1. 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 4 th, 2007

2. 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 4 th, 2007

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

4. 4 SPS LHC NA48/2 N A fixed target experiment at the CERN SPS A multipurpose K  decay in flight experiment; Record flux of K  decays (18  10 9 triggers collected); Specifically designed for precision measurement K 3  of charge asymmetries; Other goals: CKM unitarity,  scattering, lepton universality, ChPT studies. Jura mountains Geneva airport NA48/2 experiment France Switzerland

5. 5 E. Goudzovski / Saclay, June 4 th, 2007 NA48 history and future 1997-2001: NA48  simultaneous K L and K S beams, discovery of direct CPV in K 0  2  decays! 2002:NA48/1  high intensity K S and neutral hyperon beam, discovery of K S  0 e + e –, K S  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(K L  0 )~10 –11 ??? NA48: a series of experiments = the modern CERN kaon physics programme The NA48 series is producing more physics output than expected! Primary goals: SM tests complementary to those at the high energy frontier

6. 6 1cm 50100 Front-end achromat Momentum selection Quadrupole quadruplet Focusing  sweeping Second achromat Cleaning Beam spectrometer (momentum resolution ~0.7%) ~7  10 11 ppp, 400 GeV K+K+ KK Beams coincide within ~1mm all along 114m decay volume focusing beams BM z magnet K+K+ KK beam pipe Simultaneous K + and K  beams: large charge symmetrization of experimental conditions Be target 2-3M K/spill (  /K~10),  decay products stay in pipe. Flux ratio: K + /K –  1.8 P K spectra, 60  3 GeV/c 54 60 66 NA48/2: kaon beam line 10 cm 200 vacuum tank not to scale 250 m He tank + spectrometer E. Goudzovski / Saclay, June 4 th, 2007 Kaon momentum spectrum

7. 7 The NA48 detector K  beams Vacuum beam pipe Main detector components: Magnetic spectrometer (4 DCHs): 4 views/DCH: redundancy  efficiency; used in trigger logic; used in trigger logic; Δp/p = 1.0% + 0.044%*p [GeV/c]. Δp/p = 1.0% + 0.044%*p [GeV/c]. Hodoscope fast trigger; precise time measurement (150ps). precise time measurement (150ps). Liquid Krypton EM calorimeter (LKr) High granularity, quasi-homogenious;  E /E = 3.2%/E 1/2 + 9%/E + 0.42% [GeV];  x =  y =0.42/E 1/2 + 0.6mm (1.5mm@10GeV).  E /E = 3.2%/E 1/2 + 9%/E + 0.42% [GeV];  x =  y =0.42/E 1/2 + 0.6mm (1.5mm@10GeV). Hadron calorimeter, muon veto counters, photon vetoes. E. Goudzovski / Saclay, June 4 th, 2007 Drift chambers, related L2 trigger: Saclay responsibility

8. 8 NA48/2 data taking: completed 2003 run: ~ 50 days 2004 run: ~ 60 days K 3  statistics in 2 years: K      +   : ~4·10 9 K    0  0   : ~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 E. Goudzovski / Saclay, June 4 th, 2007

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

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

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

12. 12 Present observations (K,B) are phenomenologically accommodated in the SM via the CKM quark mixing c 12 c 13 s 12 c 13 s 12 e -i  –s 12 c 23 –c 12 s 23 s 13 e i  s 12 c 23 –s 12 s 23 s 13 e i  s 23 c 13 s 12 s 23 –c 12 c 23 s 13 e i  –c 12 s 23 –s 12 c 23 s 13 e i  c 23 c 13 V CKM V CKM = 3 quark generations 3  3 unitary matrix 4 observable parameters 3 angles  ij, 1 complex phase  s ij = sin  ij, c ij = cos  ij 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 CPV possible only due to the complex phase! (phases appear for N genations  3) DCPV: description in the SM E. Goudzovski / Saclay, June 4 th, 2007

13. 13 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 mechanism fails 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). DCPV: rôle in astrophysics E. Goudzovski / Saclay, June 4 th, 2007

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

15. 15 K   3   event selection Time difference for pairs of tracks Identification of the best 3-track vertex; Track times: |t i –t j |<10ns  probability of event pile-up ~10 –4 ; Z vertex >–18m (downstream the last collimator); P T <0,3 GeV/c – suppression of background decays; |M 3  –M K |<9 MeV/c 2 – 5 times the resolution. Main requirements: simplicity, charge symmetry K e4 background MC K 3  MC K 3  +  decay MC K  3  Data Z-coordinate of the decay vertex E. Goudzovski / Saclay, June 4 th, 2007

