Measurements of K ± π + π  e ± ν ( Ke4) and K ± π ± π 0 π 0 decays at NA48/2.

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Transcript of Measurements of K ± π + π  e ± ν ( Ke4) and K ± π ± π 0 π 0 decays at NA48/2.
Measurements of K±π+πe±ν (Ke4) and K± π±π0π0 decays at NA48/2.
Silvia Goy López (CERN)For the NA48/2 collaboration
HS07, September 3th 2007
9/3/2007 Silvia Goy Lopez HS07 2
Overview
The K±π+πe±ν (Ke4) decay Introduction Selection, reconstruction Form factor and ππ scattering
length measurements
The K± π±π0π0 decay Selection, reconstruction Cusp effect and
interpretation Form factors and ππ
scattering length measurements
Introduction to NA48 The NA48/2 experiment: goal, beam line, detector
Summary and Conclusions
9/3/2007 Silvia Goy Lopez HS07 3
Introduction NA48: 19972000. DCPV in neutral K
Re(/ ) = (14.7 2.2) 104
NA48/1: 2002. Rare Ks decays Br(Ks 0ee)=(5.8+2.8
2.3 ± 0.8) 109
Br(Ks 0 )=(2.8+1.51.2 ± 0.2) 109
NA48/2: 20032004. DCPV in K 3 Ag=(1.5+1.5Ag=(1.5+1.5statstat+0.9+0.9trigtrig+1.1+1.1systsyst))··101044
AgAg00=(1.8+1.7=(1.8+1.7statstat+0.5+0.5systsyst))··101044
In addition many results on rare kaon decays and on hyperon decays.
NA62. Test beam in 2006, 2007. Ke2/K2 in 2007
9/3/2007 Silvia Goy Lopez HS07 4
The N A48/2 2003 run: 2003 run: ~ 50 days~ 50 days 2004 run: ~ 60 days2004 run: ~ 60 days
Total statistics 2 years:Total statistics 2 years: KK±→±→±±000: ~1·100: ~1·1088
KK±→±→±±++: ~3·10: ~3·1099
K±π+πe±ν: ~1.106
Greatest amount of K→3 Greatest amount of K→3 ever collectedever collected
For these results 2003 for For these results 2003 for Ke4 and 90% of all data for Ke4 and 90% of all data for cuspcusp
9/3/2007 Silvia Goy Lopez HS07 5
The NA48/2 Beam Line Simultaneous, coaxial and focused K+ and K beams Central kaon momentum of 60 GeV/c and a spread of ± 3.8% (rms) Beam line and spectrometer magnet polarities periodically inverted
9/3/2007 Silvia Goy Lopez HS07 6
The NA48 Detector Magnetic spectrometer
4 DCHs, 4 views, 2 planes/view + dipole magnet
(p)/p=(1.02 0.044p)% Pt kick=120 MeV/c (t) = 1.4 ns
Charged hodoscope (t) = 200 ps
LKr electromagnetic calorimeter 27 X0 with 13212 2x2 cm2 cells (E)/E=(3.2/E 9.0/E 0.42)% (x)=(y)=0.42 /E 0.06 cm (t) = 265 ps
Muon Counters 2+1 planes 25x25 cm2 (t) = 350 ps
Mass resolutions
()= 1.7 MeV/c2 (0)=1.4 MeV/c2
9/3/2007 Silvia Goy Lopez HS07 7
Introduction to scattering lengths scattering amplitude can be expanded in partial
waves. Scattering lengths are parameters in the expansion
At low energies Swave dominates Due to Bose statistics only I=0,2 allowed Scattering lengths a0,a2 are the relevant parameters
describing interactions at low energies.
a0,a2
9/3/2007 Silvia Goy Lopez HS07 8
Introduction to scattering lengths Theory
Dispersion relations: based on causality and analiticity of scattering amplitude. Using scattering data at high energies a relation can be found a2=f(a0) Ej: UB from Roy eqn.
ChPT: a2=fChPT(a0). Predict a0 with ~2% error, related to size of condensate.
Recently lattice calculations.
