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Measurement of Scattering Lengths in Ke4 and K3p Decays at CERN SPS Experiment NA48/2

This study aims to measure the scattering lengths in Ke4 and K3p decays at the CERN SPS experiment NA48/2. The S-wave scattering lengths are important parameters in Chiral Perturbation Theory and can be measured through the cusp effect in these decays. The analysis includes data from 2003 and 2004, and the results show a clear cusp in the first derivative, indicating unexpected behavior of kaons.

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Measurement of Scattering Lengths in Ke4 and K3p Decays at CERN SPS Experiment NA48/2

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  1. ppscattering lengths measurement from Ke4 and K3p decays at CERN SPS experiment NA48/2 Sergio Giudici University of Pisa and INFN On behalf of the NA48/2 collaboration: Cambridge, CERN, Chicago, Dubna, Edimburgh, Ferrara, Firenze, Mainz, Northwestern, Perugia, Pisa, Saclay, Siegen, Torino , Wien Heavy Quarks & Lepton University of Melbourne, June 5-9 2008

  2. ppscattering lengths : why interesting ? p p R At low energy KR << 1 S-wave dominates total cross section Isospin I = 0,2 only allowed by Bose statistics Scattering matrix S|pp> =exp(2id) |pp> may be parametrized with2 phases:d0,2 = a0,2 k related to scattering lengths a0 , a2 2 clean measurements can be done cusp-effect in K3p decay: a0 , a2 phase shift in Ke4decays:ds- dp  a0 , a2 At low energy the S-wave scattering lengths are essential parameters of Chiral Pertubation Theory (CHPT)

  3. Cuspeffect inK  00 Initial curiosity was to observe p+p- bound states ( “pionium” ) annihilation in p0p0 K  (p+p-)Bound = pionium “Pionium” would produce an excess of events at the m00 = 2m+= 2x139.57 MeV 00 s =0.56 MeV at pionium 0 masses constraint optimizes Resolution at low m00 values Good Resolution due to excellent NA48 LKR calorimeter performances and small Q-value

  4. 4m+2 4m+2 Cuspeffect inK  00 Zoom in Cusp region Statistics: 2003 data : 16.0 M 2004 data : 43.6 M Total : ~ 60 M events Clear visible discontinuity in the first derivative = CUSP Unexpected Kaon Gothic behaviour  Cusp in Notre Dame, Paris ...

  5. p+ p+ p0 p+ K+ Combination of S-wave pp scattering length p0 p- p0 K+ p0 Decay Amplitude : M(K 00) = M0 + M1 + M2 + ... Theory: pp rescattering. Dalitz plot variable u = 2mK (mk/3 – Eodd)/mp2 v = 2mK (E1 – E2) /mp2 Direct emission M0 = A0 (1 + g0 u/2 + h’u2/2 + k’v2/2) M1 = -2/3 (a0-a2) m+ A+ K 3 Amplitude 1 loop Rescattering (N. Cabibbo , PRL 93 , 2004, 121801) 2 loop Rescattering: (N. Cabibbo & G. Isidori JHEP 0503:021 , 2005)

  6. Theory describes the data ... Fitting procedure Combined 2003+2004 samples 2loops Cabibbo-Isidori fit One dimensional fit to M002 distribution MINUIT minimization of 2of data/MC spectra shapes Fitting up to half spectrum 0.097 (GeV/c2) since Cabibbo Theory is an expansion around 2m+ threshold Fit to 5 parameters: Norm,g, h’ , (a0- a2) and a2 (k’ fixed) For final result 7 bins around cusp excluded from the fit : EM corrections Not yet included in the model The excess of events in this region is interpreted as pionium combined with E.M. corrections Th. Prediction = 0.8 x 10-5 (JTEP lett. 60, 1994, 689)

  7. Scattering length from CUSP a0- a2 = 0.261 ± 0.006stat ± 0.003syst ± 0.0013ext ± 0.013th a2 = -0.037 ± 0.013stat ± 0.009syst ± 0.002ext External uncertainty: from the uncertainty on the ratio of K+ → p+p+p- and K+ → p+pp decay widths A+ /A0 = 1.97  0.015 Theoretical uncertainty on (a0 – a2) ± 5% DOMINATES !!! (Cabibbo-Isidori Theory uncertainty from neglecting higher order diagrams and radiative corrections) From (a0 – a2) and a2 can be extracted a0 (taken into account the statistical error correlation coefficient ≈ -0.92) a0 = 0.224 ± 0.008stat ± 0.006syst ± 0.003ext ± 0.013th

