Recent results from NA48/2 on pion scattering lengths using Ke4 decay and cusp in K

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Recent results from NA48/2 on pion scattering
lengths using Ke4 decay and cusp in K-gtpp0p0
Stefano Venditti University of Pisa INFN
On behalf of the NA48/2 collaboration Cambridge,
CERN, Chicago, Dubna, Edinburgh, Ferrara,
Firenze, Mainz, Northwestern, Perugia, Pisa
Saclay, Siegen, Torino, Wien
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Outline

• The NA48/2 experiment
• Ke4 theory and NA48/2 analysis
• Ke4 results for form factors and interpretation
  in terms of pion scattering lengths (a0,a2)
• Cusp K3pi theory and analysis
• Cusp fit procedure and extraction of (a0-a2)
• Conclusions.

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NA48/2 beam line
Beams coincide within 1 cm over 114 m of decay
volume
Detectors
Incoming SPS 400 GeV protons
K/K- flux1.8
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NA48 DETECTORS

• Spectrometer
• 4 DCHs -gt redundancy.
• sp/p1.00.044 p(p in GeV)
• Liquid Krypton EM calorimeter
• 16000 cells -gt high granularity.
• sE/E3.2/vE 9/E 0.42
• Hodoscopes (charged, neutral)
• Trigger, time measurement.
• Muon veto, Hadronic calo, Kabes, photon vetoes.

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NA48/2 DATA
2003 run 50 days 2004 run 60 days
EVENTS SELECTED FOR K-gtppe? AND K-gtpp0p0
K3pi 108 events (greatest K3pi sample ever
collected)
Ke4 0.68 M events (from 2003 data only)
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Ke4Theory
4 body decay-gt5 independent variables Using
Cabibbo-Maksymowicz variables Sp(Mpp2),Se(Me?2),c
os?p,cos?e,F
e
p
F
?e
?p
K
p-
?
Hadronic MEltpp-A?V?Kgt(1/MK)FP?GQ?R(K-P)?
(H/M2)e?µ?sKµP?Qs
(P?dipion 4V Q?dilepton 4V K?kaon 4V)
F,G,R axial form factors
f.f. expansion wrt Se, q2 Fsfsfsq2fsq4fe(S
e/4mp2) Fpfpfpq2 Gpgpgpq2 Hphphpq2

H vector form factor
Partial wave expansion of amplitude F Fseids
Fpeidp cos?p d-wave terms G Gpeidg d-wave
terms H Hpeidh d-wave terms
q2(Sp/4mp2)-1
R negligible (relevant in Kµ4)
Fit parameters Fs , Fp , Gp , Hp , dds-dp
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Ke4 Analysis selection and BG rejection
e
Ke4-gt 3 charged tracks (2 opposite sign pions),1
?. BR 4 10-5
?

• Spectrometer for momenta measurement
• LKR info used to tag electron and pions (E/p)
• Missing energy and Pt (because of neutrino).

K
p-
p
BG checked with data wrong sign events have same
total charge but wrong electron charge (esep-p-
for K- decay)their contribution to total BG is
the same or is to be rescaled by a factor 2 wrt
real BG, depending on the process.

• Background, main sources
• ppp-, with p-gte? in-flight decay or p
  misidentified as e
• pp0,pp0p0,with p0-gtee-? Dalitz decay and,e
  misidentified and ?(s) undetected.

Mke4
Pk
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Data/MC comparison
Mpp
Me?
GeV
GeV
cos?p
cos?e
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Ke4 analysis fitting procedure
Iso-populated 10(Mpp)x5(Me?)x5(cos?e)x5(cos?p)x12(
F)15000 bins in the C-M variables used. Form
factor values used to minimize a log-likehood
estimator well-suited for small numbers.
Ten independent fits in Mpp bins, assuming
constant f.f. over single bins.
K Data 435654 events,29 evts/box MC
10.0 M events,667 evts/box K- Data 241856
events,16 evts/box MC 5.6 M events,373
evts/box

• no normalization-gtonly relative f.f. and their
  variation wrt kinematical variables
• residual variation (linear slope) observed wrt
  Mev for Fs 2-dim fit performed
• Fs from bin/bin normalization after fit.

