1. Highlights on rare kaon decays from NA48/2 Monica Pepe INFN Perugia on behalf of the NA48/2 Collaboration Cambridge, 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. Crimea 2006 2 Monica Pepe – INFN Perugia Outline  The NA48/2 experiment  The decay K ±   ±  0   formalism  experimental status  NA48/2 measurement  Charged K e4 decays (K ±      e ± )  formalism  event selection  form factors  Neutral K e4 decays (K ±   0  0 e ± )  event selection  branching ratio  form factors  Cusp effect in  ±  0  0 decays  Conclusions

3. Crimea 2006 3 Monica Pepe – INFN Perugia The NA48/2 beam line Primary proton beam  p = 400 GeV/c (7  10 11 ppp) Simultaneous K + /K − beams  p = (60 ± 3) GeV/c K + /K − beam flux  3.8 (2.6) × 10 7 ppp 114 m

4. Crimea 2006 4 Monica Pepe – INFN Perugia The NA48/2 detector Spectrometer - 4 Drift Chambers (DCH) - Magnet  p/p = 1.0% + 0.044%  p [GeV/c]  x,y ~2mm Very good resolution for charged invariant masses  (  ±  +  - ) = 1.7 MeV/c 2 E/p measurement for e/  discrimination LKr EM calorimeter  E/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/c 2 Trigger (~1MHz  ~10kHz) LVL1 hodoscope and DCH multiplicity LVL2 on-line processing of information from LKR and DCH

5. Crimea 2006 5 Monica Pepe – INFN Perugia The NA48/2 experiment data taking Total statistics: K ±   ±  0  0 ~ 1·10 8 K ±   ±  +  - ~ 4·10 9 K ±   +  - e ± ~ 1·10 6 K ±   0  0 e ± ~ 3·10 4 2003 Run ~50 days2004 Run ~60 days Primary goal: Search for CP-violating charge asymmetries in K ±  3  decays (see E. Goudzovski talk)

6. Crimea 2006 6 Monica Pepe – INFN Perugia 1. The decay K ±       Results based on a sub-sample of 2003 data (~30 % of all)

7. Crimea 2006 7 Monica Pepe – INFN Perugia Photon production mechanism IB DE IBINT DE DEIB Sensitive variable: P * K = 4-momentum of the K ± P *  = 4-momentum of the  ± P *  = 4-momentum of the radiative   ± depends on 2 variables ( T *  and W) that can be reduced to only one integrating over T * 

8. Crimea 2006 8 Monica Pepe – INFN Perugia W distributions for IB, DE, INT  IB and DE contributions are well separated in W IBINTDE

9. Crimea 2006 9 Monica Pepe – INFN Perugia K →  amplitudes Two types of contributions:  Electric ( J=l±1) dipole (E 1 )  Magnetic (J=l) dipole (M 1 ) Electric contributions are dominated by the Inner Bremsstrahlung term DE shows up only at order O(p 4 ) 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 Inner Bremsstrahlung(IB) : (2.75±0.15)·10 -4 PDG (2006) (55<T *  <90 MeV) Direct Emission (DE) : (4.4±0.7)·10 -6 PDG (2006) (55<T *  <90 MeV) Interference (INT) : not yet measured  Frac(DE) = (1.6±0.3)%

10. Crimea 2006 10 Monica Pepe – INFN Perugia BNL E787 KEK E470 Exp results for DE and INT All the measurements have been performed: in the T *  region 55-90 MeV to avoid  ±   and  ±     background assuming Interference term = 0 Interference measurements: ExperimentYear# EventsBR(DE) × 10 6 E787 [20] E470 [21] E787 [22] E470 [23] 2000 2003 2005 19836 4434 20571 10154 4.7 ± 0.8 ± 0.3 3.2 ± 1.3 ± 1.0 3.8 ± 0.8 ± 0.7 History of DE Branching ratio

11. Crimea 2006 11 Monica Pepe – INFN Perugia 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      candidates, 124k used in the fit )  Enlarged T *  region in the low energy part (0 < T *  < 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 ‰  mistagging probability for IB, DE and INT

12. Crimea 2006 12 Monica Pepe – INFN Perugia Enlarged T *  region T *   T *   DE  T *   INT  Standard region Use standard region 55 < T *  < 90 MeV as 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 *  < 80 MeV to improve statistics and sensitivity to DE

