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Measurements of K ±  π + π - e ± ν ( Ke4) and K ±  π ± π 0 π 0 decays at NA48/2.

Measurements of K ±  π + π - e ± ν ( Ke4) and K ±  π ± π 0 π 0 decays at NA48/2. Silvia Goy L ó pez (CERN) For the NA48/2 collaboration. HS07, September 3th 2007. K ±  π + π - e ± ν (Ke4) decay Introduction Selection, reconstruction

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Measurements of K ±  π + π - e ± ν ( Ke4) and K ±  π ± π 0 π 0 decays at NA48/2.

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  1. Measurements of K±π+π-e±ν (Ke4) and K± π±π0π0 decays at NA48/2. Silvia Goy López (CERN) For the NA48/2 collaboration HS07, September 3th 2007

  2. K±π+π-e±ν (Ke4) decay Introduction Selection, reconstruction Form factor and ππ scattering length measurements K± π±π0π0 decay Selection, reconstruction Cusp effect and interpretation Form factors and ππ scattering length measurements Overview • Introduction to NA48 • The NA48/2 experiment: goal, beam line, detector • Introduction to pp scattering lengths • Summary and Conclusions Silvia Goy Lopez HS07

  3. Introduction • NA48: 1997-2000. DCPV in neutral K • Re(e/ e) = (14.7  2.2) 10-4 • NA48/1: 2002. Rare Ks decays • Br(Ks p0e+e-)=(5.8+2.8-2.3 ± 0.8) 10-9 • Br(Ks p0+ -)=(2.8+1.5-1.2 ± 0.2) 10-9 • NA48/2: 2003-2004. DCPV in K 3p • Ag=(-1.5+1.5stat+0.9trig+1.1syst)·10-4 • Ag0=(1.8+1.7stat+0.5syst)·10-4 • In addition many results on rare kaon decays and on hyperon decays. • NA62 K + ->p +nn. Test beam in 2006, 2007. Ke2/Km2 in 2007 Silvia Goy Lopez HS07

  4. The N A48/2 • 2003 run: ~ 50 days • 2004 run: ~ 60 days • Total statistics 2 years: • K±→±00: ~1·108 • K±→±+-: ~3·109 • K±π+π-e±ν: ~1.106 • Greatest amount of K→3  ever collected • For these results 2003 for Ke4 and 90% of all data for cusp Silvia Goy Lopez HS07

  5. The NA48/2 Beam Line • Simultaneous, coaxial and focused K+ and K- beams • Central kaon momentum of 60 GeV/c and a spread of ± 3.8% (rms) • Beam line and spectrometer magnet polarities periodically inverted Silvia Goy Lopez HS07

  6. The NA48 Detector • Magnetic spectrometer • 4 DCHs, 4 views, 2 planes/view + dipole magnet • (p)/p=(1.02  0.044p)% • Pt kick=120 MeV/c • (t) = 1.4 ns • Charged hodoscope • (t) = 200 ps • LKr electromagnetic calorimeter • 27 X0 with 13212 2x2 cm2 cells • (E)/E=(3.2/E  9.0/E  0.42)% • (x)=(y)=0.42 /E  0.06 cm • (t) = 265 ps • Muon Counters • 2+1 planes 25x25 cm2 (t) = 350 ps Mass resolutions (pp+p-)= 1.7 MeV/c2 (pp0p0)=1.4 MeV/c2 Silvia Goy Lopez HS07

  7. Introduction to pp scattering lengths • pp scattering amplitude can be expanded in partial waves. Scattering lengths are parameters in the expansion • At low energies S-wave dominates • Due to Bose statistics only I=0,2 allowed • Scattering lengths a0,a2 are the relevant parameters describing pp interactions at low energies. a0,a2 Silvia Goy Lopez HS07

  8. Introduction to pp scattering lengths • Measurements • Ke4 form factors (d variation with Mpp) • Geneva-Saclay (~30 103 evts) • BNL E865 (~390 103 evts) • NA48/2 (~677 103 evts) • Cusp effect (NA48/2) • Pionium lifetime (DIRAC) • Theory • Dispersion relations: based on causality and analiticity of scattering amplitude. Using pp scattering data at intermediate energies a relation can be found a2=f(a0) Ej: UB from Roy eqn. • ChPT: a2=fChPT(a0). Predict a0 with <2% error, related to size of condensate. • Recently lattice calculations. • Prediction for a0-a2 inChPT a0 -a2 = 0.265 ± 0.004, a0=0.220 ± 0.005 (CGL, PLB 488 (2000) 261) ej using disper. rel. = 0.278 ± 0.016, a0=0.230 ± 0.015 (PY, PRD 71 (2005) 074016) • NA48/2 provides measurement from two independent channels Silvia Goy Lopez HS07

