(K00)= M0 + M1 Direct emission: Kaon rest frame: u = 2mK∙(mK/3Eodd)/m2 v = 2mK∙(E1E2)/m2 M0 = A0(1+g0u/2+h’u2/2+k’v2/2) Negative interferenceunder threshold Rescattering amplitude: M00 M1 = –2/3(a0–a2)m+M+ 1–( )2 2m+ Arbitrary scale K3 amplitudeat threshold Combination ofS-wave  scatteringlenghts No M1 amplitude (isospin symmetryassumed here) M1 amplitude present:13% depletionunder the threshold Theory not sufficientfor accurate description of the data! K+ 0.086 0.078 0.074 0.082 M2(00), (GeV/c2)2 E. Goudzovski / Saclay, June 4th, 2007

39. Theory (2): two-loop diagrams N. Cabibbo and G. Isidori, JHEP 503 (2005) 21 • All rescattering processes at one- & two-loop level • Five S-wave scattering lengths (ax, a++, a+–, a+0, a00)expressed as linear combinations of a0 and a2 • Isospin symmetry breaking accounted for following J. Gasser • For example, ax = (1+/3)(a0–a2)/3, where=(m+2–m02)/m+2=0.065is isospin breaking parameter • Radiative corrections missing: (a0–a2) precision ~5% One-loop diagrams: Two-loop diagrams: Prediction of thetwo-loop theory a) 2 scattering Arbitrary scale Cusp point No rescatteringamplitude Subleadingeffect b) irreducible 3 scattering c) reducible 3 scattering Leading effect 0.076 0.078 0.080 0.074 0.082 M2(00), (GeV/c2)2 E. Goudzovski / Saclay, June 4th, 2007

40. Fitting procedure 1-dimensional fit of the M00 projection Detector response matrix Rijobtained with a full GEANT-basedMonte-Carlo simulation Log(Rij) 420x420 bins Reconstructeddistribution: FjMC = RijGi Generated distributionG(M00) = G(g0,h’,a0,a2,M00) Reconstructed s3 (GeV/c2)2 Fit region Generated s3=M2(00), (GeV/c2)2 MINUIT minimization of 2of data/MC spectra shapes 5 free parameters (FDATA–NFMC)2 2(g,h’,m+(a0–a2),m+a2,N)= FDATA2+N2FMC2 s3 bins E. Goudzovski / Saclay, June 4th, 2007

41. Fit quality & pionium signature Theory is sufficientto describe the data! 7 data bins excluded from the fitdue to absence of EM correctionsin the theoretical model Combined 2003+2004 sample 2.0% 1.5% Data/Fit – 1 1.0% 0.5% 0 –0.5% –1.0% s3=M2(00), (GeV/c2)2 A number of alternative theoretical approaches developedto describe final-state scattering and formation ofbound +– states near threshold, work going on… E. Goudzovski / Saclay, June 4th, 2007

42. Uncertainties & results NA48/2 result with 2003+2004(80%) statistics (preliminary) (a0–a2)m+= 0.261  0.006stat.  0.003syst.  0.0013ext. a2m+= –0.037  0.013stat.  0.009syst.  0.0018ext. External uncertainty: due to R = (A++–/A+00)|threshold = 1.9750.015; Theory precision (rad.corr. & higher order terms neglected): (a0–a2)m+= 0.013. Unexpected possibility; precise measurement by large theory errors yet;complementary to DIRAC measurement with of pionium lifetime E. Goudzovski / Saclay, June 4th, 2007