13. Crimea 2006 13 Monica Pepe – INFN Perugia K ±   ±    selection Track Selection # tracks = 1 P  > 10 GeV E/P < 0.85 No muon veto hits 0 MeV < T *  < 80 MeV BG Rejection COG < 2 cm Overlapping  cuts |M K -M KPDG | < 10 MeV 220K events  Tagging Optimization CHA and NEU vertex compatibility Only one compatible NEU vertex  Selection N  = 3 (LKr clusters well separated in time) Min  energy > 3 GeV (>5 for the fit)

14. Crimea 2006 14 Monica Pepe – INFN Perugia Data-MC comparison W(Data)/W (IB MC ) Fitting region IB dominated region IB dominated part of the W spectrum Radiated  energy (IB dominated) Data MC for E  (W<0.5) E  min cut IB contribution is very well reproduced by MC MC − data

15. Crimea 2006 15 Monica Pepe – INFN Perugia Main BG sources  Physical BG rejection:      (IB bg)  T *  < 80 MeV, M K and COG cuts        (DE bg)  release T *  cut but cut on kaon mass (missing  and overlapping  )  Accidental BG rejection (      e      Clean beam + Very good time, space, and mass resolutions DecayBRBackground mechanism ± ±  (21.13±0.14)% +1 accidental or hadronic extra cluster  ±   ±     (1.76±0.04)% -1 missing or 2 overlapped   ±    e  (4.87±0.06)% +1 accidental  and e misidentified as a   ±      (3.27±0.06)% +1 accidental  and  misidentified as a   ±    e   (2.66±0.2)·10 −4 e misidentified as a   ±       (2.4±0.85)·10 −5  misidentified as a 

16. Crimea 2006 16 Monica Pepe – INFN Perugia K          K        BG rejection performance Source%IB%DE ±± ~1·10 -4 ~0.61·10 -2 Accidentals <0.5·10 -4 ~0.3·10 -2 Total BG < 1% of DE component  All physical BG can be explained in terms of  ±     events only  Very small contribution from accidentals is neglected Selected region 220K events

17. Crimea 2006 17 Monica Pepe – INFN Perugia Systematic uncertainties Effect Syst. DESyst. INT Energy scale +0.09-0.21 Fitting procedure 0.020.19 LVL1 Trigger ±0.17±0.43 Mistagging _±0.2 LVL2 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 Monte-Carlo Systematic effects dominated by the trigger both LVL1 and LVL2 triggers modified in the 2004 run  systematics reduced in 2004 data set

18. Crimea 2006 18 Monica Pepe – INFN Perugia Fit results  14 bins, 0.2 5 GeV  124k evts  Correlation coefficient:  = -0.92  Systematics dominated by trigger efficiency  Error dominated by statistics  To compare with previous exp: extrapolating to 55 < T*  < 90 MeV, INT=0 Frac(DE) 0 < T *  < 80 MeV = (3.35 ± 0.35 ± 0.25)% Frac(INT) 0< T *  <80 MeV = (-2.67 ± 0.81 ± 0.73)% First evidence for non zero Interference term INT=0 Frac(DE) 55< T *  <90 MeV =(0.85 ± 0.05 ± 0.02)% Preliminary

19. Crimea 2006 19 Monica Pepe – INFN Perugia 2. 2. K ±      e ±  K +- e 4   Preliminary results based on 30 days in 2003

20. Crimea 2006 20 Monica Pepe – INFN Perugia K e4 Introduction  Very precise theoretical predictions from  PT (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 a 0 0 and a 0 2 predicted as a function of q.c.  Low energies  pairs can be used for scattering length measurements  K e4  no other hadrons, no theoretical uncertainty on form factors, only on a 0 2 = f(a 0 0 )  Form factors are good constraint for  PT Lagrangian  Both modes have small BR ~ few 10 -5  high statistics and strong background rejection required

21. Crimea 2006 21 Monica Pepe – INFN Perugia Charged Ke4 formalism Ke4 decay described using 5 kinematic variables ( defined by Cabibbo-Maksymowicz) dipion dilepton Form factors of decay rate determined from a fit to experimental distributions of the 5 variables, provided the binning is small enough Form factors F = F s e i  0 0 + F p e i  1 1 cos  + d-wave term... G = G p e i  1 1 + d-wave term... H = H p e i  1 1 + d-wave term... Keeping only s and p waves, rotating phases by  1 1 only 5 form factors are left F s F p G p H p and  =  0 0 -  1 1 M , M e, cos  , cos  e,  22 Form factor formulations by Pais and Treman [Phys. Rev. 168 (1968)] and Amoros and Bijnens [J.Phys. G25 (1999)] have been used Expanding in powers of q 2, S e F s = f s + f’ s q 2 + f’’ s q 4 + f e (S e /4m 2  )+… F p = f p + f’ p q 2 +.... G p = g p + g’ p q 2 +.... H p = h p + h’ p q 2 +....

