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Highlights on rare kaon decays from NA48/2
Monica PepeINFN Perugia
on behalf of the NA48/2 Collaboration
Cambridge, CERN, Chicago, Dubna, Edinburgh, Ferrara, Firenze, Mainz, Northwestern, Perugia, Pisa, Saclay, Siegen, Torino, Vienna
CRIMEA 2006 - NEW TRENDS IN HIGH-ENERGY PHYSICSYalta, Crimea, UkraineSeptember 16-23, 2006
Crimea 2006 2 Monica Pepe – INFN Perugia
Outline The NA48/2 experiment
The decay K± ±0 formalism experimental status NA48/2 measurement
Charged Ke4 decays (K± e± ) formalism event selection form factors
Neutral Ke4 decays (K± 00e± ) event selection branching ratio form factors
Cusp effect in ± 00 decays
Conclusions
Crimea 2006 3 Monica Pepe – INFN Perugia
The NA48/2 beam line
Primary proton beam p = 400 GeV/c (71011 ppp)
Simultaneous K+/K− beams p = (60 ± 3) GeV/c
K+/K− beam flux 3.8 (2.6) × 107 ppp
114 m
Crimea 2006 4 Monica Pepe – INFN Perugia
The NA48/2 detector
Spectrometer
- 4 Drift Chambers (DCH)- Magnet
p/p = 1.0% + 0.044% p [GeV/c]
x,y ~2mm
Very good resolution for charged invariant masses (±+-) = 1.7 MeV/c2
E/p measurement for e/ discrimination
LKr EM calorimeter
E/E = (3.2/E + 9/E + 0.42)% [GeV]
x,y < 1.5mm
Very good resolution for neutral invariant masses (±00) = 1.4 MeV/c2
Trigger (~1MHz ~10kHz)
LVL1 hodoscope and DCH multiplicity
LVL2 on-line processing of information from LKR and DCH
Crimea 2006 5 Monica Pepe – INFN Perugia
The NA48/2 experiment data taking
Total statistics:
K± ±00 ~ 1·108
K± ±+- ~ 4·109
K± +- e± ~ 1·106
K± 00 e± ~ 3·104
2003 Run ~50 days
2004 Run ~60 days
Primary goal:
Search for CP-violating charge asymmetries in K± 3 decays (see E. Goudzovski talk)
Crimea 2006 6 Monica Pepe – INFN Perugia
1. The decay K± Results based on a sub-sample of 2003
data (~30 % of all)
Crimea 2006 7 Monica Pepe – INFN Perugia
Photon production mechanism
IBIB DEDE
IB INT DE
DEDEIBIB
Sensitive variable:
P*K = 4-momentum of the K±
P*= 4-momentum of the ±
P*= 4-momentum of the radiative 2
****2
)(
))((
mm
PPPPW
k
K
± depends on 2 variables (T*and W) that can be reduced to
only one integrating over T*
Crimea 2006 8 Monica Pepe – INFN Perugia
W distributions for IB, DE, INT
IB and DE contributions are well separated in W
IB INTDE
Crimea 2006 9 Monica Pepe – INFN Perugia
K→ amplitudes Two types of contributions:
Electric (J=l±1) dipole (E1)
Magnetic (J=l) dipole (M1)
Electric contributions are dominated by the Inner Bremsstrahlung term
DE shows up only at order O(p4) in CHPT: is generated by both E and M contributions
Present experimental results seem to suggest a Magnetic dominated DE
INT term is sensitive to E only
Inner Bremsstrahlung(IB) : (2.75±0.15)·10-4 PDG (2006) (55<T*<90
MeV)
Direct Emission (DE) : (4.4±0.7)·10-6 PDG (2006) (55<T*<90 MeV)
Interference (INT) : not yet measured
Frac(DE) = (1.6±0.3)%
Crimea 2006 10 Monica Pepe – INFN Perugia
BNL E787
KEK E470
Exp results for DE and INTAll the measurements have been performed:
in the T* region 55-90 MeV to avoid
±and ± background
assuming Interference term = 0
Interference measurements:
Experiment
Year
# Events
BR(DE) × 106
E787 [20]E470 [21]E787 [22]E470 [23]
2000
2003
2005
2005
198364434
2057110154
4.7 ± 0.8 ± 0.3
3.2 ± 1.3 ± 1.0
3.8 ± 0.8 ± 0.7
3.04.06.05.3
History of DE Branching ratio
Crimea 2006 11 Monica Pepe – INFN Perugia
What’s new in NA48/2 measurementIn flight Kaon decays
Both K+ and K− in the beam (possibility to check CP violation)