43. Results: Dalitz plot slopes M(K00)= M0 + M1 M0 ~ (1+g0u/2+h’u2/2+k’v2/2) NB: not the same parameterization as the PDG one: |M0|2(PDG) ~ (1+gu+hu2+kv2) [g0g, h’h–g2/4, k’k] (in reality, 2D fits involved at step 2) Technique: consecutive 1D-fits in both data projections. 1. (a0,a2,g0,h’) measurement (fixed k’=0) [2003 data] 2. k’ measurement (fixed a0,a2,g0,h’) [2003 data]  3. (a0,a2,g0,h’) second iteration (fixed k’) [2004 data] NA48/2 result: (preliminary) g= ( 64.9  0.3stat. 0.4syst. )% h’= ( –4.7  0.7stat. 0.5syst. )% k’= ( –0.97  0.03stat.  0.08syst.)% (a0,a2 are not significantly affected by neglecting the k’v2 term,but g0,h’ are biased by g0=–1.5%, h=–1.2%) E. Goudzovski / Saclay, June 4th, 2007

44. Dalitz plot distribution of K+– decays • Final result: PLB649 (2007) 349 E. Goudzovski / Saclay, June 4th, 2007

45. The first goal of the analysis Measurement of (g,h,k) parameters of the polynomial parameterization of the K3 decay used by the previous experiments (and the PDG):NEGLECT the effects of re-scattering and radiative corrections. d/dudv ~ C(u,v)(1+gu+hu2+kv2) Coulomb correction factor Kaon rest frame: u = 2mK∙(mK/3Eodd)/m2 v = 2mK∙(E1E2)/m2 |v| Pole! • Polynomial expansion: • (u,v) – kinematic variables; • (g,h,k)– slope parameters(linear and quadratic) to be measured; • term ~v forbidden by Bose symmetry. u nij • nij = 2eiej / ij • ei=1: pion charges • ij: relative velocities of pion pairs C(u,v) =  exp(nij)–1 i,j=1,2,3 ij E. Goudzovski / Saclay, June 4th, 2007

46. Fitting procedure 2-dimensional fit of both data projections Fit of the reconstructed data distribution with a weighted sum of4 reconstructed MC components(a 2D fit possible due to |M|2~finite sum) ~C(u,v)u2 60% of the 2003 sample: 0.471109 events ~C(u,v) |v| u u ~C(u,v)v2 ~C(u,v)u u MINUIT minimization of 2of data/MC spectra shapes u u (FDATA–NFMC)2 2(g,h,k,N)= FDATA2+N2FMC2 u,vbins E. Goudzovski / Saclay, June 4th, 2007

47. Uncertainties & result E. Goudzovski / Saclay, June 4th, 2007

48. Final result and prospects |M(K+–)|2= A0(1+gu+hu2+kv2) (the PDG parameterization) (Final result, 30% data set) g= ( –21.134  0.017 )% h= ( 1.848  0.040)% k= ( –0.463  0.014)%  Event density found compatible with the PDG distribution; • Slopes in fair agreement with World averages, x10 smaller uncertainties; • Slopes in agreement with NLO theoretical computations; • First measurement of non-zero h slope; • No significant higher-order slopes found. A more elaborate theoretical framework including a description of rescattering and radiative correctionsis in preparation for deeper exploration of the data E. Goudzovski / Saclay, June 4th, 2007

49. Comparison to PDG Quadratic: h102 Linear: g102 Quadratic: k102 PDG’06 PDG’06 PDG’06 Ford 72 Ford 72 Ford 72 Mast 69 Mast 69 Mast 69 Ford 72 Ford 72 Ford 72 NA48/2 NA48/2 NA48/2 Devaux 77 Devaux 77 Devaux 77 Hoffmaster 72 Hoffmaster 72 Hoffmaster 72 • Fair agreement with the measurements performed ~35 years ago, x10 improvement in precision; • Validity of the polynomial parameterization at NA48/2 precision demonstrated (rescattering effects much weaker than in K00). E. Goudzovski / Saclay, June 4th, 2007

50. Conclusions • NA48/2 has finalized a measurement of DCPV charge asymmetries in K±3 decays: x10 improvement in precision, yet no signs of New Physics found; • An anomaly in K00 decay spectra was first observed, which triggered development of theoretical approaches, and ultimately allowed a measurement of  scattering lengths. Further work is in progress. • The NA48 continues a series of discoveries and SM tests;an intensive future experimental kaon program is prepared. E. Goudzovski / Saclay, June 4th, 2007