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Interaction Study of Pionium Atoms in the NA48/2 Experiment at CERN

This seminar provides an overview of the NA48/2 experiment at CERN, focusing on the study of pionium atoms. The presentation covers topics such as diffusion lengths, pionium formation, and comparisons with other experiments. The methodology, beam setup, and data collection process are also discussed.

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Interaction Study of Pionium Atoms in the NA48/2 Experiment at CERN

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  1. Etude de l’intéractionp - pà très basse énergie auprès de l’expérience NA48/2 au CERN: longueurs de diffusion et formation d’atomes de pionium Luigi DiLella Scuola Normale Superiore, Pisa • L’expérience NA48 / 2 • Sélection et reconstruction d’ événements Kppºpº • Motivation initiale: recherche d’atomes p+p- (“pionium”) • Distribution de masse invariante pºpº • Interprétation: mesure des longueurs de diffusion p – p • Comparaison avec les résultats d’autres expériences: mesure du temps de vie du pionium (expérience DIRAC au CERN) • Conclusions Séminaire au DAPNIA, Saclay, 12.10.2005

  2. ; ; The NA 48 / 2 experiment Cambridge – CERN – Chicago – Dubna – Edinburgh – Ferrara – Firenze – Mainz – Northwestern – Perugia – Pisa – Saclay – Siegen – Torino – Vienna Approved in 2001 to search for direct violation of CP symmetry in the decay of charged K-mesons to three pions: Kpp+p- (Branching fraction 5.57%) Kppp (Branching fraction 1.73%) METHOD: Search for K+ / K - difference of “odd pion” energy distribution “Odd pion”:p- in K+p+p+p- ; p+ in K-p-p-p+ ; p in K ppp Kinematic variables: (i = 3 : odd pion) Matrix element: Violation of CP symmetry:

  3. NA48/2 main goal: • Measure Ag in both K pp+p- and K ppp decay modes with accuracies δAg<2.2x10-4 and δAg<3.5x10-4 , respectively • Required statistics: > 2x109 events in “charged” mode; >108 events in “neutral” mode NA48/2 method: maximal cancellations (robustness) • Two simultaneousK+ and K− beams, superimposedin space • Detect asymmetry only from slopes of ratios of normalized u distributions • Equalize averaged K+ and K–acceptances by frequently changing polarities of relevant magnets

  4. 54 60 66 PK spectra, 60 GeV/c BM z 10 cm 200 250 m 1cm 50 100 NA48/2 beam setup 2 ÷ 3 M K / spill (π/ K ~ 12)π decay products stay in pipe magnet K+ K+ ~71011 ppp focusing beams K K− Second achromat • Cleaning • Beam spectrometer (0.7%) Beams coincide within ~1mm all along 114m decay volume,always in vacuum Quadrupole quadruplet Front-end achromat • Momentum • selection • Focusing •  sweeping vacuum tank He tank + spectrometer not to scale

  5. K decay volume 114 m long vacuum tank Diameter: 1.92 m (first 66 m) 2.40 m (last 48 m)

  6. The NA48 detector • Main detector components: • Magnetic spectrometer (4 DCHs): • 4 views: redundancy  efficiency • σp/p = 1.02% + 0.044% p [GeV/c] • Hodoscope • fast trigger • precise time measurement (150ps) • Liquid Krypton EM calorimeter (LKr) • High granularity, quasi−homogeneous • σE/E = 3.2%/√E + 9%/E + 0.42% [GeV] • e/π discrimination • Hadron calorimeter, photon vetos, • muon veto counters Beam pipe (at the end of the decay volume)

  7. Data taking: completed 2003run:~ 50 days 2004run: ~ 60 days Total statistics in 2 years: K  + −: ~ 4x109 K  0 0 : ~ 1.5x108 ~ 200 TB of data recorded

  8. Liquid Krypton electromagnetic calorimeter ~ homogeneous ionization chamber ~ 10 m3 liquid Krypton Thickness: 27 radiation lengths 13248 projective cells, 2 x 2 cm2 No longitudinal segmentation Energy resolution: (E in GeV) s(E) ≈ 142 MeV for E = 10 GeV Space resolution: sx = sy≈ 1.5 mm for E = 10 GeV

