Highlights on rare kaon decays from NA48/2

1. Highlights on rare kaon decays from NA48/2 Monica Pepe INFN Perugia on behalf of the NA48/2 CollaborationCambridge, CERN, Chicago, Dubna, Edinburgh, Ferrara, Firenze, Mainz, Northwestern, Perugia, Pisa, Saclay, Siegen, Torino, Vienna CRIMEA 2006 - NEW TRENDS IN HIGH-ENERGY PHYSICS Yalta, Crimea, Ukraine September 16-23, 2006

2. Outline • The NA48/2 experiment • The decayK±  p± p0 g • formalism • experimental status • NA48/2 measurement • Charged Ke4 decays (K±  p+p-e± n) • formalism • event selection • form factors • Neutral Ke4 decays (K±  p0p0e±n) • event selection • branching ratio • form factors • Cusp effect in p±p0p0decays • Conclusions 2

3. The NA48/2 beam line 114 m • Primary proton beam  p = 400 GeV/c (71011 ppp) • Simultaneous K+/K− beams  p = (60 ± 3) GeV/c • K+/K− beam flux  3.8 (2.6) × 107 ppp 3

4. The NA48/2 detector LKr EM calorimeter DE/E = (3.2/E + 9/E + 0.42)% [GeV] x,y < 1.5mm Very good resolution for neutral invariant masses(±00)= 1.4 MeV/c2 • Spectrometer • 4 Drift Chambers (DCH)- Magnet • Dp/p = 1.0% + 0.044% p [GeV/c] • x,y ~2mm • Very good resolution for charged invariant masses (±+-)= 1.7 MeV/c2 • E/p measurement for e/pdiscrimination Trigger (~1MHz  ~10kHz) LVL1 hodoscope and DCH multiplicity LVL2 on-line processing of information from LKR and DCH 4

5. The NA48/2 experiment data taking 2003 Run ~50 days 2004 Run ~60 days Total statistics: K± ±00 ~ 1·108 K± ±+- ~ 4·109 K± +- e± n~ 1·106 K± 00 e± n~ 3·104 Primary goal: Search for CP-violating charge asymmetries in K±  3decays (see E. Goudzovski talk) 5

6. 1.The decay K±  p±p0g Results based on a sub-sample of 2003 data (~30 % of all) 6

7. IB DE DE IB IB INT DE P*K = 4-momentum of the K±P*p = 4-momentum of the p±P*g = 4-momentum of the radiative g Photon production mechanism G±depends on 2 variables (T*p and W) that can be reduced to only one integrating overT*p Sensitive variable: 7

8. IB DE INT W distributions for IB, DE, INT • IB and DE contributions are well separated in W 8

9. Inner Bremsstrahlung(IB) : (2.75±0.15)·10-4 PDG (2006)(55<T*p<90 MeV) Direct Emission (DE): (4.4±0.7)·10-6 PDG(2006)(55<T*p<90 MeV) Interference (INT): not yet measured  Frac(DE) =(1.6±0.3)% K→ppgamplitudes • Two types of contributions: • Electric (J=l±1) dipole (E1) • Magnetic (J=l) dipole (M1) • Electric contributions are dominated by the Inner Bremsstrahlungterm • DE shows up only at order O(p4) in CHPT: is generated by both E and M contributions • Present experimental results seem to suggest a Magnetic dominated DE • INT term is sensitive to E only 9

10. History of DE Branching ratio Interference measurements: BNL E787 KEK E470 Exp results for DE and INT • All the measurements have been performed: • in the T*pregion55-90 MeVto avoidp±p0 andp±p0p0background • assuming Interference term = 0 10

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(220kp±p0gcandidates, 124k used in the fit ) • EnlargedT*pregion in the low energy part (0 <T*p< 80 MeV) • Negligiblebackground 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‰ gmistagging probability for IB, DE and INT 11