Very high statistics (220k candidates, 124k used in the fit )
Enlarged T* region in the low energy part (0 <T*
< 80 MeV)
Negligible background contribution < 1% of the DE component
Good W resolution mainly in the high statistic region
More bins in the fit to enhance sensitivity to INT
Order ‰ mistagging probability for IB, DE and INT
Crimea 2006 12 Monica Pepe – INFN Perugia
Enlarged T*region
T* T*
DE T*INT
Standard region Standard
region
Standard region
Use standard region 55<T*<90 MeV as safe choice for BG rejection
But…. region <55 MeV is the most interesting to measure DE and INT
This measurement is performed in the region
0 < T*< 80 MeV
to improve statistics and sensitivity to DE
Crimea 2006 13 Monica Pepe – INFN Perugia
K± ± selectionTrack Selection• # tracks = 1
• P > 10 GeV
• E/P < 0.85
• No muon veto hits
• 0 MeV < T* < 80 MeV
BG Rejection
• COG < 2 cm
• Overlapping cuts
• |MK-MKPDG| < 10 MeV
220K events
Tagging Optimization• CHA and NEU vertex compatibility
• Only one compatible NEU vertex
Selection•N = 3 (LKr clusters well separated in time)
•Min energy > 3 GeV (>5 for the fit)
Crimea 2006 15 Monica Pepe – INFN Perugia
Main BG sources
Physical BG rejection: (IB bg) T*
< 80 MeV , MK and COG cuts
(DE bg) release T* cut but cut on kaon mass
(missing and overlapping )
Accidental BG rejection (e Clean beam + Very good time, space, and mass resolutions
Decay BR Background mechanism± (21.13±0.14)% +1 accidental or hadronic extra
cluster
± ± (1.76±0.04)% -1 missing or 2 overlapped
± e (4.87±0.06)% +1 accidental and e misidentified as a
± (3.27±0.06)% +1 accidental and misidentified as a
±
e(2.66±0.2)·10−4 e misidentified as a
±
(2.4±0.85)·10−5 misidentified as a
Crimea 2006 16 Monica Pepe – INFN Perugia
•K
•K
BG rejection performance
Source %IB %DE
± ~1·10-4 ~0.61·10-2
Accidentals
<0.5·10-4 ~0.3·10-2
Total BG < 1% of DE component
All physical BG can be explained in terms of ±events only
Very small contribution from accidentals is neglected
Selected region 220Kevents
Crimea 2006 17 Monica Pepe – INFN Perugia
Systematic uncertainties
Effect Syst. DE Syst. INT
Energy scale +0.09 -0.21
Fitting procedure 0.02 0.19
LVL1 Trigger ±0.17 ±0.43
Mistagging _ ±0.2
LVL2 Trigger ±0.17 ±0.52
Resolutions difference <0.05 <0.1
LKr non linearity <0.05 <0.05
BG contributions <0.05 <0.05
TOTAL ±0.25 ±0.73
Many systematic checks have been performed using both data and Monte-Carlo
Systematic effects dominated by the trigger
both LVL1 and LVL2 triggers modified in the 2004 run
systematics reduced in 2004 data set
Crimea 2006 18 Monica Pepe – INFN Perugia
Fit results
14 bins, 0.2 < W < 0.9, E> 5 GeV
124k evts
Correlation coefficient: = -0.92
Systematics dominated by trigger efficiency
Error dominated by statistics
To compare with previous exp: extrapolating to 55 < T*< 90 MeV , INT=0
Frac(DE)0<T*<80 MeV = (3.35 ± 0.35 ± 0.25)%
Frac(INT)0<T*<80 MeV = (-2.67 ± 0.81 ± 0.73)%
First evidence for
non zero Interference term
INT=0Frac(DE)55<T*<90 MeV =(0.85 ± 0.05 ± 0.02)%
Prelimina
ry
Crimea 2006 19 Monica Pepe – INFN Perugia
2. K± e±K+-
e4Preliminary results based on 30 days in 2003
Crimea 2006 20 Monica Pepe – INFN Perugia
Ke4 Introduction
Very precise theoretical predictions from PT (2%) depending only on one free parameter (quark condensate) to be determined experimentally it determines the relative size of mass and momentum in the power expansion scattering lengths a0
0 and a02 predicted as a function of q.c.
