Etude de l’intéraction p - p à 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

Cambridge – CERN – Chicago – Dubna – Edinburgh – Ferrara – Firenze – 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:

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 simultaneous K+ and K− beams, superimposed in 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

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

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

(at the end of the decay volume) The NA48 detector (at the end of the decay volume) 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

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

electromagnetic calorimeter 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

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 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): (R∞ : Bohr radius for Mnucleus = ∞ ) Rpionium >> strong interaction radius ( ~10-13 cm)  rather low decay rate for the strong interaction process p+p-  pºpº Pionium mean lifetime: tpionium ≈ 2.9 x 10 -15 s  VERY NARROW WIDTH

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

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

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 Liquid Krypton electromagnetic calorimeter 60 GeV beam 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)

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

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

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

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 from MonteCarlo simulation)

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 vs Moo Arrow: Moo = 2m+ m+ : p+ mass

Experimental M002 distribution for 22.87 x 106 K±  p± pp decays Sudden change of slope (“cusp”) at Moo = 2m+

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

Fits to the experimental Moo2 distribution METHOD Generate theoretical Moo2 distribution 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 bin i is detected and measured in bin k (Tik includes both acceptance and resolution) Produce “reconstructed” Moo2 distribution Rk : Fit distribution Rk to experimental Moo2 distribution

(from MonteCarlo simulation) Log(Tik) (from MonteCarlo simulation)

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

Fit using modified PDG prescription for decay amplitude: where : 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.

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

D ≡ (data – fit) /data versus Moo2

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

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

M1 : real, < 0 for M00 < 2m+ 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 M1 : real, < 0 for M00 < 2m+  destructive interference imaginary for M00 > 2m+  no interference known matrix element for K+  p+p+p- p+p-  pºpº scattering length

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

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

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

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

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

D  (data – best fit) / data 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 D D  (data – best fit) / data M002 (GeV2) (a0 – a2)m+ = 0.284  0.007 a2m+ = -0.077  0.015 (statistical errors only)

D Add pionium contribution: (a0 – a2)m+ = 0.269  0.009 M002 (GeV2) (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

D Final fit: exclude 7 bins centred at Moo = 2m+ 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 : Parameter Analysis A Analysis B Arithmetic average (a0 – a2)m+ 0.269 ± 0.010 0.268 ± 0.010 a2m+ -0.053 ± 0.020 -0.030 ± 0.022 -0.041 ± 0.022 g0 0.643 ± 0.004 0.647 ± 0.004 0.645 ± 0.004 h’ -0.055 ± 0.010 -0.039 ± 0.012 -0.047 ± 0.012 Arithmetic average of best fit parameter values  parameter measurement ; one half of their difference  systematic uncertainty on the acceptance calculation

Systematic uncertainties Parameter Acceptance calculation Trigger efficiency Fit interval upper edge K+ / K- difference p± – g min. distance LKr resolution, non-linearity Total syst.error (a0- a2)m+ ±0.001 ±0.0025 - ±0.002 ±0.004 a2m+ ±0.012 ±0.005 ±0.006 ±0.014 g0 ±0.008 ±0.009 h’ ±0.003 ±0.011 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

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)

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: pº momentum in A rest frame QED and QCD corrections d = 0.058  0.012 Cross – section for pionium production in an l = 0 state: Pionium wave function at the origin n: principal quantum number Double inclusive production cross – section for p+p- pairs from short – lived sources without Coulomb interaction

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 (94 mm, 98 mm) Ni foils Pionium Lorentz factor g ≈ 17 on average Detect p+p- pairs in coincidence Measure precisely p+ and p- momentum Expectations from pionium break – up: within measurement errors

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

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

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 = 2 m+ 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 - 04 will 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