12. T*p(IB) T*p(INT) T*p(DE) Standard region Standard region Standard region Enlarged T*p region Use standard region55<T*p<90 MeVas safe choice for BG rejection But…. region <55 MeV is the most interesting to measure DE and INT This measurement is performed in the region 0 < T*p< 80 MeV to improve statistics and sensitivity to DE 12

13. 220K events K±p±p0gselection • Track Selection • #tracks = 1 • Pp+> 10 GeV • E/P < 0.85 • No muon veto hits • 0 MeV< T*p< 80 MeV • BG Rejection • COG < 2 cm • Overlappinggcuts • |MK-MKPDG| < 10 MeV • gSelection • Ng=3 (LKr clusters well separated in time) • Mingenergy > 3 GeV (>5 for the fit) • gTagging Optimization • CHA and NEU vertex compatibility • Only one compatible NEU vertex 13

14. Main BG sources • Physical BG rejection: • p±p0(IB bg)T*p < 80 MeV , MKand COG cuts • p±p0p0(DE bg)release T*pcut but cut on kaon mass (missinggand overlappingg) • Accidental BG rejection (p±p0, Ke3, Km3) • Clean beam + Very good time, space, and mass resolutions 15

15. K± p±p0p0 • K±p±p0g BG rejection performance • All physical BG can be explained in terms ofp±p0p0events only • Very small contribution from accidentals is neglected Selected region 220Kevents Total BG < 1% of DE component 16

16. Systematic uncertainties Many systematic checks have been performed using both data and Monte-Carlo Systematic effects dominated by the trigger both LVL1 and LVL2 triggers modified in the 2004 run systematics reduced in 2004 data set 17

17. INT=0 Frac(DE)55<T*p<90MeV =(0.85 ± 0.05 ± 0.02)% Fit results Frac(DE)0<T*p<80MeV = (3.35 ± 0.35 ± 0.25)% Frac(INT)0<T*p<80MeV = (-2.67 ± 0.81 ± 0.73)% Preliminary First evidence for non zero Interference term • 14 bins, 0.2 < W < 0.9, Eg > 5 GeV  124k evts • Correlation coefficient: r = -0.92 • Systematics dominated by trigger efficiency • Error dominated by statistics • To compare with previous exp:extrapolating to 55< T*p< 90MeV,INT=0 18

18. K±  p+p-e±n (K+-e4)Preliminary results based on 30 days in 2003 19

19. Ke4 Introduction • Very precise theoretical predictions from cPT(2%) depending only on one free parameter (quark condensate) to be determined experimentally  it determines the relative size of mass and momentum in the power expansion  scattering lengths a00and a02 predicted as a function of q.c. • Low energiesp-ppairs can be used for scattering length measurements • Ke4 no other hadrons, no theoretical uncertainty on form factors, only on a02 = f(a00)  Form factors are good constraint forcPTLagrangian • Both modes have small BR ~ few 10-5  high statistics and strong background rejection required 20

20. 2 2 Mp p, Men, cosp,cose , dipion dilepton Charged Ke4 formalism Ke4 decay described using 5 kinematic variables (defined by Cabibbo-Maksymowicz) Form factors of decay rate determined from a fit to experimental distributions of the 5 variables, provided the binning is small enough Expanding in powers of q2, Se Fs = fs+ f’s q2 + f’’s q4 + fe(Se/4m2p )+… Fp = fp+ f’p q2 +.... Gp = gp+ g’p q2 +.... Hp = hp+ h’p q2 +.... Form factors F = Fs ei00+ Fp ei11cos+ d-wave term... G = Gp ei11+ d-wave term... H = Hp ei11+ d-wave term... Keeping only s and p waves, rotating phases by 11only 5 form factors are left Fs Fp Gp Hp and  = 00 - 11 Form factor formulations by Pais and Treman [Phys. Rev. 168 (1968)] and Amoros and Bijnens [J.Phys. G25 (1999)] have been used 21