Low energies pairs can be used for scattering length measurements
Ke4 no other hadrons, no theoretical uncertainty on form factors, only on a0
2 = f(a00)
Form factors are good constraint for PT Lagrangian
Both modes have small BR ~ few 10-5
high statistics and strong background rejection required
Crimea 2006 21 Monica Pepe – INFN Perugia
Charged Ke4 formalism
Ke4 decay described using 5 kinematic variables (defined by Cabibbo-Maksymowicz)
dipion
dilepton
Form factors of decay rate determined from a fit to experimental distributions of the 5 variables, provided the binning is small enough
Form factors
F = Fs ei0
0 + Fp e
i11 cos + d-wave
term...
G = Gp ei1
1 + d-wave term...
H = Hp ei1
1 + d-wave term...
Keeping only s and p waves, rotating phases by 1
1 only 5 form factors are left
Fs Fp Gp Hp and = 00 - 1
1
M , Me , cos , cose , 22
Form factor formulations by Pais and Treman [Phys. Rev. 168 (1968)] and Amoros and Bijnens [J.Phys. G25 (1999)] have been used
Expanding in powers of q2, Se
Fs = fs + f’s q
2 + f’’s q4 + fe(Se/4m2
)+…
Fp = fp + f’p q
2 +....
Gp = gp + g’p q
2 +....
Hp = hp + h’p q
2 +....
Crimea 2006 22 Monica Pepe – INFN Perugia
K± e± Signal and Background
pK(GeV/c)
K+−e4 candidates (2003) ~370000 events with 0.5%
background
Bkg main sources±eor mis-ID as e)
±Dalitz
(eewith e mis-ID as and undetected)
Reconstruction of C.M. Variables:• Assume fixed 60Gev/c Kaon along Z to extract Pwithout ambiguity: assign missing Pt to and compute the mass of the system• or use costrain to solve energy-momentum conservation equation get PK
• Boost in the Kaon and dipion/dilepton rest frame to get angular variables
Residual Bkg estimated from data: Wrong Sign events have same total charge (can only be Bkg) Right Sign Bkg appears in the data with same or twice ( the rate as in Wrong Sign events
Crimea 2006 23 Monica Pepe – INFN Perugia
Form Factor Determination
CP symmetry:
opposite K+/K- φ distributions
K-
K+
• K+ (235000 evts) 16 evts/bin
• K- (135000 evts) 9 evts/bin
Use equal population bins in the 5-dim space of C.M. variables
10 independent fits (one in each M bin) assuming ~constant form factors in each bin
For each fit 1500 equal population bins:
Crimea 2006 24 Monica Pepe – INFN Perugia
Results: F, G, H
No overall normalization from Branching Ratio quote relative form factors
Preliminary
Se (M2e) dependence measurement consistent
with 0
Crimea 2006 25 Monica Pepe – INFN Perugia
Results: a00 and a0
2
Prelimina
ry
• Use the Universal Band parametrization to extract a00 with a0
2= f(a0
0) [Descotes et al. EPJ C24 (2002)]
= 00 - 0
1 distribution fitted with 1 parameter a00 function given in the
numerical solution of Roy equation in [Ananthanarayan et al. Phys. Rept. 353(2001)]
• a00 and a0
2 constrained to lie on the centre of UB
Crimea 2006 26 Monica Pepe – INFN Perugia
fs'/fs = 0.169 ± 0.009stat ± 0.034syst