  9. Rare decay: Br(K±π+π-e±ν)=(4.08±0.09) 10-5 (PDG06) Kinematic variables (Cabibbo – Maksymowicz ) Sπ(M2ππ) (related to q2) Se (M2eν) cos qπ cos qe f (related to pp scattering phases related to scattering lengths) p*(e+) p*(p+) f Direction of the total p+p- momentum in the K+ rest frame Direction of the total e+ne momentum in the K+ rest frame qp qe K+ p- ne The K±e4 decay: Introduction Silvia Goy Lopez HS07

  10. The K±e4 decay: Introduction • Form factors F,G,R (axial, R relevant only for Km4 ) and H (vector) determined by fitting the data distributions. • Because of small values of sp in Ke4 expansion restricted to s&p waves. Fit Fs, Fp, Gp , Hp and d = ds-dp • Expanding in terms of q2 (Sp), Se ds : the pp scattering phase shift in the I = 0 , l = 0 state (s – wave) dp : the pp scattering phase shift in the I = 1 , l =1 state (p – wave) Silvia Goy Lopez HS07

  11. Selection: Three tracks, two opposite charged pions, one electron, missing energy and pt(separation p /e given by LDA: linear discriminator analysis) Background: K   pp+p-with p en is dominant p misidentified as electron K   pp0(p0) with p0 Dalitz decay (e+e-g) with e misid. as p , and g undetected Estimation using MC and data (‘Wrong sign’ events) in agreement In data ‘Wrong sign’ events (e different sign than kaon) can be only due to background. Scaling factor depending on process. Total background level  0.5% The K±e4 decay: Selection Silvia Goy Lopez HS07

  12. Reconstruction. Two approaches: Use constrain given by n to solve energy-momentum conservation equations and get kaon momentum. Take solution closest to 60 GeV/c Assume a 60 GeV/c kaon along the z axis, assign the missing pt to the n and compute the resulting kaon invariant mass. Take events within ± 20 MeV/c2 The K±e4 decay: Reconstruction PK(GeV/c) mK(GeV/c2) • Statistics: 2003 data sample, ~677500 events Silvia Goy Lopez HS07

  13. The K±e4 decay: Fitting of form factors • 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. K+/K-~1.8 MC/Data ~23 Silvia Goy Lopez HS07

  14. Mpp (GeV) cosqp Mez(GeV) cosqe The K±e4 decay: Kinematic Distributions • Distribution of kinematic variables for data (symbols) and MC after fit (hist.) • Background distribution taken from data (hardly visible) K+ K- f(rad)  distribution shown separately for K+ and K- (CP symmetry f  p + f) Silvia Goy Lopez HS07

  15. 0.309 < Mpp < 0.318 GeV 2m+ < Mpp < 0.291 GeV f f -p p -p p 0.335 < Mpp < 0.345 GeV 0.373 GeV < Mpp < mK f f -p p -p p The K±e4 decay: Kinematic Distributions: f • d of the Ke4 decay amplitude is extracted from the measured asymmetry of the f distribution as a function of Mpp • The asymmetry of the f distribution increases with Mpp  increaing sensitivity to d Silvia Goy Lopez HS07

  16. The K±e4 decay: Form Factors: F2s (normalization) • No absolute normalization available for the moment (no BR measurement)  can only get relative form factors and variation with q2 and with Se (all results are given wrt to Fs(q=0) constant term) • F2s obtained from relative bin to bin normalization of Data/MC after fit • Once q2 dependency is extracted residual Men variation can be observed • A 2D fit (Mpp, Men) is used to get the slopes of the Fs expansion First measurement of f’’e≠0 Silvia Goy Lopez HS07

  17. The K±e4 decay: Form Factors: Fp,Gp, Hp • Once the normalization variation has been deconvoluted can extract variation of Fp,Gp and Hp with q2 First measurement of fp≠0 Silvia Goy Lopez HS07

  18. The K±e4 decay: Form Factors • The d = d s-dpvariation with Mpp was fitted using Universal Band(numerical solution of Roy equations (A, Phys. Rep. 353 (2001) 207) • 1 parameter function to extract a0 with a2=f(a0) in center of UB • High sensitivity to scattering length due to good acceptance for high Mpp Silvia Goy Lopez HS07