22. Crimea 2006 22 Monica Pepe – INFN Perugia K ±      e ± Signal and Background p K (GeV/c) K +− e4 candidates (2003) ~370000 events with 0.5% background Bkg main sources  ±       e  or  mis-ID as e)  ±         Dalitz (ee  with e mis-ID as  and  undetected) Reconstruction of C.M. Variables: Assume fixed 60Gev/c Kaon along Z to extract P  without ambiguity: assign missing P t to  and compute the mass of the system or use  costrain to solve energy-momentum conservation equation  get P K Boost in the Kaon and dipion/dilepton rest frame to get angular variables Residual Bkg estimated from data: Wrong Sign events have same total charge (can only be Bkg)  Right Sign Bkg appears in the data with same or twice (  the rate as in Wrong Sign events

23. Crimea 2006 23 Monica Pepe – INFN Perugia Form Factor Determination CP symmetry: opposite K + /K - φ distributions K-K- K+K+ K + (235000 evts)  16 evts/bin K - (135000 evts)  9 evts/bin  Use equal population bins in the 5-dim space of C.M. variables  10 independent fits (one in each M  bin) assuming ~constant form factors in each bin  For each fit 1500 equal population bins:

24. Crimea 2006 24 Monica Pepe – INFN Perugia Results: F, G, H No overall normalization from Branching Ratio  quote relative form factors Preliminary S e (M 2 e ) dependence measurement consistent with 0

25. Crimea 2006 25 Monica Pepe – INFN Perugia Results: a 0 0 and a 0 2 Preliminary Use the Universal Band parametrization to extract a 0 0 with a 0 2 = f(a 0 0 ) [Descotes et al. EPJ C24 (2002)]  =  0 0 -  0 1 distribution fitted with 1 parameter a 0 0 function given in the numerical solution of Roy equation in [Ananthanarayan et al. Phys. Rept. 353(2001)] a 0 0 and a 0 2 constrained to lie on the centre of UB

26. Crimea 2006 26 Monica Pepe – INFN Perugia f s '/f s = 0.169 ± 0.009 stat ± 0.034 syst f s ''/f s = -0.091 ± 0.009 stat ± 0.031 syst f p /f s = -0.047 ± 0.006 stat ± 0.008 syst g p /f s = 0.891 ± 0.019 stat ± 0.020 syst g p '/f s = 0.111 ± 0.031 stat ± 0.032 syst h p /f s = -0.411 ± 0.027 stat ± 0.038 syst a 0 0 = 0.256 ± 0.008 stat ± 0.007 syst ± 0.018 theo K ±      e ± Preliminary Result and Systematics 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  S e dependence: possible bias from neglected dependence estimated by MC tests NA48/2 2003 data Preliminary

27. Crimea 2006 27 Monica Pepe – INFN Perugia 3. 3. K ±      e ±  K 00 e 4   Preliminary results based on 2003+2004 data

28. Crimea 2006 28 Monica Pepe – INFN Perugia K ±      e ± Signal and Background     e ±  Signal Topology: 2      in Lkr, 1 charged track from e (E/p),  missing E and P T Background main sources         +    mis-ID as e (dominant)   e ±   + accidental   Estimated from data reversing cuts K 00 e 4 candidates 2003  ~ 9600 events with 3% bkg K 00 e 4 candidates 2004  ~28000 events with 2% bkg Preliminary results  Branching Ratio from 2003 data using K ±   ±      as normalization channel  Form Factors from 2003+2004 data Systematic Uncertainties  Acceptance  Trigger efficiency  Energy measurement in LKr 2003+2004

29. Crimea 2006 29 Monica Pepe – INFN Perugia  Using part of the 2003 data (9642 events) and       as 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. Results: Branching Ratio NA48/2 2003 data Br(K 00 e4) = (2.587 ± 0.026 stat ± 0.019 syst ± 0.029 norm ) x 10 -5 Preliminary

