Chiral Perturbation Theory from Charged Kaon Decays at NA482 R. Fantechi INFN Sezione di Pisa on beh

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Chiral Perturbation Theoryfrom Charged Kaon
Decays at NA48/2R. FantechiINFN Sezione di
Pisaon behalf of the NA48/2 Collaboration

• QCD08, Montpellier, July 10th, 2008

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Outline

• The NA48/2 beam and detector
• K p p0 g - DE/INT part measurement
• K p g g - branching ratio measurement
• K p ee- g - first observation, BR
  measurement, c estimation
• K p ee- - Model dependent and independent
  BR estimation, related parameters
• Conclusions

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The NA48/2 beam line
focusing quadrupoles
Detectors
K/K- flux1.8
Incoming SPS 400 GeV protons
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The NA48/2 detector
Beam time
2003 50 days 2004 60 days

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

18 109 triggers collected
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K pp0g
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K pp0g

• 3 terms (pure IB and DE, INT) in the decay
  width, can be disentangled using W variable (and
  integrating over Tp)

Tp Pion CM kin. energy
E electric dipole M magnetic dipole
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K pp0g

• DE has magnetic (M) and electric (E) parts
• DE magnetic part is due to chiral anomaly
  contribution (calculable) and direct
  contributions (non predictable)
• DE electric part is non predictable
• DE electric part interferes with IB amplitude,
  giving INT amplitude

A measurement of DE and IB contributions allows
to measure M and E
Current PDG values
IB term (2.750.15) 10-4 (55 MeV lt Tp lt 90
MeV) DE term (4.40.8) 10-6 (55 MeV lt Tp lt 90
MeV) INT term not yet measured
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K pp0g
Tp(IB)
Tp(DE)
Tp(INT)
CUT

• 55 MeV lt Tp lt 90 MeV cut used in previous
  analyses to reject BG (mostly pp0 and pp0p0)
• However this cut excludes most of the DE events
• It was then decided to cut at Tp lt 80 MeV.

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K pp0g
EVENT SELECTION

• At least 1 track and 3 clusters
• Acceptance and BG-rejection cuts (MK, COG)

BG CHANNELS

• Residual BG (due only to K pp0p0) less than
  1 of DE
• mistagging probability (self BG) at level

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K pp0g
Fit function used
WDATA(1-A-B)WIBAWDEBWINT
with A,B free parameters

• A,B highly correlated (corr.-0.92)
• systematics dominated by trigger efficiency
• B ? 0 first evidence of INT term

Preliminary result on 2003 data
FRACDE(0.2ltWlt0.9)(3.350.35stat.0.25syst.) FRAC
INT(0.2ltWlt0.9)(-2.670.81stat.0.73syst.)
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K pgg
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K pgg
Ppion 4-momentum q1,2photon 4-momenta
(q1q2)2
M2??
z

M2K
M2K
(only z is dynamically relevant)
A,B,C,D depend on z and on the parameter c
ChPT contributions to the amplitude
O(p4) A(z,c) responsible for cusp at m??2mp C?0
for WZW anomaly (poles and tadpoles) BD0
DAmbrosio, Portolés, PLB386 (1996) 403
O(p6) unitarity corrections can increase BR by
30-40 (depending on c value)
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K pgg
Branching ratio dependence on c (O(p4)) BR(K
pgg) (5.26 1.64c 0.32c20.49) 10-7 Þ gt 4
10-7
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K pgg
Normalization channel K pp0 (6M events
selected)

• Event selection
• at least 1 p track, 2 clusters
• COG, CDA, chd vertex cuts
• 0 lt M?? lt MK-Mp (kinematic limit)

• 1164 events selected
• 40 of full datasample
• 40 times larger than total world sample
• 3 BG (mainly from pp0?)

trigger cut _at_ 475 MeV
pp0
PDG value from BNL E787(1991) 31 candidates, 5
BG events BR(1.100.32)10-6 c1.8 0.6
p??
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K pgg
MK
M??
BG mainly from pp0?
Good agreement with c2 generated MC sample
BR(1.070.04stat.0.08syst.)10-6

• Main systematics
• pion-gamma cut
• Efficiency measurement

PRELIMINARY
Future task precise c estimation
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K pee-g
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K pee-g

• Theory is similar to K pgg decay.
• Naive expectation BR(pee?) BR(p??) 2a 1.6
  10-8
• Theoretical expectation (0.9-1.6) 10-8
  Gabbiani, Phys. Rev. D 59
• BR again depends on c parameter (as in K
  pgg)
• Higher-order (O(p6)) ChPT corrections increase
  the BR

• GOALS
• Model-independent BR measurement
• Estimation of c from data
• Use c to compute model-dependent BR

BR prediction at O(p4) and O(p6) as a function of
c
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K pee-g
Event selection
BG suppression