Measurements Ke4 form factors ( variation
with M) GenevaSaclay (~30 103
evts) BNL E865 (~390 103 evts) NA48/2 (~677 103 evts)
Cusp effect (NA48/2) Pionium lifetime (DIRAC)
NA48/2 provides measurement from two independent channels, different theoretical inputs and different systematic effects
9/3/2007 Silvia Goy Lopez HS07 9
The K±e4 decay: Introduction
K
p*(e)
e
e
Direction of the total e+e
momentumin the K+
rest frame
Direction of the total momentum
in the K+
rest frame
p*()
Rare decay: Br(K±π+πe±ν )=(4.08±0.09) 105 (PDG06) Kinematic variables (Cabibbo – Maksymowicz )
Sπ (M2ππ) (related to q2)
Se (M2eν )
cos π
cos e related toscattering phases related to scattering lengths
9/3/2007 Silvia Goy Lopez HS07 10
The K±e4 decay: Introduction Form factors F,G,R (axial, R relevant only for K4 ) and H
(vector) determined by fitting the data distributions. Because of small values of s in Ke4 expansion restricted to
s&p waves. Fit Fs, Fp, Gp , Hp and = sp
Expanding in terms of q2 (S), Se
h
g
ps
ip
ip
ip
is
eHHeGG
eFeFF
cos
......
......4/
2'
2'
2'
24''2'
qhhHqggGqffF
mSfqfqffF
ppp
ppp
ppp
eessss
s : the scattering phase shift in the I = 0 , l = 0 state (s – wave) p : the scattering phase shift in the I = 1 , l =1 state
(p – wave)
9/3/2007 Silvia Goy Lopez HS07 11
The K±e4 decay: Selection Selection:
Three tracks, two opposite charged pions, one electron, missing energy and pt (separation /e given by LDA: linear discriminator analysis)
Background:  with e is dominant misidentified as electron 0) with Dalitz decay (ee) with e misid. as , and undetected
Estimation using MC and data (‘Wrong sign’ events) in agreement In data ‘Wrong sign’ events (e different sign than kaon) can be only due
to background. Scaling factor depending on process. Total background level 0.5%
9/3/2007 Silvia Goy Lopez HS07 12
The K±e4 decay: Reconstruction Reconstruction. Two approaches:
Use constrain given by to solve energymomentum conservation equations and get kaon momentum. Take solution closest to 60 GeV/c
Assume a 60 GeV/c kaon along the z axis, assign the missing pt to the and compute the resulting kaon invariant mass. Take events within ± 20 MeV/c2
Statistics: 2003 data sample, ~677500 events
PK(GeV/c) mK(GeV/c2)
9/3/2007 Silvia Goy Lopez HS07 13
The K±e4 decay: Fitting of form factors Define 10x5x5x5x12 isopopulated bins in (Mππ , Meν , cos π , cos e , ) The form factors are extracted from the data using simulated events by
minimizing a loglikehood estimator in each of the M bins: In each M bin the form factors are assumed to be constant 10 independent fits (one fit per M bin) of 4 parameters (Fp, Gp , Hp and )
plus free normalization (related to Fs) in 4D space. The correlation between the 4+1 parameters is taken into account. K+ and K fitted separately and combined.