16. 16 Selected statistics even pion in beam pipe 3.11x10 9 The final 2003+2004 data sample: 3.11x10 9 events selected K + : 2.00x10 9 events  odd pion in beam pipe  M =1.7 MeV/c 2 Events  K  : 1.11x10 9 events E. Goudzovski / Saclay, June 4 th, 2007

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

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

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

20. 20 More cancellations (2) Double ratio: cancellation of local beam line biases effects (slight differences in beam shapes and momentum spectra): R S = R US × R DS R J = R UJ × R DJ f 2 (u)=n∙(1+ Δg S  u/(1+gu+hu 2 )) 2 f 2 (u)=n∙(1+ Δg J  u/(1+gu+hu 2 )) 2 R = R US ×R UJ ×R DS ×R DJ f 4 (u)=n∙(1+  g  u/(1+gu+hu 2 )) 4 (3) Quadruple ratio: maximum cancellation The method is independent of K + /K – flux ratio and relative sizes of the samples collected Δg = 2g  A g ≈ −0.43  A g [IMPORTANT: SIMULTANEOUS BEAMS] (1) Double ratio: cancellation of global time instabilities (rate effects, analyzing magnet polarity inversion): [IMPORTANT: SIMULTANEOUS BEAMS] R U = R US × R UJ R D = R DS × R DJ f 2 (u)=n∙(1+ Δg U  u/(1+gu+hu 2 )) 2 f 2 (u)=n∙(1+ Δg D  u/(1+gu+hu 2 )) 2 Normalization Slope difference E. Goudzovski / Saclay, June 4 th, 2007

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

22. 22 Monte-Carlo simulation 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 (~10 10 events). Example of data/MC agreement: mean beam positions @DCH1 K + data K  data K + MC K  MC K+K+ KK Due to acceptance cancellations, the analysis does not rely on Monte-Carlo to calculate acceptance Due to acceptance cancellations, the analysis does not rely on Monte-Carlo to calculate acceptance E. Goudzovski / Saclay, June 4 th, 2007

23. 23 Systematics: spectrometer 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 Maximumequivalent transverse shift: ~200  m @DCH1 or ~120  m @DCH2 or ~280  m @DCH4 Sensitivity to DCH4 horizontal shift: |  M/  x|  1.5 keV/  m The effect of imperfect inversion of spectrometer field cancels in double ratio [due to simultaneous beams] Effects of permanent fields in the spectrometer region remain, systematic uncertainty computed based on expected stray field magnitude:  (  g)=0.3  10 –4 Transverse alignment Magnetic field M3M3 M3M3 Max. effect in 2004  Much more stable alignment in 2004 Subsample E. Goudzovski / Saclay, June 4 th, 2007

24. 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 of charge, time and K momentum Y, cm Sample beam profile at DCH1 0 0.4 0.8-0.4 -0.8 0 0.4 0.8 -0.4 -0.8 X, cm Beam width: ~ 1 cm Position stability: ~ 2 mm Y, cm “Virtual pipe” also corrects the differences between the upper and lower beam paths 2mm 12% Statistics loss: 12% [Special treatment of permanent magnetic fields effect on measured beam positions] E. Goudzovski / Saclay, June 4 th, 2007 Uncertainty due to effects of permanent fields:  (  g)=0.2  10 –4

25. 25 Systematics: trigger 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 inefficiency 1–  ≈ 0.9  10 -3 (no correction) Only charge-asymmetric trigger inefficiency dependent on u can bias the result 0.4 0.2 0.6 0.8 1.0 1.2 1.4 1.6 Inefficiency, % L2 inefficiency vs time (2003 data) Beginning of 2003 run: L2 algorithm tuning Trigger efficiencies measured using control data samples triggered by downscaled low bias triggers Statistical errors due to limited sizes of the control samples are propagated into the result 0.4 0.2 0.6 0.8 1.0 1.2 1.4 1.6 Inefficiency x10 3 L2 inefficiency vs u (normal conditions) 1.0 1.50.50.0-0.5 -1.5 U Max. inefficiency in 2004 E. Goudzovski / Saclay, June 4 th, 2007