fs''/fs = -0.091 ± 0.009stat ± 0.031syst
fp/fs = -0.047 ± 0.006stat ± 0.008syst
gp/fs = 0.891 ± 0.019stat ± 0.020syst
gp'/fs = 0.111 ± 0.031stat ± 0.032syst
hp/fs = -0.411 ± 0.027stat ± 0.038syst
a00 = 0.256 ± 0.008stat ± 0.007syst ± 0.018theo
K± e± Preliminary Result and Systematics
Systematics Checks
Two independent analyses (different selections, K reconstruction, acceptance corrections, fit method and MC parameters)
Acceptance vs Time estimated by varying beam conditions of simulated events
Background level checked with data (varying cuts) and MC
Electron-ID uncertainty estimated by variation of e-π rejection efficiency
Radiative Corrections: quote fraction of total effect with or w/o using PHOTOS
Se dependence: possible bias from neglected dependence estimated by MC tests
NA48/2
2003 data
Preliminary
Crimea 2006 27 Monica Pepe – INFN Perugia
3. K± e±K00
e4Preliminary results based on 2003+2004 data
Crimea 2006 28 Monica Pepe – INFN Perugia
K± e± Signal and Background
e±Signal Topology:
2 in Lkr, 1 charged track from e (E/p) ,
missing E and PT
Background main sources
+mis-ID as e (dominant)
e± + accidental
Estimated from data reversing cuts
K00e4 candidates 2003 ~ 9600 events with 3%
bkg
K00e4 candidates 2004 ~28000 events with 2%
bkgPreliminary results
Branching Ratio from 2003 data using K± ±as normalization channel
Form Factors from 2003+2004 data
Systematic Uncertainties
Acceptance
Trigger efficiency
Energy measurement in LKr
2003+2004
Crimea 2006 29 Monica Pepe – INFN Perugia
Using part of the 2003 data (9642 events) and as normalization channel
Result cross-checked using Ke3 as normalization
Improved measurement compared with recent results:
KEK-E470 (216 events) BR = (2.29 ± 0.33) x 10-5
.
Results: Branching Ratio
BR Ke400
1,5
1,7
1,9
2,1
2,3
2,5
2,7
2,9
2003 2004 2005 2006 2007
Year
BR
*10-
5 PDG 2005
KEK E470
NA48/2
NA48/2 2003 data
Br(K00e4) = (2.587 ± 0.026stat ± 0.019syst ± 0.029norm) x 10-5 Prelim
ina
ry
Crimea 2006 30 Monica Pepe – INFN Perugia
Fit performed using both 2003 and 2004 data (~38K events)
Results: Form Factors Same formalism as for K+-
e4 but for simmetry of the 0 0 system only ONE form factor F (no P-wave)
fs'/fs = 0.129 ± 0.036stat ± 0.020syst
fs''/fs = -0.040 ± 0.034stat ± 0.020syst
Bkg
Bkg
Signal
Signal • Consistency with K+-
e4 measurement
• Errors are stat + sys assuming same correlation for both
Preliminary
Crimea 2006 31 Monica Pepe – INFN Perugia
4. Cusp effect in
Results based on 2003 data – Phys. Lett. B633 (2006)
Crimea 2006 32 Monica Pepe – INFN Perugia
Data Sample: 23 · 106 K± ±00 decays (2003)
Observation of a Cusp in K± ±00
• a0-a2 determined performing 1-dim fit to M200distribution based
on the improved Cabibbo-Isidori rescattering model (JHEP 0503 (2005) 021)
* In the matrix element g0 and h’ are free parameters while the slope parameter k’ is set to 0