K/K-1.8 (both data and MC) MC/Data23 (both
K and K-)
Fs2(1fs q2 fs q4 fe Se/4mp2)2
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fp,hp?0, no q2 dependence
gp linear wrt q2
Correlation
gp
gp
-0.914
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Ke4 form factors results
All f.f. parameters measured within 5 to 15
relative precision

• Relative form factors f.f./Fs(0)
• measured separatedly for K,K- and then
  combined
• Fs obtained from bin/bin normalization,Fp,Gp,Hp
  deconvoluted from observed Fs(q2,Se) variation.

valuestat.syst.
fs/fs0.1650.0110.006 fs/fs-0.0920.0110.00
7 fe/fs0.0810.0110.008 fp/fs-0.0480.0040.00
4 gp/fs0.8730.0130.012 gp/fs0.0810.0220.014
hp/fs-0.4110.0190.007

• SYSTEMATIC CHECKS
• Two independent analyses
• Acceptance control
• BG level and shape control
• Radiative correction included
• Possible bin-to-bin correlation considered.

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Ke4 d phase shift and a0,a2 extraction

• Extraction of pion scattering lengths from
  d(d00-d11) phase shift can be done through
  external experimental and theoretical (e.g. Roy
  equation) inputs, which relate d and (a0,a2)
• The Universal Band parameterization corresponds
  to a 1-dimensional fit of d with a fixed relation
  between a0 and a2.

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Ke4 comparison with other experiments

• Thanks to the independent bin analysis, the
  scattering length extraction can be performed on
  old data even if the collaboration doesnt exist
  anymore
• E865 quotes values ranging from a00.203 to
  a00.237, NA48 seems to obtain slightly higher
  values
• Further checks are ongoing to understand the two
  different results, expecially in the last Mpp bin.

a00.25
a00.20
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Plane (a0,a2) theory and experiments

• Several equations relating a0 and a2 exist
  (ACGL,DFGS,)
• A 2-dimensional fit (on a0 and a2) can also be
  performed (dotted lines in figure,centered on
  best ?2 and including 68 of events)
• E865 and NA48/2 point at slightly different
  regions of the universal band removing the last
  E865 bin brings the two results closer and
  decreases ?2.

Isospin breaking corrections neglected so far.
This contribution was considered negligible until
short time ago. Calculations to apply this
correction are ongoing.
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K3piselection
m0 pion mass Ei,Ej ? energies Zik p0 vertex
distance from LKR

• For each photon pair (e.g. i,j) a decay vertex
  reconstructed along beam axis assuming p0 mass
• m022EiEk(1-cosß)EiEk(Dik)2/(Zik)2 Zik
• Pair of photons minimizing ?ZZjl-Zik chosen
• Compatibility within 6 MeV wrt PDG kaon
• mass requested.

LKR
?
?
Dik
?
Zij
Zkl
K
Djl
?Z
?
pp invariant mass
Excellent at low Mpp values
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Primary goal asymmetry measurement
Dalitz variables u(s3-s0)/p2 v(s2-s0)/p2
Comparison between Dalitz plot distribution for
K and K- to look for direct CP violation.
Matrix element M(u,v)2 1guhu2kv2...
3s0Mk2Mp22Mp02 si(Pk-Pi)2 (i1,2,33odd pion)
Ag?0-gtdirect CP violation
p(even)
p-(odd)
K
p(even)

• SM Ag predictions in range 10-6-10-5
• Beyond SM models enhance the prediction

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Acceptance equalization
Y
X
Achromats K Up
Jura
B
KK-
B?
Saleve

• In each ratio the charged pions are deflected
  towards the same side of the detector (left-right
  asymmetry cancels out)
• In each ratio the event at the numerator and
  denominator are collected in subsequent period of
  data taking (global time variations)
• The whole data taking is subdivided periods in
  which all the field configurations are present.

4-ple ratio R4RUSRUJRDSRDJ n(1Dg/f(u))4

• 3-fold cancellation
• L-R asymmetry
• Beam shape asimmetry
• Global time variations.

RESULTS
Slope difference ?g(2.22.1stat0.7syst)10-4 Ch
arge asymmetry Ag(1.81.7stat0.5syst)10-4
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Bonus goal cusp in M2p0p0 distribution
2003 16.0 mln events
2004 (80) 43.6 mln events
80k

• Cusp analysis not foreseen at the beginning of
  the experiment
• First cusp observation on 2003 data, 2004 data
  now included (80 of the whole statistics)
• A cusp can be seen in M2(p0p0) distribution at
  4Mp value and is the effect of the interference
  of (at least) two amplitudes.