Statistics Data MC
K+ evts 435654
29
10.0 M
667 Evts/bin
K evts 241856
16
5.6 M
373 Evts/bin
K+/K~1.8MC/Data ~23
9/3/2007 Silvia Goy Lopez HS07 14
The K±e4 decay: Kinematic Distributions Distribution of kinematic variables for data (symbols) and MC after fit
(hist.) Background distribution taken from data (hardly visible)
M(GeV)
Me(GeV)
radcos
cose
K+
K
distribution shown separately for K+ and K (CP symmetry )
9/3/2007 Silvia Goy Lopez HS07 15
The K±e4 decay: Kinematic Distributions: of the Ke4 decay
amplitude is extracted from the measured asymmetry of the distribution as a function of M
The asymmetry of the distribution increases with Mincreaing sensitivity to
0.309 < M < 0.318 GeV
0.335 < M < 0.345 GeV
0.373 GeV < M < mK
2m+ < M < 0.291 GeV
9/3/2007 Silvia Goy Lopez HS07 16
No absolute normalization available for the moment (no BR measurement) can only get relative form factors and variation with q2 and with Se (all results are given wrt to Fs(q=0) constant term)
F2s obtained from relative bin to bin normalization of Data/MC after fit Once q2 dependency is extracted residual Me variation can be observed A 2D fit (M, Me) is used to get the slopes of the Fs expansion
The K±e4 decay: Form Factors: F2s (normalization)
First measurement of f’’e≠0
9/3/2007 Silvia Goy Lopez HS07 17
The K±e4 decay: Form Factors: Fp,Gp, Hp Once the normalization variation has been deconvoluted can
extract variation of Fp,Gp and Hp with q2
First measurement of fp≠0
9/3/2007 Silvia Goy Lopez HS07 18
The K±e4 decay: Form Factors The spvariation with M was fitted using Universal Band (numerical solution of Roy
equations (A, Phys. Rep. 353 (2001) 207)
1 parameter function to extract a0 with a2=f(a0) in center of UB High sensitivity to scattering length due to good acceptance for high M
9/3/2007 Silvia Goy Lopez HS07 19
The K±e4 decay: Results Systematic checks
Two analysis with different reconstructions, acceptance corrections, fitting methods
Beam simulation (acceptance changes)
Background level Electron identification Radiative corrections Possible Se dependence Possible bin to bin
correlations investigated and taken into account
f’s/ fs = 0.165± 0.011stat ± 0.006syst
f’’s/ fs = 0.092± 0.011stat ± 0.007syst
f’e/ fs = 0.081± 0.011stat ± 0.008syst
fp/ fs = 0.048± 0.004stat ± 0.004syst
gp/ fs = 0.873± 0.013stat ± 0.012syst
g’p/ fs = 0.081± 0.022stat ± 0.014syst
hp/fs = 0.411± 0.019stat ± 0.007syst
NA48/2 Preliminary: 2003 data
First observation of f’e and fpAll form factors measured to 5 to 15% accuracyError dominated by statistics
9/3/2007 Silvia Goy Lopez HS07 20
The K±e4 decay: Results comparison points from
different experiments can be fitted together to the center of UB.
Value for a0 is lower than given by NA48 data alone
Mainly due to last point of BNL (under investigation)
Superposed are the predictions for vs M for a0=0.26 and a0=0.22
Fit to all experimental points
Predictions for a0=0.26 and a0=0.22
9/3/2007 Silvia Goy Lopez HS07 21
The K±e4 decay: Results comparison Different methods can
be used to relate measurements to a0,a2 Fit 1 parameter a0
with a2=f(a0) by Roy eqn.
Fit 1 parameter a0 with a2=f(a0) by ChPT
Fit 2 parameters a2,a0
NA48/2 and E865 favor slightly different regions of UB
9/3/2007 Silvia Goy Lopez HS07 22
The K±e4 decay: Results comparison Theory improvements
(Gasser): Measured has to be corrected by isospin symmetry breaking effects before extracting a0
After this correction (preliminary) a0 values are in good consistency with ChPT predictions
Using different methods a0 are in the range [0.209,0.255] ±0.006stat±0.005syst and values of a2 around 0.045
9/3/2007 Silvia Goy Lopez HS07 23
The K± π±π0π0 decay: Cusp effect 2003: Observation of sudden slope variation in the invariant mass
distribution seen at M002=(2m+)2 An unexpected discovery from the
NA48/2 Initial motivation for this study: use large statistics and good M00
2 resolution to try to detect + atom formation in K± → ± + decays, followed by pionium annihilation to
Standard Dalitz plot parameterization shows deficit in data before cuspStandard Dalitz plot parameterization
Whole region
2/ndf=9225/149!
Above cusp:
2/ndf=133/110
Data
FitData
Subsample of 2003
9/3/2007 Silvia Goy Lopez HS07 24
The K± π±π0π0 decay: Cusp effect Now 2003+80% of 2004 combined: 59,624,170 fully reconstructed K± →
±
4m+2 4m+
2
Zoom in cusp region
9/3/2007 Silvia Goy Lopez HS07 25
The K± π±π0π0 decay: Reconstruction Reconstruction:
At least 4 clusters 15 cm away from any track and 10 cm away from other clusters.