21. K± p+p-e±nSignal andBackground K+−e4candidates (2003) ~370000 events with 0.5% background • Reconstruction of C.M. Variables: • Assume fixed 60Gev/c Kaon along Z to extract Pnwithout ambiguity: assign missing Ptto n and compute the mass of the system • or use n costrain to solve energy-momentum conservation equation  get PK • Boost in the Kaon and dipion/dilepton rest frame to get angular variables Residual Bkg estimated from data:Wrong Signeventshave same total charge (can only be Bkg) Right Sign Bkg appears in the data with same or twice (3p) the rate as in Wrong Sign events Bkg main sources p±p+p-+(pen orp mis-ID as e) p±p0 (p0) + p0 Dalitz (eegwith e mis-ID as p and gundetected) pK(GeV/c) 22

22. Use equal population bins in the 5-dim space of C.M. variables • 10 independent fits (one in each Mp p bin) assuming ~constant form factors in each bin • For each fit 1500 equal population bins: • K+ (235000 evts) 16 evts/bin • K- (135000 evts) 9 evts/bin Form Factor Determination K+ CP symmetry: opposite K+/K-φdistributions K- 23

23. Preliminary Results: F, G, H No overall normalization from Branching Ratio  quote relative form factors Se (M2en) dependence measurement consistent with 0 24

24. Results: a00 and a02 • Use the Universal Band parametrization to extract a00 with a02= f(a00) [Descotes et al. EPJ C24 (2002)] = 00 - 01distribution fitted with 1 parameter a00function given in the numerical solution of Roy equation in [Ananthanarayan et al. Phys. Rept. 353(2001)] • a00anda02 constrained to lie on the centre of UB Preliminary 25

25. K±  p+p-e±nPreliminary Result and Systematics fs'/fs = 0.169 ± 0.009stat± 0.034systfs''/fs = -0.091 ± 0.009stat± 0.031systfp/fs = -0.047 ± 0.006stat± 0.008systgp/fs = 0.891 ± 0.019stat± 0.020systgp'/fs = 0.111 ± 0.031stat± 0.032systhp/fs = -0.411 ± 0.027stat± 0.038syst a00 = 0.256 ± 0.008stat ± 0.007syst ± 0.018theo Preliminary NA48/2 2003 data Systematics Checks • Two independent analyses (different selections, K reconstruction, acceptance corrections, fit method and MC parameters) • Acceptance vs Time estimated by varying beam conditions of simulated events • Background level checked with data (varying cuts) and MC • Electron-ID uncertainty estimated by variation of e-π rejection efficiency • Radiative Corrections: quote fraction of total effect with or w/o using PHOTOS • Se dependence: possible bias from neglected dependence estimated by MC tests 26

26. K±  p0p0e±n (K00e4)Preliminary results based on 2003+2004 data 27

27. K±  p0p0e±nSignal andBackground p0p0e±n Signal Topology: 2p04gin Lkr, 1 charged track from e (E/p) , nmissing E and PT 2003+2004 Backgroundmain sources p±p0p0+p mis-ID as e (dominant) p0e±n g+ accidental g Estimated from data reversing cuts K00e4 candidates 2003  ~ 9600 events with 3% bkg K00e4 candidates 2004  ~28000 events with 2% bkg Preliminary results • Branching Ratio from 2003 data using K± p±p0p0 as normalization channel • Form Factors from 2003+2004 data Systematic Uncertainties • Acceptance • Trigger efficiency • Energy measurement in LKr 28

28. NA48/2 2003 data Results: Branching Ratio • Using part of the 2003 data (9642 events) and p±p0p0as normalization channel • Result cross-checked using Ke3 as normalization • Improved measurement compared with recent results: KEK-E470 (216 events)  BR = (2.29 ± 0.33) x 10-5 Br(K00e4) = (2.587 ± 0.026stat± 0.019syst± 0.029norm) x 10-5 Preliminary . 29

29. Results: Form Factors • Same formalism as forK+-e4 but for simmetry of the p0 p0 system  only ONE form factor F (no P-wave) • Fit performed usingboth 2003 and 2004data(~38K events) fs'/fs = 0.129 ± 0.036stat ± 0.020systfs''/fs = -0.040 ± 0.034stat ± 0.020syst Preliminary Signal • Consistency with K+-e4 measurement • Errors are stat + sys assuming same correlation for both Bkg Signal Bkg 30