200k
60k
160k
120k
40k
80k
20k
40k
0
M2(?0?0), (GeV2)
M2(?0?0), (GeV2)
45k
120k
110k
40k
100k
35k
90k
30k
80k
?? threshold
?? threshold
25k
70k
0.079
0.080
0.079
0.078
0.077
0.076
0.078
0.077
0.076
M2(?0?0), (GeV2)
M2(?0?0), (GeV2)
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Cusp theory final state rescattering
N. Cabibbo, PRL 93 (2004) 121801
M(K pp0p0)M1M2
M0 direct emission amplitude
A0(1g0u/2hu2/2kv2/2)
p
Not the same parameterization used for asymmetry!
Amplitude parameterized (rather than matrix
element)
K
p0
p0
M1 rescattering amplitude -2/3(a0-a2)mMv
1-(M00/2m)2


K-gt3p amplitude at threshold
Negative interference under 2m
no rescattering
S-wave pp scattering lengths
1-loop rescattering
p
p
p0
K
M24m2p
p0
p-
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M2p0p0(GeV2)
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Cusp theory higher order diagrams
N. Cabibbo and G. Isidori, JHEP 503 (2005) 21

• 1 and 2-loop processes included
• Five S-vawe scattering lengths (ax, a, a-,
  a0, a00), expressed as linear combinations of a0
  and a2
• Isospin symmetry breaking (2) considered
• Radiative corrections missing -gt a0-a2 precision
  gt 5 .

Examples of 2-loop diagrams
p
p0
p
K
p
p0
p
Two loop effect on cusp
p
p0
No cusp
p
p
K
Cusp (2-loop correction)
Cusp
Arbitrary scale
p0
No rescattering
Imaginary amplitude
p
p
p
p
K
p0
Negative amplitude
p
p
p0
p
0.076
0.078
0.080
0.074
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M2p0p0(GeV2)
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Cusp fit procedure

• Detector response computed with a full GEANT MC
  resolution matrix (computed on s3 variable)
  applied on MC-generated data
• Five free parameters (g0, h,m(a0-a2),ma2,N)
  in MC data. Use of MINUIT to minimize ?2 based on
  difference data-MC.

Resolution smears MC bins FiMC? RijGj
Reconstructed s3
generated MC bin
GG(M00,g0,h,m(a0-a2),ma2)
Generated s3M2(?0?0)(GeV2)
(Fdata-NFMC)2
?2(g0, h,m(a0-a2),ma2,N)?
dF2datad2N2F2MC
bins
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Cusp dealing with pionium

• Pionium created when relative velocity between
  two opposite-sign pions is 0. It is created by
  EM interaction, decays (10-16 sec) by strong
  interaction
• No Coulomb corrections -gt Pionium cannot be
  accounted for in this model -gt 7 bins (3.5
  resolution ss around dipion mass) excluded from
  Data/MC comparison.

7 bins excluded (0.0775-0.0785 GeV2)
If excess in data all interpreted as pionium, one
gets
R?(K???A2?)/?(K??????) (1.82?0.21)?105
Theoretical predictionR0.8?105 Z.K.
Silagadze, JETP Lett. 60 (1994) 689
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• Geometric acceptance
• MC sample
• LKR showers
• V-dependence of amplitude.

• Analysis technique
• Trigger inefficiency
• Resolution
• LKR non-linearity

Systematic checks
Cusp results
(20032004 data, 80 of statistics)
(a0a2)m 0.261 ? 0.006stat. ? 0.003syst. ?
0.013ext. a2m 0.037 ? 0.013stat. ? 0.009syst.
? 0.018ext.
Using a chiral symmetry constraint Colangelo et
al., PRL 86 (2001) 5008 a2 0.0444
0.236(a00.22) 0.61(a00.22)2 9.9(a00.22)3
(a0a2)m 0.263 ? 0.003stat. ? 0.0014syst. ?
0.013ext.
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Conclusions

• The NA48 results for a0 and a2 following two
  different paths (ke4 and cusp) are consistent
• Agreement is also found with DIRAC result, which
  computes a0 and a2 measuring pionium lifetime
• Both analyses are still ongoing, room for
  improvements.

QCD_at_WORK 2007
Stefano Venditti
17/06/2007