Among all the possible pairings, the couple for which 2 is smallest is selected
M002 computed using average vertex of two 0
m02 = 2EiEk(1cos) ≈ EiEk2 = EiEk (Dik)2/(zik)2
No physical background
LKr
z
dij
i
jZ(i,j)Z(k,l)
Vertex22
2
Km
K
z
mz
9/3/2007 Silvia Goy Lopez HS07 26
Cusp on K± π±π0π0. Checks for instrumental effects Good resolution near
cusp region Acceptance linear near
the cuspM00
2 reconstructed distributions for three generated values of M00
2 Acceptance
= 0.56 MeV at M00 = 4m+
9/3/2007 Silvia Goy Lopez HS07 27
Cusp on K± π±π0π0.Checks for instrumental effects DataMC comparisons above and below cusp MC simulation describes well the of detector efficiency
around cusp. Event deficit is real effect
9/3/2007 Silvia Goy Lopez HS07 28
Cusp on K± π±π0π0. Interpretation Two amplitudes contribute to K± π±π0π0
Direct emission Given by M0
Charge exchange (π+π π0π0)
in final state of K± π± π+π Given by M1 , proportional to M+
and to one extra parameter ax=(a0 a2) /3 in limit of exact isospin symmetry
These amplitudes interfere destructively below threshold Rescattering model at oneloop (C, PRL 93 (2004) 121801)
22
0 vk'2
1uh'
2
1gu
2
11M (k’ first observed
by NA48/2)
DE
CE
9/3/2007 Silvia Goy Lopez HS07 29
Cusp on K± π±π0π0. Interpretation More complete formulation of the
model includes all rescattering processes at oneloop and twoloop level (CI, JHEP 0503 (2005) 21) has been used to extract NA48/2 result. More parameters than just ax
Isospin correction applied in order to extract a0 and a2 from fits to data.
Theoretical uncertainty of ~ 5% but radiative corrections and threeloops can be computed to reach ~1%
9/3/2007 Silvia Goy Lopez HS07 30
Cusp on K± π±π0π0: Fitting procedure One dimensional fit to M00
2 distribution
MINUIT minimization of 2of data/MC spectra shapes
Fitting up to 0.097 (GeV/c2) Fits to 5 parameters: norm, g,
h’,a0 a2 and a2 () (k’ fixed) For final result 7 bins around
cusp excluded from the fit in order to reduce sensitivity to Coulomb corrections and pionium.
The excess of events in this region is interpreted as pionium signature (E.M. corrections?)
R=(K+A2)/(K+–) = (1.820.21)10–5 (th. prediction 0.8 10 5)
9/3/2007 Silvia Goy Lopez HS07 31
The K± π±π0π0 decay. Quadratic term Matrix element for DE (different from PDG
parameterization)
Technique: Consecutive 1Dfits in both data projections (a0,a2,g0,h’) measurement (fixed k’=0) [2003 data] k’ measurement (fixed a0,a2,g0,h’) [2003 data] (a0,a2,g0,h’) second iteration (fixed k’) [2004 data]
a0,a2 are not significantly affected by neglecting the k’v2 term, but g0,h’ are biased by g0=–1.5%, h=–1.2%
M0 ~ (1+g0u/2+h’u2/2+k’v2/2)
9/3/2007 Silvia Goy Lopez HS07 32
The K± π±π0π0 decay. Quadratic term Change of Dalitz variables, from (s3, s2s1 to (s3, cos
k’ = 0.0097 ± 0.0003stat ± 0.0008syst
NA48/2 Preliminary: 2003 data
Define asangle between π± and π0 in π0π0 COM
Fitting new Dalitz plot above cusp
DataMC comparison for cos for different k’ values
Change in value and meaning of g and h’ with respect to previous matrix element No change of a0a2 and a2
9/3/2007 Silvia Goy Lopez HS07 33
Cusp on K± π±π0π0. Results Systematic effects: analysis technique, acceptance
determination, trigger efficiency, resolution, fitting interval, electromagnetic shower simulation, vdependence of amplitude
g = 0.649 ± 0.003stat ± 0.004syst
h’ = 0.047 ± 0.007stat ± 0.005syst
k’ = 0.097 ± 0.003stat ± 0.008syst
First evidence of k≠0
9/3/2007 Silvia Goy Lopez HS07 34
Cusp on K± π±π0π0. Results
External uncertainty: from the uncertainty on the ratio of K+ → p+p+p and K+ → p+pp decay widths
Theoretical uncertainty on (a0 – a2): ± 5% (estimated effect from neglecting higher order diagrams and radiative corrections)
Fit imposing ChPT constrain between a0 and a2 (CGL, PRL 86 (2001) 5008)
From (a0 – a2) and a2 extract a0 (must take into account the statistical error correlation coefficient ≈ 0.92)
a0 a2 = 0.261 ± 0.006stat ± 0.003syst ± 0.0013ext ± 0.013th
a2 = 0.037 ± 0.013stat ± 0.009syst ± 0.002ext
a0 a2 = 0.263 ± 0.003stat ± 0.014syst ± 0.0013ext ± 0.013th
a0 = 0.224 ± 0.008stat ± 0.006syst ± 0.003ext ± 0.013th
9/3/2007 Silvia Goy Lopez HS07 35
Comparison Cusp and DIRAC DIRAC: Pionium
lifetime related to scattering lengths. Proportional to a0a22
The yellow area represents theoretical uncertainty (assumed Gaussian) Also dashed bars.