26. 26 Other systematic effects 0.5MeV/c 2 No magnetic field correction correction Magnetic field corrected for Field map in decay volume: Y projection Decay volume: Z coordinate 0.4 0 -0.4 -0.8 -1.2 [Gauss] Residual effects of stray magnetic fields (magnetized vacuum tank, earth field) minimized by explicit field map correction 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. E. Goudzovski / Saclay, June 4 th, 2007

27. 27 Supersamples collected RunSupersampleDatesSubsamples K 3  events selected (millions) 2003 0 22/06  25/07 26697.69 1 06/08  20/08 12421.50 2 20/08  03/09 12413.37 3 03/09  07/09 4134.13 2004 4 16/05  07/06 87362.07 5 27/06  07/07 48221.74 6 07/07  19/07 86301.83 7 24/07  01/08 66304.98 8 01/08  11/08 62255.29 Total4033112.59 Supersample: a minimal independent self-consistent set of data (including all magnetic field polarities) E. Goudzovski / Saclay, June 4 th, 2007

28. 28 Fit of the K + /K – ratio R 4 (u) E. Goudzovski / Saclay, June 4 th, 2007 f(u)=n(1+  gu/(1+gu+hu 2 )) 4 R 4 (u) averaged over supersamples bin-by-bin

29. 29 Time-stability & control quantities 2003 Physics asymmetry (results consistent) 2004 R LR (u)=R S /R J Control quantities cancelling in the result quadruple ratio components rearranged (smallness demonstrates: second order effects are negligible) R UD (u)=R U /R D Control of setup time-variable biases Control of differences of the two beam paths Monte-Carlo (reproduces apparatus asymmetries) E. Goudzovski / Saclay, June 4 th, 2007

30. 30 Systematic effects: summary Systematic effect Effect on  g  10 4 Spectrometer alignment ±0.1 Spectrometer magnetic field ±0.3 Beam geometry, stray magnetic fields ±0.2 Accidental activity (pile-up) ±0.2 Resolution and fitting technique ±0.2 Total systematic uncertainty ±0.5 L1 trigger: uncertainty only±0.3 L2 trigger: correction  0.1±0.3 Total trigger correction  0.1±0.4 Systematic & trigger uncertainty ±0.6 Raw  g 0.7±0.7 stat  g corrected for L2 inefficiency 0.6±0.7 stat E. Goudzovski / Saclay, June 4 th, 2007

31. 31 The result Ford et al. (1970) HyperCP (2000) preliminary 2003 final 2003 final 2003+2004 NA48/2 (results superseding each other)  g = (0.6 ± 0.7 stat ± 0.4 trig ± 0.5 syst )  10 -4  g = (0.6 ± 0.9)  10 -4 A g = (  1.5 ± 1.5 stat ± 0.9 trig ± 1.1 syst )  10 -4 A g = (  1.5 ± 2.1)  10 -4  g = (0.6 ± 0.7 stat ± 0.4 trig ± 0.5 syst )  10 -4  g = (0.6 ± 0.9)  10 -4 A g = (  1.5 ± 1.5 stat ± 0.9 trig ± 1.1 syst )  10 -4 A g = (  1.5 ± 2.1)  10 -4 FINAL RESULT based on the full statistics accumulated in 2003 and 2004 runs Measurements of A g 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! A g  10 4 E. Goudzovski / Saclay, June 4 th, 2007

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

33. 33 K     0  0 selection principle LKr D ik zzzz z ik z lm K-decay vertex ElEl EiEi EkEk EmEm m 0 2 = 2E i E k (1 – cos  ) ≈ E i E k  2 = E i E k (D ik ) 2 (z ik ) 2 accidental photon selected photon z M 2 (  0  0 ), (GeV/c 2 ) 2 0.08 0.09 0.10 0.11 0.12 , MeV/c 2 0 3  mass resolution … excellent at low M 00 ! For each photon pair (i,k) a decay vertex reconstructed along beam axis under the assumption of  0  decay m 0 – mass of  0 E i, E k – energy of  i,  k D ik – distance between  i and  k on LKr z ik – distance from  0   decay vertex to LKr E. Goudzovski / Saclay, June 4 th, 2007

34. 34  M =1.1 MeV/c 2 M(3  ), GeV/c 2 Events U |V| Final result with 2003+2004 sample (based on 91  10 6 events) A g 0 = (1.8±1.8)  10 -4 Statistical precision in A g 0 similar to “charged” mode: Ratio of “neutral” to “charged” statistics: N 0 /N ± ~1/30; Ratio of slopes: |g 0 /g ± |  3/1; A favourable Dalitz-plot distribution (gain factor f~1.5). K     0  0 asymmetry analysis E. Goudzovski / Saclay, June 4 th, 2007