30. Crimea 2006 30 Monica Pepe – INFN Perugia  Fit performed using both 2003 and 2004 data (~38K events) Results: Form Factors  Same formalism as for K +- e4 but for simmetry of the  0  0 system  only ONE form factor F (no P-wave) f s '/f s = 0.129 ± 0.036 stat ± 0.020 syst f s ''/f s = -0.040 ± 0.034 stat ± 0.020 syst Bkg Signal Consistency with K +- e4 measurement Errors are stat + sys assuming same correlation for both Preliminary

31. Crimea 2006 31 Monica Pepe – INFN Perugia 4. Cusp effect in       Results based on 2003 data – Phys. Lett. B633 (2006)

32. Crimea 2006 32 Monica Pepe – INFN Perugia  Data Sample: 23 · 10 6 K ±   ±  0  0 decays (2003) Observation of a Cusp in K ±   ±  0  0 a 0 -a 2 determined performing 1-dim fit to M 2 00 distribution based on the improved Cabibbo-Isidori rescattering model (JHEP 0503 (2005) 021) * In the matrix element g 0 and h’ are free parameters while the slope parameter k’ is set to 0 * Isospin breaking effects included + D.E. Ch. Ex.  +  - →  0  0 Sudden change of slope (“cusp”) at (M 00 ) 2 = (2m + ) 2 M 00 2 zoom on the cusp region M 00 2 (GeV 2 )

33. Crimea 2006 33 Monica Pepe – INFN Perugia Cusp in K ±   ±  0  0 : Fit and Results The scattering length difference: (a 0 -a 2 )m + = 0.268 ± 0.010 stat ± 0.004 syst ± 0.013 ext and (a 2 )m + = -0.041 ± 0.022 stat ± 0.014 syst if correlation between a 0 and a 2 predicted by ChPT is taken into account: (a 0 -a 2 )m + = 0.264 ± 0.006 stat ± 0.004 syst ± 0.013 ext From same fit slope parameters are obtained: g 0 = 0.645 ± 0.004 stat ± 0.009 syst h' = -0.047 ± 0.012 stat ± 0.011 syst Main Systematic Uncertainties: Acceptance, Trigger efficiency, Fit interval NA48/2 measurements of   scattering lengths from Ke4 Charged decays:  scattering lengths extracted in a model dependent way (input a 0 2 = f(a 0 0 ))  use Universal Band function NA48/2 Preliminary (370k decays)  a 0 0 = 0.256 ± 0.008 stat ± 0.007 syst ± 0.018 theo Previous published results: CERN/PS Geneva-Saclay (30k decays)  a 0 0 = 0.253 ± 0.037 stat+sys ± 0.014 theo BNL E865 (400k decays)  a 0 0 = 0.229 ± 0.012 stat ± 0.004 sys ±0.014 theo (but beware of different theoretical frameworks when comparing Cusp and ke4.......)

34. Crimea 2006 34 Monica Pepe – INFN Perugia 2-dim fit to the Dalitz plot  evidence for k’>0 term cos  = angle between  ± and  0 in  0  0 cms NA48/2 preliminary result (2003 data) k’ = 0.0097 ±0.0003 stat ±0.0008 syst  corresponding changes in the g 0 and h’ parameters are of order 2% and 25% respectively  no change in a 0 -a 2 and a 2 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 :

35. Crimea 2006 35 Monica Pepe – INFN Perugia Conclusions Frac(DE) 0<T*  <80 MeV = (3.35 ± 0.35 ± 0.25)% Frac(INT) 0<T*  <80 MeV = (-2.67 ± 0.81 ± 0.73)%  First measurement of the DE and INT terms in the decay K ±   ±  0   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 K e4 form factors:  K +- e4  Form factor measurement dominated by systematics;  scattering dominated by external error of 7% (stat and syst uncertainties ~3% relative each) a 0 0 = 0.256 ± 0.008 stat ± 0.007 syst ± 0.018 theo  K 00 e4  Form factors consistent with K +- e4. Improved (by factor 8) measurement of B.R. Br(K 00 e4 ) = (2.587 ± 0.026 stat ± 0.019 syst ± 0.029 norm ) x 10 -5  Cusp observed in K ±   ±  0  0 decays  interpreted as  charge exchange process providing a new method to extract scattering lengths (a 0 -a 2 )m + = 0.268 ± 0.010 stat ± 0.004 syst ± 0.013 ext  first evidence for a value of k’  0 in the K ±   ±  0  0 Dalitz plot k’ = 0.0097 ± 0.0003 stat ± 0.0008 syst