9/3/2007 Silvia Goy Lopez HS07 36
Comparison Cusp and Ke4 results.
9/3/2007 Silvia Goy Lopez HS07 37
Comparison Cusp and Ke4 results.
9/3/2007 Silvia Goy Lopez HS07 38
Summary and Conclusions NA48/2NA48/2 exploited two different procedure to measure the
scattering lengths. Ke4Ke4: the phase shift can be related to the a0 and a2 using
theoretical input (e.g. Roy equations) K→K→0000: the scattering lengths are extracted from the
study of rescattering contribution in the M00 mass distribution (the error is dominated by the theoretical error)
Applying the isosping breaking corrections the two results are fully compatible.
The results are compatible with the DIRAC experiment results and with ChPT predictions.
9/3/2007 Silvia Goy Lopez HS07 39
SPARES
9/3/2007 Silvia Goy Lopez HS07 40
Cusp on K± π±π0π0. Results NA48/2 results on partial sample of 2003 data (PLB 633 (2006)) Systematic effects: Acceptance determination, trigger efficiency, fitting
interval
Prediction for a2 in ChPT a2 = 0.0444 ± 0.0010 (CGL, PLB 488 (2000) 261) Prediction for a0a2 in ChPT a0 a2 = 0.265 ± 0.004 (CGL, PLB 488 (2000) 261)
using disper. rel. = 0.278 ± 0.016 (PY, PRD 71 (2005) 074016)
Fit imposing ChPT constrain between a0 and a2 (CGL, PRL 86 (2001) 5008)
g = 0.645 ± 0.004stat ± 0.009syst
h’ = 0.047 ± 0.012stat ± 0.011syst
a0 a2 = 0.261 ± 0.006stat ± 0.003syst ± 0.013ext ± 0.013th
a2 = 0.037 ± 0.013stat ± 0.009syst ± 0.002ext
a0 = 0.220 ± 0.006stat ± 0.004syst ± 0.011ext
a0 a2 = 0.263 ± 0.003stat ± 0.014syst ± 0.013ext ± 0.013th
9/3/2007 Silvia Goy Lopez HS07 41
The K±e4 decay: Results before Isospin symmetry breaking corrections
a0 (UB)= 0.256± 0.008stat ± 0.007syst ± 0.018th
a2 = 0.031± 0.015stat ± 0.015syst ± 0.019th
NA48/2 Preliminary: PARTIAL Sub sample 2003 data
Prediction for a0 in ChPT a0= 0.220 ± 0.005 (CGL, PLB 488 (2000) 261)
9/3/2007 Silvia Goy Lopez HS07 42
Summary and conclusions Pion scattering lenghts have been measured
in NA48/2 with two independent channels: From K±e4
From cusp on K± π±π0π0
But with different theoretical frameworks!