  8. Uncertainties - CUSP method

  9. Comparison: NA48 vs DIRAC DIRAC experiment measured pionium 1S state lifetime to be Corresponding to (PLB 619, 50, 2005) Black Ellipse = NA48 CUSP measurement (Statistical systematic error) Yellow area = theoretical uncertainty in Cabibbo-Isidori Model (assumed Gaussian)

  10. p*(e+) p*(p+) f qp qe en direction in the K+ rest frame pp direction in the K+ rest frame K+ p- ne K  +-e±ν: Theory 5 kinematic variables (Cabibbo – Maksymowicz) N.B. Kaon and electron with same sign DS = DQ rule S = M2 , Se = M2eν, cosθ, cosθe and Φ Expansion in power of q2 = Sp/4m2p Partial wave (S,P) expansion of the Amplitude: F,G = Axial Form Factors F = FS e id s + FP e id pcosθ + d-wave term G = GPe idg + d-wave term H = Vector Form Factor H = HP eidh + d-wave term Assuming same phase for F,G,H The fit parameter are : FS FP GP HP and d = ds - dp

  11. K  +-e±ν: Selection and background Topology: 3 charged track , Signal: 2p with opposite charge 1 e identified with E/p ~1 , additional Missing v energy and pt cuts Background main sources: p+p+p-decays and p eν (dominant) or p misidentified as e p+p0p0decays and p0 dalitz decay , g undetected or e misidentified as p Background estimated by Montecarlo Simulation ... But.... Wrong sign events Event p+p+e- (violating DS = DQ rule) provide a check for MC background estimate

  12. Fitting procedure and Statistics • Define 10x5x5x5x12 iso-populated bins in (Mππ,Meν ,cos qπ ,cos qe ,f) • The form factors are extracted from the data using simulated events by minimizing a log-likehood estimator in each of the Mpp bins: • In each Mpp bin the form factors are assumed to be constant • 10 independent fits (one fit per Mpp bin) of 4 parameters (Fp, Gp , Hp and d) plus free normalization (related to Fs) in 4D space. • The correlation between the 4+1 parameters is taken into account. • K+ and K- fitted separately and combined.

  13. 0.309 < Mpp < 0.318 GeV 2m+ < Mpp < 0.291 GeV f f 0.335 < Mpp < 0.345 GeV 0.373 GeV < Mpp < mK f f f distributions d= ds – dpof the Ke4 decay amplitude is extracted from the measured asymmetry of the f distribution as function of Mpp The asymmetry of the f distribution increases with Mpp  Increasing sensitivity to d K+ and K- have opposite f asymmetry

  14. Phase shift VS Mpp Direct measured points (NO MODEL ASSUMED SO FAR) From NOW on MODEL assumptions are needed To extract information from d variation, some theoretical work is needed: Numerical solution of Roy equation which relatesdand a0 , a2 (ACGL Phys. Rep. 352 , 2001 ; DFGS EPJ C24 , 2002)

  15. Phase shift : Comparison BNL E865 quotes various values ranging from a0 = 0.203 to a0 = 0.237 Note the last BNL point !!! Predictions for a0=0.26 and a0=0.22

  16. NA48/2 Ke4 (a0, a2) plane Ke4 result Under the assumption of Isospin symmetry and using Roy Equation a0 = 0.233  0.016 stat  0.007 syst a2 = - 0.0471  0.011 stat  0.004 syst EPJC 54, 2008, 411 CHPT predictions a0 = 0.220  0.005 a2 = - 0.0444  0.0010 NPB 603, 125 , 2001

  17. Conclusions The pion pion scattering lengths have been measured by NA48/2. Two methods based on two different charge Kaon decay processes Give results in good agreement. The experimental measured scattering lengths agree with CHPT predicted values at the per cent level. This measurement is one of the most stringent test for CHPT ... Final Invitation ...

  18. Ratio data / prediction 4m+2 CUSP effect in KL30 Change of slope where it has to be.... K long sample of ~ 100M events collected in 2000 The CUSP visibility is ~13 smaller CALL TO KTEV : LET THE CUSP BE SEEN IN YOUR HUGE Klong statistics

  19. two possible p+p-pairs M+ + -:K+→ p+ p+ p-matrix element M+ 0 0:K+→ p+ p pmatrix element M+ - 0:KL→ p+ p- pmatrix element M0 0 0:KL→ p p pmatrix element R(K+) R(KL) ≈ 13 CUSP VISIBILITY Calculate matrix elements at cusp point (Mpp = 2m+) from measured partial width ratios and slope parameters: R(K+) ≈ 6.1 ; R(KL) ≈ 0.47 Cusp “visibility” is ~ 13 times higher in K+ → p+pp decays than in KL → ppp decays

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