36. Crimea 2006 36 Monica Pepe – INFN Perugia Backup slides

37. Crimea 2006 37 Monica Pepe – INFN Perugia General expression for decay rate  ± depends on 2 variables (W e T    that can be reduced to only one integrating over T *    leading to the above formula where W is a Lorentz invariant variable. The above formula shows the 3 contributions separately: IB, DE, INT. The INT may arise only between the electrical contribution of DE and the IB term. If the INT term near 0 the electrical contributions in the DE term has to be very small. With this parametrization the ratio data/MC(IB) has the form 1+  W 2 +  W 4 IB DE IBINT DE P * K = 4-momentum of the K ± P *  = 4-momentum of the  ± P *  = 4-momentum of the radiative 

38. Crimea 2006 38 Monica Pepe – INFN Perugia Reconstruction strategy Z V (CHA) 11 33 22 Z V (2-3) Z V (1-3) Z V (NEU) LKr Two independent determination of K decay vertex: 1) charged vertex Z V (CHA) using K and  flight directions (DCH) 2) neutral vertex Z V (NEU) imposing  0 mass to γ γ pairs (LKr) Three Z V (NEU) combinations : Z V (12), Z V (23), Z V (13) choose the vertex giving the best kaon mass. identify the radiated 

39. Crimea 2006 39 Monica Pepe – INFN Perugia Overlapping  rejection 1) Split 1 out of the 3 clusters in two  of energies:  1 =xE CL  2 =(1-x)E CL  get 4  and reconstruct the event as a  ±    . 2) Compute Z V (x) pairing the gammas and extract x imposing: Zv(   1 )= Zv(  0 2 ) ( The two  0 come from the same K!) Zv(  0 2 ) Zv(   1 ) 3) Use x in the Zv(  0 2 ) to get the real Z V (neu) If |Zv(CHA)-Zv(neu)|<400 cm  the  are really overlapped  REJECT Overlapped gamma events are a very dangerous BG source: - M K, and COG cut automatically satisfied! - Releasing the T *  cut they can give sizable contribution Powerful rejection using the NA48 calorimeter - high granularity (2x2 cm cells) - good Z vertex resolution Multi step algorithm looped over clusters:

40. Crimea 2006 40 Monica Pepe – INFN Perugia ■ DE ▼IB Mistagged  events: a self BG Mistagged gamma events behave like BG because they can induce fake shapes in the W distribution. In fact due to the slope of IB W distribution they tend to populate the region of high W simulating DE events. The mistagging probability has been evaluated in MC as a function of the mistagging cut to be 1.2‰ at 400 cm 2 steps rejection of mistagged events : 1. Compatibility of charged and neutral vertices (2.5% mistagging) 2. Distance between best and second best neutral vertices > xx cm Very similar mistagging probabilities for IB and DE events

41. Crimea 2006 41 Monica Pepe – INFN Perugia Fitting algorithm To get the fractions of IB(  ), DE(  ), INT(  ), from data we use an extended maximum likelihood approach: The fit has been performed in 14 bins, between 0.2-0.9, with a minimum  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

42. Crimea 2006 42 Monica Pepe – INFN Perugia INT=0 fit: just for comparison For comparison with other experiments we have extracted the fraction of DE, with the INT term fixed to 0 in the region 55-90 MeV. A likelihood fit using IB & DE MC only has been performed in the region 0<T *  <80 MeV. Extrapolating to the 55-90 region using MC: The analysis of fit residuals shows a bad  2 Description in term of IB+DE only is unable to reproduce W data spectrum.