35. 35 Fit of the K + /K – ratio R 4 (u) E. Goudzovski / Saclay, June 4 th, 2007 f(u)=n(1+  gu/(1+gu+hu 2 )) 4 R 4 (u) averaged over supersamples bin-by-bin

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

37. 37 Observation of the “cusp” 0.080 0.079 0.078 0.0770.076 0.0800.079 0.078 0.0770.076 80k 60k 40k 20k 0 40k 80k 120k 160k 200k 80k 120k 110k 100k 90k 25k 45k 2004 data: 43.6 mln events M 2 (  0  0 ), (GeV/c 2 ) 2 Events 70k 30k 35k 40k  +  – threshold E. Goudzovski / Saclay, June 4 th, 2007  +  – threshold A sudden change of slope near 2m  threshold: anomaly never observed before. Realized to be due to final-state interactions (  rescattering) 2003 data: 16.0 mln events

38. 38 Theory: final state rescattering N. Cabibbo, PRL 93 (2004) 121801 M (K     0  0 ) = M 0 + M 1 M 0 = A 0 (1+g 0 u/2+h’u 2 /2+k’v 2 /2) ++ 00 00 K+K+ Kaon rest frame: u = 2m K ∙(m K /3  E odd )/m  2 v = 2m K ∙(E 1  E 2 )/m  2 Direct emission: Rescattering amplitude: 1–( ) 2 M 1 = –2/3(a 0 –a 2 )m + M + M 00 2m + Combination of S-wave  scattering lenghts K   3   amplitude at threshold No M 1 amplitude M 1 amplitude present: 13% depletion under the threshold K+K+ Arbitrary scale M 2 (  0  0 ), (GeV/c 2 ) 2 0.074 0.078 0.082 (isospin symmetry assumed here) E. Goudzovski / Saclay, June 4 th, 2007 Theory not sufficient for accurate description of the data! Negative interference under threshold 0.086

39. 39 Theory (2): two-loop diagrams b) irreducible 3  scattering One-loop diagrams: Two-loop diagrams: All rescattering processes at one- & two-loop level Five S-wave scattering lengths (a x, a ++, a +–, a +0, a 00 ) expressed as linear combinations of a 0 and a 2 Isospin symmetry breaking accounted for following J. Gasser For example, a x = (1+  /3)(a 0 –a 2 )/3, where  =(m + 2 –m 0 2 )/m + 2 =0.065 is isospin breaking parameter Radiative corrections missing: (a 0 –a 2 ) precision ~5% c) reducible 3  scattering a) 2  scattering N. Cabibbo and G. Isidori, JHEP 503 (2005) 21 Arbitrary scale No rescattering amplitude Subleading effect M 2 (  0  0 ), (GeV/c 2 ) 2 0.074 0.0760.0780.080 0.082 Cusp point Leading effect Prediction of the two-loop theory E. Goudzovski / Saclay, June 4 th, 2007

40. 40 Fitting procedure  2 (g,h’,m + (a 0 –a 2 ),m + a 2,N)=  (F DATA –NF MC ) 2  F DATA 2 +N 2  F MC 2 s 3 bins Generated distribution G(M 00 ) = G(g 0,h’,a 0,a 2,M 00 ) Detector response matrix R ij obtained with a full GEANT-based Monte-Carlo simulation Generated s 3 =M 2 (  0  0 ), (GeV/c 2 ) 2 Reconstructed s 3 (GeV/c 2 ) 2 Log(R ij ) Reconstructed distribution: F j MC =  R ij G i Fit region MINUIT minimization of  2 of data/MC spectra shapes 5 free parameters 1-dimensional fit of the M 00 projection 420x420 bins E. Goudzovski / Saclay, June 4 th, 2007

41. 41 Fit quality & pionium signature s 3 =M 2 (  0  0 ), (GeV/c 2 ) 2 0 1.0% –1.0% Data/Fit – 1 1.5% 0.5% –0.5% 2.0% Combined 2003+2004 sample 7 data bins excluded from the fit due to absence of EM corrections in the theoretical model E. Goudzovski / Saclay, June 4 th, 2007 Theory is sufficient to describe the data! A number of alternative theoretical approaches developed to describe final-state scattering and formation of bound  +  – states near threshold, work going on…