  9. Motivation for a measurement of the pºpº invariant mass (M00) • distribution from K ppºpº decay with optimal M00 resolution: • search for p+p- atoms (pionium) produced in K  pp+p- decay • (I. Mannelli) • K pp+p- event topologies with p+p- invariant mass M+- = 2m+ • possibility of pionium formation (Coulomb interaction), followed by pionium decay to pºpº pairs p mass (R∞ : Bohr radius for Mnucleus = ∞ ) First observation of pionium atoms at the 70 GeV Serpukhov proton synchrotron L.G. Afanasyev et al., Phys. Lett. B 308 (1993) 200 Pionium radius in the ground state (n = 1): Rpionium>> strong interaction radius ( ~10-13cm)  rather low decay rateforthe strong interaction process p+p-  pºpº Pionium mean lifetime: tpionium≈ 2.9x10 -15s  VERY NARROW WIDTH

  10. Expected spectrum without pionium M002 (GeV2) M002 (GeV2) Details of the pionium region (Pionium mass)2≈0.0779 GeV2 Example of pionium expectation (from MonteCarlo simulation) 420 bin M002 distribution ; 1 bin = 0.00015 GeV2 Full spectrum with pionium Pionium signal covers ~7 bins

  11. Event selection • At least one charged particle with momentum p> 5 GeV/c • At least 4 photons with Eg> 3 GeV detected in the Liquid Krypton (LKr) calorimeter • Geometrical cuts to eliminate detector edge effects (near beam tube and near outer edges of drift chambers and LKr calorimeter) • Distance between photons at LKr > 10 cm • Distance between photons and charged particle at LKr > 15 cm

  12. Liquid Krypton electromagnetic calorimeter 60 GeV beam Reconstruction of the pp pair For each photon pair (i,k) reconstruct common vertex along beam axis (zik) under the assumption of p  gg decay m0: p mass Ei , Ek : photon energies (measured in LKr) Dik : distance between the two photons on the LKr face zik : distance between LKr and p decay vertex Among all possible pp pairs select the pair with minimum difference | Dz |= |zik – zlm| < 500 cm (i , k≠l , m)

  13. Dz (cm) Dz distribution Main source of tails in Dz distribution at this stage: wrong photon pairing

  14. 1 3 4 2 z34 z12 To first order: 60 GeV beam Optimal resolution on the pp invariant mass M00 (~ perfect resolution for M00=2m0) Choice of common ppvertex along beam axis (z coordinate): the middle point between the two vertices

  15. LKr front face at z = 12109 cm Distribution of reconstructed pp vertices along beam axis

  16. ppp invariant mass M(ppp) Origin of the tails in the Dm distribution: p±m± decay in flight Select events with |Dm| = | M(ppp) - mK(PDG) | < 0.006 GeV Fraction of events with wrong photon pairings ~0.25% (as estimated fromMonteCarlo simulation)

  17. pp invariant mass resolution and event acceptance (from MonteCarlo simulation) Expected M002 distributions for five generated values of Moo and Moo resolution (r.m.s., MeV) Moo resolution (r.m.s.) at pionium mass = 0.56 MeV Event acceptance vsMoo Arrow: Moo = 2m+ m+ : p+ mass

  18. Experimental M002distribution for 22.87 x 106 K± p± ppdecays Sudden change of slope (“cusp”) at Moo = 2m+

  19. M002(GeV2) Experimental M002 distribution “Zoom” on the cusp region STRUCTURE IS TOO BROAD TO BE CONSISTENT WITH EXPECTED NARROW PEAK FROM PIONIUM

  20. Fits to the experimental Moo2distribution METHOD • Generate theoretical Moo2distribution Gi (420 bins of 0.00015 GeV2 ) • From MonteCarlo simulation derive 420 x 420 matrix Tik Tik = probability that an event generated with Moo in bini is detected and measured in bink (Tik includes both acceptance and resolution) • Produce “reconstructed” Moo2distribution Rk : • Fit distribution Rk to experimental Moo2distribution

  21. Log(Tik) (from MonteCarlo simulation)

  22. DATA FIT INTERVAL Fit interval: 0.0741 < Moo2 < 0.0967 GeV2

  23. where : • Fit using modified PDG prescription for decay amplitude: Very bad fit: c2= 9225 / 149 d.o.f. • Move lower limit of fit interval 13 bins above cusp point Reasonable fit: c2= 133.6 / 110 d.o.f.