  19. The K±e4 decay: Results NA48/2 Preliminary: 2003 data • Systematic checks • Two analysis with different reconstructions, acceptance corrections, fitting methods • Beam simulation (acceptance changes) • Background level • Electron identification • Radiative corrections • Possible Se dependence • Possible bin to bin correlations investigated and taken into account f’s/ fs = 0.165± 0.011stat ± 0.006syst f’’s/ fs = -0.092± 0.011stat ± 0.007syst f’e/ fs = 0.081± 0.011stat ± 0.008syst fp/ fs = -0.048± 0.004stat ± 0.004syst gp/ fs = 0.873± 0.013stat ± 0.012syst g’p/ fs = 0.081± 0.022stat ± 0.014syst hp/fs = -0.411± 0.019stat ± 0.007syst First observation of f’e and fp All form factors measured to 5 to 15% accuracy Error dominated by statistics Silvia Goy Lopez HS07

  20. The K±e4 decay: Results comparison • d points from different experiments can be fitted together to the center of UB. • Value for a0 is lower than given by NA48 data alone • Mainly due to last point of BNL (under investigation) • Superposed are the predictions for d vs Mpp for a0=0.26 and a0=0.22 Fit to all experimental points Predictions for a0=0.26 and a0=0.22 Silvia Goy Lopez HS07

  21. The K±e4 decay: Results comparison • Different methods can be used to relate d measurements to a0,a2 • Fit 1 parameter a0 with a2=f(a0) by Roy eqn. • Fit 1 parameter a0 with a2=f(a0) by ChPT • Fit 2 parameters a2,a0 • NA48/2 and E865 favor slightly different regions of UB Silvia Goy Lopez HS07

  22. The K±e4 decay: Results comparison • Theory improvements (Gasser): Measured d has to be corrected by isospin symmetry breaking effects before extracting a0 • After this correction (preliminary) a0 values are in good consistency with ChPT predictions • Using different methods a0 are in the range [0.209,0.255] ±0.006stat±0.005syst and values of a2 around -0.045 Silvia Goy Lopez HS07

  23. 2003: Observation of sudden slope variation in the pp invariant mass distribution seen at M002=(2mp+)2 An unexpected discovery from the NA48/2 Initial motivation for this study: use large statistics and good M002 resolution to try to detect p+p- atom formation in K± → p± p+p- decays, followed by pionium annihilation to pp Standard Dalitz plot parameterization shows deficit in data before cusp Standard Dalitz plot parameterization Whole region: c2/ndf=9225/149! Above cusp: c2/ndf=133/110 The K± π±π0π0 decay: Cusp effect Subsample of 2003 Silvia Goy Lopez HS07

  24. 4m+2 4m+2 The K± π±π0π0 decay: Cusp effect • Now 2003+80% of 2004 combined: 59,624,170 fully reconstructed K± →p±pp Zoom in cusp region Silvia Goy Lopez HS07

  25. Reconstruction: At least 4 clusters 15 cm away from any track and 10 cm away from other clusters. Among all the possible g pairings, the couple for which c2 is smallest is selected M002 computed using average vertex of two p0 m02 = 2EiEk(1-cosa) ≈ EiEka2 = EiEk (Dik)2/(zik)2 No physical background i dij Vertex LKr j Z(i,j) Z(k,l) Dz The K± π±π0π0 decay: Reconstruction Silvia Goy Lopez HS07

  26. Cusp on K± π±π0π0. Checks for instrumental effects • Good resolution near cusp region • Acceptance linear near the cusp M002 reconstructed distributions for three generated values of M002 Acceptance s = 0.56 MeV at M00 = 4m+ Silvia Goy Lopez HS07

  27. Cusp on K± π±π0π0.Checks for instrumental effects • Data-MC comparisons above and below cusp • MC simulation describes well the of detector efficiency around cusp. Event deficit is real effect Silvia Goy Lopez HS07

  28. Cusp on K± π±π0π0. Interpretation • Two amplitudes contribute to K± π±π0π0 • Direct emission • Given by M0 • Charge exchange (π+π- π0π0) in final state of K± π± π+π • Given by M1 , proportional to M+ and to one extra parameter ax=(a0- a2) /3 in limit of exact isospin symmetry • These amplitudes interfere destructively below threshold • Rescattering model at one-loop (C, PRL 93 (2004) 121801) DE (k’ first observed by NA48/2) CE Silvia Goy Lopez HS07