* Isospin breaking effects included
...'2
1'
2
1
2
11 22
000 vkuhugM+
D.E. Ch. Ex. +- → 00
Sudden change of slope (“cusp”)at (M00)2 = (2m+)2
M002 zoom on the cusp region
M002 (GeV2)
Crimea 2006 33 Monica Pepe – INFN Perugia
Cusp in K± ±00: Fit and ResultsThe scattering length difference:
(a0-a2)m+ = 0.268 ± 0.010stat ± 0.004syst ± 0.013ext
and
(a2)m+ = -0.041 ± 0.022stat ± 0.014syst
if correlation between a0 and a2 predicted by ChPT is taken into account:
(a0-a2)m+ = 0.264 ± 0.006stat ± 0.004syst ± 0.013ext
From same fit slope parameters are obtained:
g0 = 0.645 ± 0.004stat ± 0.009syst
h' = -0.047 ± 0.012stat ± 0.011syst
Main Systematic Uncertainties: Acceptance, Trigger efficiency, Fit interval
NA48/2 measurements of scattering lengths from Ke4 Charged decays:
scattering lengths extracted in a model dependent way (input a02= f(a0
0)) use Universal Band function
NA48/2 Preliminary (370k decays) a00 = 0.256 ± 0.008stat ± 0.007syst ±
0.018theo
Previous published results:CERN/PS Geneva-Saclay (30k decays) a0
0 = 0.253 ± 0.037stat+sys ±
0.014theo
BNL E865 (400k decays) a00 = 0.229 ± 0.012stat ± 0.004sys ±0.014theo
(but beware of different theoretical frameworks when comparing Cusp and ke4 .......)
Crimea 2006 34 Monica Pepe – INFN Perugia
2-dim fit to the Dalitz plot evidence for k’>0 term
...'2
1'
2
1
2
11 22
00 vkuhugM
cos = angle between ± and 0 in 0 0 cms
NA48/2 preliminary result (2003 data)
k’ = 0.0097 ±0.0003stat±0.0008syst
corresponding changes in the g0 and h’ parameters are of order 2% and 25% respectively
no change in a0-a2 and a2
Update to 2003 result: Effect on K termThe above result was obtained assuming no quadratic
term in v (k’=0) for the unperturbated matrix element but....
analysis shows evidence for a non-zero quadratic v term:
Crimea 2006 35 Monica Pepe – INFN Perugia
Conclusions
Frac(DE)0<T*<80 MeV = (3.35 ± 0.35 ± 0.25)%
Frac(INT)0<T*<80 MeV = (-2.67 ± 0.81 ± 0.73)%
First measurement of the DE and INT terms in the decay K± ±0
Error dominated by statistics: will be reduced analyzing full 2003 and 2004 data
Using part of 2003-2004 data NA48/2 has performed improved measurements of Ke4 form factors:
K+-e4 Form factor measurement dominated by systematics; scattering
dominated by external error of 7% (stat and syst uncertainties ~3% relative each)
a00 = 0.256 ± 0.008stat ± 0.007syst ± 0.018theo
K00e4 Form factors consistent with K+-
e4 . Improved (by factor 8) measurement of B.R.
Br(K00e4) = (2.587 ± 0.026stat ± 0.019syst ± 0.029norm) x 10-5
Cusp observed in K± ±0 0 decays interpreted as charge exchange process providing a new method to extract scattering lengths
(a0-a2)m+ = 0.268 ± 0.010stat ± 0.004syst ± 0.013ext
first evidence for a value of k’0 in the K± ±0 0 Dalitz plot
k’ = 0.0097 ± 0.0003stat ± 0.0008syst
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