Form factors for K±e4 and K± π±π0π0 have been measured Non zero quadratic term in K± π±π0π0 k’ = 0.0097 ± 0.0003stat ± 0.0008syst
a0 (UB)= 0.256± 0.008stat ± 0.007syst ± 0.018th
a0 a2 = 0.268 ± 0.010stat ± 0.004syst ± 0.013ext
For comparison evaluation of a0 for previous experiments using center of UB:
Geneva Saclay: a0(UB) = 0.253 ± 0.037 (stat+syst)
± 0.014 th
E865: a0 (UB) = 0.229 ± 0.012stat ±
0.004syst ± 0.014 th
9/3/2007 Silvia Goy Lopez HS07 43
E. Goudzovski / Frascati, May 22E. Goudzovski / Frascati, May 22thth, 2007, 2007
Results: Dalitz plot slopesResults: Dalitz plot slopes
Technique: consecutive 1Dfits in both data projections. 1. (a0,a2,g0,h’) measurement (fixed k’=0) [2003 data] 2. k’ measurement (fixed a0,a2,g0,h’) [2003 data] 3. (a0,a2,g0,h’) second iteration (fixed k’) [2004 data]
M(K00) = M0 + M1
M0 ~ (1+g0u/2+h’u2/2+k’v2/2)
g = ( 64.9 0.3stat. 0.4syst. )%h’ = ( –4.7 0.7stat. 0.5syst. )%k’ = ( –0.97 0.03stat. 0.08syst. )%
(preliminary)
M02(PDG) ~ (1+gu+hu2+kv2) [g0g, h’h–g2/4,
k’k]
NB: not the same parameterization as the PDG one:
(a0,a2 are not significantly affected by neglecting the k’v2 term,but g0,h’ are biased by g0=–1.5%, h=–1.2%)
(in reality, 2D fits involved at step 2)
NA48/2 result:
9/3/2007 Silvia Goy Lopez HS07 44
(a0 – a2)m+ = 0.261 ± 0.006 ± 0.003 ± 0.0013 ± 0.013 (stat.) (syst.) (ext.) (theor.)
a2m+ = 0.037 ± 0.013 ± 0.009 ± 0.002(the sensitivity to a2 comes from higherorder terms)
Fit results:
Theoretical uncertainty on (a0 – a2)m+: ± 5%
(estimated effect from neglecting higher order diagrams and radiative corrections)
External uncertainty: from the uncertainty on the ratio of K → and K → decay widths:
giving at the Dalitz plot centres (u = v = 0)
015.0975.1)(
)(00
KA
KA
047.0182.3)(
)(00
K
K (PDG 2006)
(exact isospin symmetry predicts 2)
Fit with analiticity and chiral symmetry constraint between a0 and a2 (Colangelo, Gasser, Leutwyler, PRL 86 (2001) 5008)
(a0 – a2)m+ = 0.263 ± 0.003 ± 0.0014 ± 0.0013 ± 0.013 (stat.) (syst.) (ext.) (theor.)
9/3/2007 Silvia Goy Lopez HS07 45
GOOD AGREEMENT WITH THE RESULT OF THE DIRAC EXPERIMENT
s 10)91.2( 1524.0
43.01
s
020.0
011.020264.0
maa
NA48/2 : (a0 – a2)m+ = 0.261 ± 0.006 ± 0.003 ± 0.0013 ± 0.013 stat. syst. ext. theor.
Pionium mean lifetime
9/3/2007 Silvia Goy Lopez HS07 46
Correlations PARAMETER CORRELATION
COEFFICIENTS for the normalisation fit fs' 1.000 0.955 0.085 fs" 0.955 1.000 0.015 fe 0.085 0.015 1.000 which gives ,once reduced to 2 significant digits :
0.96 0.08 0.02
Including fe almost do not alter the value of the other parameters, very little correlation.
For gp(0)&g’p = 0.914
9/3/2007 Silvia Goy Lopez HS07 47
KL → 87,950,601 events (NA48)
(3 entries per event)
1 entryper event
4m+2
CUSP STRUCTUREMUCH LESS VISIBLE
THAN IN K±→ ± DECAY
9/3/2007 Silvia Goy Lopez HS07 48
K+ → + , KL→ comparison
00
2
00
002
)(
2)(
MM
MMM
R K
two possible pairs
000
0
2
000
0000
)()(
MM
MMM
R LK
Calculate matrix elements at cusp point (M = 2m+)
from measured partial width ratios and slope parameters:
R(K+) ≈ 6.1 ; R(KL) ≈ 0.47R(K+)
R(KL)≈ 13
Cusp “visibility” is ~ 13 times higher in K+ → + decaysthan in KL → decays
M:K→ matrix element
M:K→ matrix element
M:KL→ matrix element
M:KL→ matrix element