  29. Cusp on K± π±π0π0. Interpretation • More complete formulation of the model includes all re-scattering processes at one-loop and two-loop level (CI, JHEP 0503 (2005) 21) has been used to extract NA48/2 result. • More parameters than just ax • Isospin correction applied in order to extract a0 and a2 from fits to data. • Theoretical uncertainty of ~ 5% but radiative corrections and three-loops can be computed to reach ~1% Silvia Goy Lopez HS07

  30. Cusp on K± π±π0π0: Fitting procedure • One dimensional fit to M002 distribution • MINUIT minimization of 2of data/MC spectra shapes • Fitting up to 0.097 (GeV/c2) • Fits to 5 parameters: norm, g, h’,a0- a2 and a2 () (k’ fixed) • For final result 7 bins around cusp excluded from the fit in order to reduce sensitivity to Coulomb corrections and pionium. The excess of events in this region is interpreted as pionium signature (E.M. corrections?) R=(K+A2)/(K+–) = (1.820.21)10–5 (th. prediction 0.8 10 -5) Silvia Goy Lopez HS07

  31. The K± π±π0π0 decay. Quadratic term • Matrix element for DE (different from PDG parameterization) • Technique: Consecutive 1D-fits in both data projections • (a0,a2,g0,h’) measurement (fixed k’=0) [2003 data] • k’ measurement (fixed a0,a2,g0,h’) [2003 data]  • (a0,a2,g0,h’) second iteration (fixed k’) [2004 data] • a0,a2 are not significantly affected by neglecting the k’v2 term, but g0,h’ are biased by g0=–1.5%, h=–1.2% M0 ~ (1+g0u/2+h’u2/2+k’v2/2) Silvia Goy Lopez HS07

  32. NA48/2 Preliminary: 2003 data k’ = 0.0097 ± 0.0003stat ± 0.0008syst The K± π±π0π0 decay. Quadratic term • Change of Dalitz variables, from (s3, s2-s1 )to (s3, cosq) • Define q asangle between π±and π0 in π0π0 COM • Fitting new Dalitz plot above cusp • Data-MC comparison for cosq for different k’ values • Change in value and meaning of g and h’ with respect to previous matrix element • No change of a0-a2 and a2 Silvia Goy Lopez HS07

  33. Cusp on K± π±π0π0. Results • Systematic effects: analysis technique, acceptance determination, trigger efficiency, resolution, fitting interval, electromagnetic shower simulation, v-dependence of amplitude g = 0.649 ± 0.003stat ± 0.004syst h’ = -0.047 ± 0.007stat ± 0.005syst k’ = 0.097 ± 0.003stat ± 0.008syst First evidence of k≠0 Silvia Goy Lopez HS07

  34. Cusp on K± π±π0π0. Results • External uncertainty: from the uncertainty on the ratio of K+ → p+p+p- and K+ → p+pp decay widths • Theoretical uncertainty on (a0 – a2): ± 5% (estimated effect from neglecting higher order diagrams and radiative corrections) • Fit imposing ChPT constrain between a0 and a2(CGL, PRL 86 (2001) 5008) • From (a0 – a2) and a2 extract a0 (must take into account the statistical error correlation coefficient ≈ -0.92) a0- a2 = 0.261 ± 0.006stat ± 0.003syst ± 0.0013ext ± 0.013th a2 = -0.037 ± 0.013stat ± 0.009syst ± 0.002ext a0- a2 = 0.263 ± 0.003stat ± 0.014syst ± 0.0013ext ± 0.013th a0 = 0.224 ± 0.008stat ± 0.006syst ± 0.003ext ± 0.013th Silvia Goy Lopez HS07

  35. Comparison Cusp and DIRAC • DIRAC: Pionium lifetime related to scattering lengths. Proportional to |a0-a2|2 • The yellow area represents theoretical uncertainty (assumed Gaussian) Also dashed bars. Silvia Goy Lopez HS07

  36. Comparison Cusp and Ke4 results. Silvia Goy Lopez HS07

  37. Comparison Cusp and Ke4 results. Silvia Goy Lopez HS07

  38. Summary and Conclusions • NA48/2 exploited two different procedure to measure the pp scattering lengths. • Ke4: the pp phase shift can be related to the a0 and a2 using theoretical input (e.g. Roy equations) • K→pp0p0: the pp scattering lengths are extracted from the study of pp rescattering contribution in the M00 mass distribution (the error is dominated by the theoretical error) • Applying the isosping breaking corrections the two results are fully compatible. • The results are compatible with the DIRAC experiment results and with ChPT predictions. Silvia Goy Lopez HS07