  24. Data – fit comparison shows important “deficit” of events below cusp point Data: 7.261 x 105 events; extrapolated fit:8.359 x 105 events

  25. D≡ (data – fit) /data versus Moo2

  26. Is the observed “deficit” due to detector effects? Study event shape distributions in two equal M00 intervals below (I-) and above (I+) cusp; Normalize I+ and I- to the same area and compare I+/ I- ratio to MonteCarlo prediction Variation of shape of photon energy distribution across cusp point Points: data Histogram: MC agrees with MonteCarlo prediction

  27. Variation of shapes of photon distance distributions across cusp point Points: data Histograms: MC a) distance between LKr centre and closest photon b) distance between LKr centre and farthest photon c) minimum distance between photons at LKr d) minimum distance between photons and tracks at LKr Very good agreement with MC predictions for all distributions

  28. M1 : real, < 0 for M00<2m+  destructive interference imaginary for M00>2m+  no interference N. Cabibbo Determination of the a0–a2 Pion Scattering Length from K+ p+ppdecay Phys. Rev. Letters 93 (2004) 121801 Matrix element for K+ p+pºpº: Contribution from charge exchange diagram Normalization: M1= 0 at M00 = 2m+ unperturbed amplitude; Real, > 0 known matrix element for K+p+p+p- p+p-pºpº scattering length

  29. Assumption: EXACT isospin symmetry a0 (a2) : p – p scattering length in isospin I = 0 (I = 2) state (scattering length = scattering amplitude at zero energy) • Relative p momentum at threshold = 0  only S – waves are allowed • Pions are BOSONS Y(p1, p2) = Y(p2, p1) • The isospin wave function of a pp pair with I = 1 is antisymmetric only I = 0 and I = 2 are allowed Predictions from current algebra and partially conserved axial current (Weinberg 1966) a0 m+ = 0.159 ; a2 m+= -0.045 Recent predictions in the framework of Chiral Perturbation Theory (ChPT) (Weinberg 1967; Gasser & Leutwyler 1984; Colangelo, Gasser & Leutwyler 1984) a0 m+ = 0.220  0.005 ; a2 m+= -0.0444  0.0010 ; (a0 - a2)m+ = 0.265  0.004 ChPT : PRECISION STRONG INTERACTION THEORY AT ENERGIES NEAR THRESHOLD

  30. D (data – best fit) / data D M002 (GeV2) Cabibbo’s rescattering model for K+ p+pºpº: only one additional free parameter: (a0 – a2)m+ Great c2 improvement (from 9225 / 149 to 420.1 / 148 d.o.f.) but still an unsatisfactory fit (especially in the cusp region)

  31. N. Cabibbo and G. Isidori: Pion – pion scattering and the K 3p decay amplitudes JHEP03 (2005) 021 More one-loop diagrams :

  32. ... and also two-loop and three-pion diagrams

  33. Exact I-spin symmetry Scattering length Subprocess ; ; ; ; Five scattering lengths in the Cabibbo – Isidori model: Isospin symmetry breaking corrections at tree level: (van Kolck 1993; Maltman and Wolfe 1997; Knecht and Urech 1998)

  34. D D (data – best fit) / data M002 (GeV2) Fit to the Cabibbo – Isidori rescattering model Add quadratic term to the unperturbed K+p+pºpº scattering amplitude: Two free parameters: g0, h’ + a0 + a2 + an overall normalization constant  five free parameters (a0 – a2)m+ = 0.284  0.007 a2m+ = -0.077  0.015 (statistical errors only)