30. 4. Cusp effect inp±p0p0 Results based on 2003 data – Phys. Lett. B633 (2006) 31

31. Observation of a Cuspin K±  ±00 • a0-a2 determined performing 1-dim fit toM200distribution based on the improved Cabibbo-Isidori rescattering model • (JHEP 0503 (2005) 021) • * In the matrix element g0 and h’ are free parameters while the • slope parameter k’is set to 0 * Isospin breaking effects included M002 zoom on the cusp region Sudden change of slope (“cusp”) at (M00)2 = (2m+)2 D.E. Ch. Ex. p+p- →p0p0 + M002 (GeV2) • Data Sample: 23 · 106K±  ±00 decays (2003) 32

32. Cuspin K±  ±00: Fit and Results The scattering length difference: (a0-a2)m+= 0.268 ± 0.010stat ± 0.004syst ± 0.013ext and (a2)m+= -0.041 ± 0.022stat ± 0.014syst if correlation between a0and a2predicted by ChPT is taken into account: (a0-a2)m+= 0.264 ± 0.006stat ± 0.004syst ± 0.013ext From same fit slope parameters are obtained: g0 = 0.645 ± 0.004stat ± 0.009syst h' = -0.047 ± 0.012stat ± 0.011syst Main Systematic Uncertainties: Acceptance, Trigger efficiency, Fit interval • NA48/2 measurements ofpp scattering lengths from Ke4 Charged decays: • scattering lengths extracted in a model dependent way (input a02= f(a00)) • use Universal Band function • NA48/2 Preliminary (370k decays) a00= 0.256 ± 0.008stat ± 0.007syst ± 0.018theo • Previous published results: • CERN/PS Geneva-Saclay (30k decays) a00= 0.253 ± 0.037stat+sys ± 0.014theo • BNL E865 (400k decays) a00= 0.229 ± 0.012stat ± 0.004sys ±0.014theo • (but beware of different theoretical frameworks when comparing Cusp and ke4 .......) 33

33. Update to 2003 result: Effect on K term • The above result was obtained assuming no quadratic term in v (k’=0) for the unperturbated matrix element but.... analysis shows evidence for a non-zero quadratic v term: 2-dim fit to the Dalitz plot  evidence for k’>0 term NA48/2 preliminary result (2003 data) k’ = 0.0097 ±0.0003stat±0.0008syst cos = angle betweenp±andp0 inp0 p 0cms • corresponding changes in theg0andh’parameters are of order2%and25% respectively • no change in a0-a2 and a2 34

34. First measurement of the DE and INT termsin the decayK±  p± p0 g • Error dominated by statistics: will be reduced analyzing full 2003 and 2004 data • Using part of 2003-2004 data NA48/2 has performed improved measurements of Ke4form factors: • K+-e4  Form factor measurement dominated by systematics; pp scattering dominated by external error of 7% (stat and syst uncertainties ~3% relative each) a00 = 0.256 ± 0.008stat ± 0.007syst ± 0.018theo • K00e4  Form factors consistent with K+-e4 . Improved (by factor 8) measurement of B.R. Br(K00e4) = (2.587 ± 0.026stat± 0.019syst± 0.029norm) x 10-5 • Cusp observed in K±  p± p0 p0decays • interpreted aspp charge exchange process providing anew method to extract scattering lengths (a0-a2)m+= 0.268 ± 0.010stat ± 0.004syst ± 0.013ext • first evidence for a value of k’0 in the K± p± p0 p0Dalitz plot k’ = 0.0097 ± 0.0003stat ± 0.0008syst Frac(DE)0<T*p<80 MeV = (3.35 ± 0.35 ± 0.25)% Frac(INT)0<T*p<80 MeV = (-2.67 ± 0.81 ± 0.73)% Conclusions 35