42. 42 Uncertainties & results Systematic effect (a 0 –a 2 )  10 2 a 2  10 2 Analysis technique ±0.10 ±0.20 Trigger inefficiencynegl. ±0.50 Description of resolution±0.06±0.11 LKr non-linearity±0.06±0.26 Geometric acceptance±0.02±0.01 MC sample±0.03±0.21 Simulation of LKr showers±0.17±0.50 V-dependence of amplitude±0.17±0.38 Total ±0.28 ±0.90 (a 0 –a 2 )m + = 0.261  0.006 stat.  0.003 syst.  0.0013 ext. a 2 m + = –0.037  0.013 stat.  0.009 syst.  0.0018 ext. NA48/2 result with 2003+2004(80%) statistics Theory precision (rad.corr. & higher order terms neglected):  (a 0 –a 2 )m + = 0.013. External uncertainty: due to R = (A ++– /A +00 )| threshold = 1.975  0.015; (preliminary) E. Goudzovski / Saclay, June 4 th, 2007 Unexpected possibility; precise measurement by large theory errors yet; complementary to DIRAC measurement with of pionium lifetime

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

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

45. 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. u |v| C(u,v) =  n ij exp(n ij )–1 n ij = 2  e i e j /  ij e i =  1: pion charges  ij : relative velocities of pion pairs i,j=1,2,3 ijij Polynomial expansion: (u,v) – kinematic variables; (g,h,k) – slope parameters (linear and quadratic) to be measured; term ~v forbidden by Bose symmetry. d  /dudv ~ C(u,v)  (1+gu+hu 2 +kv 2 ) Coulomb correction factor Kaon rest frame: u = 2m K ∙(m K /3  E odd )/m  2 v = 2m K ∙(E 1  E 2 )/m  2 Pole! E. Goudzovski / Saclay, June 4 th, 2007

46. 46 Fitting procedure u |v| 60% of the 2003 sample: 0.471  10 9 events u u u u ~C(u,v)  u ~C(u,v)  v 2 ~C(u,v) ~C(u,v)  u 2 Fit of the reconstructed data distribution with a weighted sum of 4 reconstructed MC components (a 2D fit possible due to |M| 2 ~finite sum)  2 (g,h,k,N)=  (F DATA –NF MC ) 2  F DATA 2 +N 2  F MC 2 u,v bins MINUIT minimization of  2 of data/MC spectra shapes 2-dimensional fit of both data projections E. Goudzovski / Saclay, June 4 th, 2007

47. 47 Uncertainties & result Effect g  10 2 h  10 2 k  10 2 Fitting procedure ±0.009 ±0.007 ±0.006 Pion momentum resolution ±0.004 ±0.031 ±0.009 Spectrometer field±0.002±0.008±0.004 Spectrometer alignment±0.002±0.002±0.001 Stray magnetic field±0.001±0.002±0.001 Total systematic error ±0.010 ±0.033 ±0.012 Statistical uncertainty±0.009±0.015±0.005 Trigger correction (L1+L2) (mainly due to HODO inefficiency)–0.008±0.0050.116±0.0090.033±0.003 MC statistical uncertainty ±0.008 ±0.013 ±0.004 Final result–21.134±0.0171.848±0.040–0.463±0.014 PDG 2006 [for K + only] –21.54±0.35 1.20±0.80–1.01±0.34 Full ChPT NLO computation [Gámiz et al., JHEP 10 (2003) 042] –22.0±2.0 1.2±0.5–0.54±0.15 E. Goudzovski / Saclay, June 4 th, 2007

48. 48 Final result and prospects |M (K     +  – ) | 2 = A 0 (1+gu+hu 2 +kv 2 ) g = ( –21.134  0.017 )% h = ( 1.848  0.040 )% k = ( –0.463  0.014)% (Final result, 30% data set) (the PDG parameterization)  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 corrections is in preparation for deeper exploration of the data E. Goudzovski / Saclay, June 4 th, 2007

49. 49 Comparison to PDG Mast 69 Hoffmaster 72 Ford 72 Devaux 77 NA48/2 Ford 72 Devaux 77 NA48/2 Mast 69 Hoffmaster 72 Ford 72 Devaux 77 NA48/2 Mast 69 Hoffmaster 72 Ford 72 PDG’06 Linear: g  10 2 Quadratic: h  10 2 Quadratic: k  10 2  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 4 th, 2007

50. 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 4 th, 2007