• at least 3 tracks with Qtot1 and compatible
  decay vertex
• at least 1 cluster not associated to track
• E/p gt 0.94 for e, E/p lt 0.8 for p
• 54 GeV lt Etot lt 66 GeV

• Many BG sources considered and evaluated with MC
• Mee? gt 260 MeV (low BG area)
• cut on e-? angle to reject K pee-
• 480 MeV ltMpee?lt 505 MeV (K mass)

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K pee-g
120 candidate events in the accepted
region 7.31.7 estimated BG events.
Normalized to K pp0D, (14 M events) PDG value
used to compute absolute BR.
c1.8 for MC generation
FIRST OBSERVATION OF THIS DECAY
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K pee-g
Model-independent BR in bins of Mee? (5 MeV
steps) Least squares fit on Mee? to extract c
c1.8
c0.9
BRMI (1.190.12stat0.04syst)10-8 c
0.900.45
(cfr c 1.80.6 in Kp??, BNL E787)
Model-dependent branching ratio (c 0.9) BR
(1.290.13exp0.03c)10-8

• Main systematics
• BG subtraction
• Normalization
• MC statistics

Errors dominated by statistics
Phys. Lett. B 659 (2008) 493
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K pee-
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K pee-
through suppressed FCNC.
K pg pee-
3 models tested for W(z)
BNL E865 10300 evts BR (2.94 0.15) 10-7

• polynomial GFMK2f0(1?z)
• ChPT O(p6) GFMK2(abz) W??(z) JHEP 8
  (1998) 4
• Dubna ChPT W(Ma, M?, z) hep-ph/0611175

• GOALS
• Model independent BR in accepted kinematic range
• parameter and model-dependent BR estimations for
  the 3 models.

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K pee-
Selection cuts signal
Selection cuts normalization (K pp0D)

• 3-track vertex
• E/p lt 0.85 (p), E/p gt 0.95
• opposite sign electrons
• Mee gt 140 MeV
• Cut on kaon (pee-) mass, total and transverse
  momentum

• Selection of good ?
• Cut on kaon (pee-?) mass

The use of a very similar channel cancels
systematics (trigger, PID) in the BR ratio
BG subtraction MC was used only to identify the
BGs, BG estimation DIRECTLY ON DATA with same
sign (SS) events.

• K pp0D with misid. e and p
• K e?p0D with misid. e
• ee- pairs (conversions and Dalitz)

SIGNAL 7103 events BG 56 events BG/SIG. 0.8
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K pee-
Normal and SS events
Normal-2x SS events
2x same-sign events (Kpp0DD)
Mee cut
Mee cut
Mee (all cuts applied except Mee gt 140 MeV or
zgt0.08)
The region Mee lt 140 MeV is dominated by
background After background subtraction, the p0
ee- peak (500 evts) can be seen
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K pee-
cut
cut
Signal
Normalization
cut
cut
12.23 M candidates
BG/Signal 0.15
7103 candidates
Kaon decay flux (20032004)?K1.70?1011 with K
pp0 PDG BR
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K pee-
All models reasonably agree with data.

• Model-independent BR integrating Mee
• Model dependent BRs using fit parameters.

Data
MC
Polynomial ChPT O(p6) Dubna ChPT
Angle between e and p in (e,e-) rest frame
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K pee- - Preliminary results
Including uncertainty due to the model dependence
BR (3.08?0.04stat?0.04syst?0.08ext?
0.07model)?107 (3.08?0.12)?107
CPV parameter (first measurement! correlated
K/K uncertainties excluded)
?(K??ee) (BRBR) / (BRBR)
(2.1?1.5stat?0.3syst)
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Conclusions

• First evidence of the interaction term in K
  pp0? decay amplitude
• Statistics on K p?? improved wrt previous
  measurements by a factor 40
• First observation of K pee-?, estimation of
  ChPT parameter c
• Model-independent BR estimation in K pee-
  and test of various models
• There is an ongoing analysis also on K pen?
• Measurement of the branching ratio
• Search for T violation

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Experimental results for DE and INT
All the measurements have been performed in the
Tp region 55-90 MeV to avoid pp0p0 BG All of
them are assuming the Interference term to be 0
Interference measurements
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INT0 fit just for comparison
Just for comparison with what other experiments
did we have also extracted the fraction of DE,
with the INT term fixed to 0 in the region 55-90
MeV.A likelihood fit using IB DE MC only has
been performed in the region 0ltTplt80 MeV.
Extrapolating to the 55-90 region using MC we get
The analysis of fit residuals shows a bad
c2 Description in term of IBDE only is unable
to reproduce W data spectrum.
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K pp0g
W(Data)/W (IBMC)

• IB, DE and INT MC sample produced separately
• Fit in 0.2ltWlt0.9 region
• Looking for DE and IB weights (wrt IB)
  minimizing data/MC.

Data/MC agreement lost where DE,INT sizable wrt IB
DATA/MC(IB)