  39. SPARES Silvia Goy Lopez HS07

  40. Cusp on K± π±π0π0. Results • NA48/2 results on partial sample of 2003 data(PLB 633 (2006)) • Systematic effects: Acceptance determination, trigger efficiency, fitting interval • Prediction for a2 inChPT a2 = -0.0444 ± 0.0010 (CGL, PLB 488 (2000) 261) • Prediction for a0-a2 inChPT a0 -a2 = 0.265 ± 0.004 (CGL, PLB 488 (2000) 261) using disper. rel. = 0.278 ± 0.016 (PY, PRD 71 (2005) 074016) • Fit imposing ChPT constrain between a0 and a2(CGL, PRL 86 (2001) 5008) g = 0.645 ± 0.004stat ± 0.009syst h’ = -0.047 ± 0.012stat ± 0.011syst a0- a2 = 0.261 ± 0.006stat ± 0.003syst ± 0.013ext ± 0.013th a2 = -0.037 ± 0.013stat ± 0.009syst ± 0.002ext a0 = 0.220 ± 0.006stat ± 0.004syst ± 0.011ext a0- a2 = 0.263 ± 0.003stat ± 0.014syst ± 0.013ext ± 0.013th Silvia Goy Lopez HS07

  41. The K±e4 decay: Results before Isospin symmetry breaking corrections NA48/2 Preliminary: PARTIAL Sub sample 2003 data a0 (UB)= 0.256± 0.008stat ± 0.007syst ± 0.018th  a2 = -0.031± 0.015stat ± 0.015syst ± 0.019th • Prediction for a0 in ChPT a0= 0.220 ± 0.005 (CGL, PLB 488 (2000) 261) Silvia Goy Lopez HS07

  42. Summary and conclusions • Pion scattering lenghts have been measured in NA48/2 with two independent channels: • From K±e4 • From cusp on K± π±π0π0 • But with different theoretical frameworks! • Form factors for K±e4 and K± π±π0π0 have been measured • Non zero quadratic term in K± π±π0π0 For comparison evaluation of a0 for previous experiments using center of UB: a0 (UB)= 0.256± 0.008stat ± 0.007syst ± 0.018th Geneva Saclay: a0(UB) = 0.253 ± 0.037 (stat+syst) ± 0.014 th E865: a0 (UB) = 0.229 ± 0.012stat± 0.004syst  ± 0.014 th a0- a2 = 0.268 ± 0.010stat ± 0.004syst ± 0.013ext k’ = 0.0097 ± 0.0003stat ± 0.0008syst Silvia Goy Lopez HS07

  43. Correlations • PARAMETER  CORRELATION COEFFICIENTS   for the normalisation fit        fs'       1.000 -0.955 0.085        fs"     -0.955 1.000   0.015        fe        0.085 0.015  1.000    which gives ,once reduced to 2 significant digits : -0.96  0.08     0.02 Including fe almost do not alter the value of the other parameters, very little correlation. • For gp(0)&g’p = -0.914 Silvia Goy Lopez HS07

  44. 1 entry per event 4m+2 Cusp in KL → ppp 87,950,601 events(3 entries per event) CUSP STRUCTURE MUCH LESS VISIBLE THAN IN K±→p±pp DECAY Silvia Goy Lopez HS07

  45. 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 K+ → p+pp , KL→ ppp comparison 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 Silvia Goy Lopez HS07

  46. Summary and conclusions • Pion scattering lenghts have been measured in NA48/2 with two independent channels: • From K±e4 • From cusp on K± π±π0π0 • But with different theoretical frameworks! • Form factors for K±e4 and K± π±π0π0 have been measured • Non zero quadratic term in K± π±π0π0 For comparison evaluation of a0 for previous experiments using center of UB: a0 (UB)= 0.256± 0.008stat ± 0.007syst ± 0.018th Geneva Saclay: a0(UB) = 0.253 ± 0.037 (stat+syst) ± 0.014 th E865: a0 (UB) = 0.229 ± 0.012stat± 0.004syst  ± 0.014 th a0- a2 = 0.268 ± 0.010stat ± 0.004syst ± 0.013ext k’ = 0.0097 ± 0.0003stat ± 0.0008syst Silvia Goy Lopez HS07

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