  35. D M002 (GeV2) Add pionium contribution: (a0 – a2)m+ = 0.269  0.009 a2m+ = -0.054  0.019 (K+  p+ + pionium) / (K+  p+pºpº) = (1.61  0.66) x 10-5  2.4 s evidence for pionium Compare with theoretical prediction (Pilkuhn and Wycech 1978; Silagadze 1994) (K+  p+ + pionium) / (K+  p+pºpº) = 0.8 x 10-5 Fix pionium contribution at the theoretical prediction: c2 = 149.9 / 146 d.o.f. (a0 – a2)m+ = 0.274  0.007 a2m+ = -0.063  0.015

  36. Cabibbo – Isidori’s rescattering model does NOT include radiative corrections, very important near M00 = 2m+ and contributing to pionium formation Final fit: exclude 7 bins centred at Moo= 2m+ D M002 (GeV2) Two independent analyses with two independent acceptance calculations : Arithmetic average of best fit parameter values  parameter measurement ; one half of their difference  systematic uncertainty on the acceptance calculation

  37. Systematic uncertainties Theoretical uncertainty on (a0 – a2)m+ =  5% (from neglecting higher – order rescattering digrams and radiative corrections) Final NA48/2 result: (a0 – a2)m+ = 0.268  0.010(stat)  0.004(syst)  0.013(theor) a2m+ = -0.041  0.022(stat)  0.014(syst) Reminder of theoretical predictions: (a0 – a2)m+ = 0.265  0.004 ; a2m+ = -0.0444  0.0010

  38. Constraint between a0 and a2 from chiral symmetry and analyticity (Colangelo, Gasser, Leutwyler 2001) Use this constraint in the fit: a0 m+ = 0.220  0.006(stat)  0.004(syst)  0.011(theor) equivalent to (a0 – a2)m+ = 0.264  0.006(stat)  0.004(syst)  0.013(theor) Compare with measurement of K+  p+p-e+ne (BNL experiment 865): a0 m+ = 0.216  0.013(stat)  0.002(syst)  0.002(theor) (also obtained using theoretical constraints)

  39. QED and QCD corrections d = 0.058  0.012 pº momentum in A rest frame Double inclusive production cross – section for p+p- pairs from short – lived sources without Coulomb interaction Pionium wave function at the origin n: principal quantum number Measurement of the pionium lifetime in the DIRAC experiment at the CERN PS An independent method to measure |a0 – a2| m+ A pionium atom; pionium decay Apºpº Decay rate in the n = 1, l = 0 state: Cross – section for pionium production in an l = 0 state:

  40. Expectations from pionium break – up: within measurement errors Pionium production in thin targets • Two competing processes • pionium decay: Apºpº • pionium break – up (ionization): Ap+p-(calculable!) • DIRAC (DImeson Relativistic Atom Complex) experiment at the CERN PS • 24 GeV protons on thin (94mm, 98mm) Ni foils • Pionium Lorentz factor g≈17 on average • Detect p+p-pairs in coincidence • Measure precisely p+ and p- momentum

  41. Evidence for pionium production and break – up in the DIRAC experiment: relative momentum (Q) distribution for p+p- pairs with QT< 4 MeV/c Peak at small Q and QL values is due to pionium formation and break-up

  42. Calculate number of produced pionium atoms (NA) • Measure number of observed pionium atoms (nA) • Break – up fraction Pbr = nA/NA

  43. CONCLUSIONS • A clear cusp has been observed by NA48 / 2 in the pp invariant mass distribution from K±p± p p decay at Moo= 2m+ • The new level of precision of the NA48 / 2 data requires a redefinition of the parameters generally used to describe K±p± p p decay (e.g., PDG 2004) • This cusp is the effect of pp scattering in the final state, dominated by the charge exchange process p+p- pp • The study of the pp invariant mass distribution from K±p± p pdecay offers a new, precise method to measure (a0 – a2)m+ independently of other methods (e.g., measurement of pionium lifetime) • Result in excellent agreement with theoretical predictions, precision comparable to (or better than) other experiments (K+p+p-e+ne , pionium lifetime) • The final K±p± p p decay sample collected in 2003 - 04will contain ~108 events • Need improvements of the rescattering model (higher – order diagrams, radiative corrections) in order to extract values of the pp scattering parameters from these data with the best possible precision

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