1. 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,

2. 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:

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 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

4. NA48/2 beam setup K+ K+ z K K− BM ~71011 ppp focusing beams
PK spectra,
60 GeV/c
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

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

6. (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% % 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 % [GeV]
e/π discrimination
Hadron calorimeter, photon vetos,
muon veto counters
Beam pipe

7. 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

8. 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

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
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 s
 VERY NARROW WIDTH

10. Example of pionium expectation (from MonteCarlo simulation)
420 bin M002 distribution ; 1 bin = GeV2
M002 (GeV2)
M002 (GeV2)
Details of the pionium region
(Pionium mass)2 ≈ GeV2
Expected
spectrum
without
pionium
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. 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)

13. 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

14. 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)

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

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) | < GeV
Fraction of events with wrong photon pairings ~ 0.25%
(as estimated from MonteCarlo 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 vs Moo
Arrow: Moo = 2m+
m+ : p+ mass

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

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

20. Fits to the experimental Moo2 distribution
METHOD
Generate theoretical Moo2 distribution Gi (420 bins of 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

21. (from MonteCarlo simulation)
Log(Tik)
(from MonteCarlo simulation)

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

23. 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 = / 110 d.o.f.

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

28. 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)
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

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+ = ; a2 m+ =
Recent predictions in the framework of Chiral Perturbation Theory (ChPT)
(Weinberg 1967; Gasser & Leutwyler 1984; Colangelo, Gasser & Leutwyler 1984)
a0 m+ =  ; a2 m+ =  ; (a0 - a2)m+ =  0.004
ChPT : PRECISION STRONG INTERACTION THEORY
AT ENERGIES NEAR THRESHOLD

30. 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 / 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. 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)
; ; ; ;

34. 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+ =  0.007
a2m+ =  0.015
(statistical errors only)

35. D Add pionium contribution: (a0 – a2)m+ = 0.269  0.009
M002 (GeV2)
(a0 – a2)m+ =  0.009
a2m+ =  0.019
(K+  p+ + pionium) / (K+  p+pºpº) = (1.61  0.66) x 10-5
 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 = / 146 d.o.f.
(a0 – a2)m+ =  0.007
a2m+ =  0.015

36. 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+
± 0.020
± 0.022
± 0.022 g0
0.643 ± 0.004
0.647 ± 0.004
0.645 ± 0.004 h’
± 0.010
± 0.012
± 0.012
Arithmetic average of best fit parameter values  parameter measurement ;
one half of their difference  systematic uncertainty on the acceptance calculation

37. 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+ =  0.010(stat)  0.004(syst)  0.013(theor)
a2m+ =  0.022(stat)  0.014(syst)
Reminder of theoretical predictions:
(a0 – a2)m+ =  ; a2m+ = 

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

39. 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 =  0.012
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

40. 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

42. 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

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

44. 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 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