43. Crimea 2006 43 Monica Pepe – INFN Perugia L1 trigger NT-PEAK 4 cm Y view X view X OR Y > 2 view

44. Crimea 2006 44 Monica Pepe – INFN Perugia Aim to reject K ± →  ±  0 events and get  ±  0  0. It’s based on the online computation of Mfake: Mfake ~ M K for K ± →  ±  0 events in fact m  2 –MM 2 ~ 0. Only events with M FAKE < 475 MeV, are collected by the trigger MBX1TR-P LVL2 trigger

45. Crimea 2006 45 Monica Pepe – INFN Perugia K +- e4 Event selection      track with p>5 GeV, no associated in time cluster or E/p < 0.8  e  track with associated in time cluster with 0.9 3 GeV  no other clusters with E>3 GeV, close in space and time  momentum obtained as as difference between kaon momentum and that of all visible particles, assuming P k = 60 GeV along z  looser criteria to measure efficiency (release or lower E/p cut)  Selection criteria optimized using both Signal and Background MC samples

46. Crimea 2006 46 Monica Pepe – INFN Perugia K+K+ K-K-

47. Crimea 2006 47 Monica Pepe – INFN Perugia Form Factor Determination  Use equal population bins in the 5-dim space of C.M. variables one defines a grid of 10  5  5  5  12=15000 boxes  The set of form factor values are used to minimiza the T 2, a log- likelihood estimator well suited for small numbers of data events/bin (Nj) and taking into account the statistics of the simulation (Mj simulated events/bin and Rj expected events/bin)

48. Crimea 2006 48 Monica Pepe – INFN Perugia K 00 e4 Event selection  ≥ 4 good  clusters in LKr  ≥ 1 good track with E/p ≥ 0.95  2 good  0 with similar Z V vertex position (Neutral vertex)  shower width cut to distinguish e and   Use the K for momentum from KABES to evaluate momentum assuming P T =0  The Kaon mass can be evaluated

49. Crimea 2006 49 Monica Pepe – INFN Perugia Measurement technique for BR The Kaon flux has been measured using K ± →  ±      For the BR(K ± →  ±      new result from KLOE has been used: BR(K ± →  ±     )=(1.763±0.013±0.022)%

50. Crimea 2006 50 Monica Pepe – INFN Perugia 2003 BG estimates 9642 events with the following BG: 260±94 from K ± →        ± 2 accidental BG form K e3 (  ) 1.K ± →       →same final state of signal IF  misidentified as an e - E over P and shower width cut to identify hadronic showers from EM ones - Elliptic cut in the P T and M K (  ±     ) plane to identify  ±     decays 2.K ± →e ±  0 (  )  → plus an accidental  Quite clean sample BG less than 3%

51. Crimea 2006 51 Monica Pepe – INFN Perugia The K ±   ±  0  0 decay Matrix element |M(u,v)| 2 ~ 1 + gu + hu 2 + kv 2 just a polinomial expansion Linear slope g dominates over quadratic terms h, k (g = 0.652 ± 0.031) Lorentz-invariants 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 = 2m K ∙(m K /3-E odd )/m  2 v = (s 2 -s 1 )/m  2 = 2m K ∙(E 1 -E 2 )/m  2 NOTE: symmetry  º 1 ↔  º 2  only even powers of v are allowed (0, 2, ….) u v odd (charged) pion in the beam pipe

52. Crimea 2006 52 Monica Pepe – INFN Perugia Structure in K ±   ±  0  0 decay Search for pionium atoms in the K ±   ±  0  0 channel as a resonance in the  0  0 invariant mass (threshold for  +  - production) exploiting Very high statistics, very good calorimeter resolution proper M 00 reconstruction strategy Data reveal a structure in the region N. Cabibbo: “It is a clean and beautiful example of a general cusp-like behaviour of cross sections next to threshold for new channels” A method based on first principles (unitarity, analiticity) for extracting information on strong interaction at low energy  First observation of  scattering effects in the Dalitz plot  Precise and model independent measurement of a 0 -a 2 (the difference between  scattering lengths in the isospin I=0 and I=2 states)

53. Crimea 2006 53 Monica Pepe – INFN Perugia Results on the scattering lengths NA48/2 Batley et al., Phys. Lett. B 633 (2006) 173 Stat. Syst.Ext. (a 0 -a 2 )m + 0.268± 0.010 ± 0.004± 0.013 a2m+a2m+ -0.041± 0.022 ± 0.014 Final results of the unconstrained fit to the re-scattering model Performing the fit with constraints imposed on a 0 and a 2 by analycity and chiral symmetry (after Colangelo et al. PRL 86 (2001) 5008) leads to the following Stat. Syst.Ext. (a 0 -a 2 )m + 0.264± 0.006 ± 0.004± 0.013 a0m+a0m+ 0.220± 0.006 ± 0.004± 0.011 N.B. The two statistical errors from the fit are strongly correlated (-0.86)