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

Measurements of K±π+π-e±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

Summary and Conclusions

Overview

K±π+π-e±ν (Ke4) decay Introduction Selection, reconstruction Form factor and ππ scattering

length measurements

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 Introduction to scattering lengths


Introduction NA48: 1997-2000. DCPV in neutral K

Re(/ ) = (14.7 2.2) 10-4

NA48/1: 2002. Rare Ks decays Br(Ks 0ee-)=(5.8+2.8

-2.3 ± 0.8) 10-9

Br(Ks 0 -)=(2.8+1.5-1.2 ± 0.2) 10-9

NA48/2: 2003-2004. DCPV in K 3 Ag=(-1.5+1.5Ag=(-1.5+1.5statstat+0.9+0.9trigtrig+1.1+1.1systsyst))··1010-4-4

AgAg00=(1.8+1.7=(1.8+1.7statstat+0.5+0.5systsyst))··1010-4-4

In addition many results on rare kaon decays and on hyperon decays.

NA62 K + ->. Test beam in 2006, 2007. Ke2/K2 in 2007


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+π-e±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


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


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


Introduction to scattering lengths scattering amplitude can be expanded in partial

waves. Scattering lengths are parameters in the expansion

At low energies S-wave 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


Introduction to scattering lengths Theory

Dispersion relations: based on causality and analiticity of scattering amplitude. Using scattering data at intermediate 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) Geneva-Saclay (~30 103

evts) BNL E865 (~390 103 evts) NA48/2 (~677 103 evts)

Cusp effect (NA48/2) Pionium lifetime (DIRAC)

Prediction for a0-a2 in ChPT a0 -a2 = 0.265 ± 0.004, a0=0.220 ± 0.005 (CGL, PLB 488 (2000) 261)

ej using disper. rel. = 0.278 ± 0.016, a0=0.230 ± 0.015 (PY, PRD 71 (2005) 074016)

NA48/2 provides measurement from two independent channels


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+π-e±ν )=(4.08±0.09) 10-5 (PDG06) Kinematic variables (Cabibbo – Maksymowicz )

Sπ (M2ππ) (related to q2)

Se (M2eν )

cos π

cos e related toscattering phases related to scattering lengths


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 = s-p

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)


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%


The K±e4 decay: Reconstruction Reconstruction. Two approaches:

Use constrain given by to solve energy-momentum 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)


The K±e4 decay: Fitting of form factors Define 10x5x5x5x12 iso-populated bins in (Mππ , Meν , cos π , cos e , ) The form factors are extracted from the data using simulated events by

minimizing a log-likehood 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


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 )


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


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


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


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


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


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


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


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


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


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


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(1-cos) ≈ 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


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+


Cusp on K± π±π0π0.Checks for instrumental effects Data-MC comparisons above and below cusp MC simulation describes well the of detector efficiency

around cusp. Event deficit is real effect


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 one-loop (C, PRL 93 (2004) 121801)

22

0 vk'2

1uh'

2

1gu

2

11M (k’ first observed

by NA48/2)

DE

CE


Cusp on K± π±π0π0. Interpretation More complete formulation of the

model includes all re-scattering processes at one-loop and two-loop 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 three-loops can be computed to reach ~1%


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)


The K± π±π0π0 decay. Quadratic term Matrix element for DE (different from PDG

parameterization)

Technique: Consecutive 1D-fits 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)


The K± π±π0π0 decay. Quadratic term Change of Dalitz variables, from (s3, s2-s1 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

Data-MC 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 a0-a2 and a2


Cusp on K± π±π0π0. Results Systematic effects: analysis technique, acceptance

determination, trigger efficiency, resolution, fitting interval, electromagnetic shower simulation, v-dependence 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


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 = 0.224 ± 0.008stat ± 0.006syst ± 0.003ext ± 0.013th


Comparison Cusp and DIRAC DIRAC: Pionium lifetime

related to scattering lengths. Proportional to |a0-a2|2

The yellow area represents theoretical uncertainty (assumed Gaussian) Also dashed bars.

020.0

011.020264.0

maa


Comparison Cusp and Ke4 results.


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.


SPARES


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 a0-a2 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


a2 = -0.037 ± 0.013stat ± 0.009syst ± 0.002ext

a0 = 0.220 ± 0.006stat ± 0.004syst ± 0.011ext



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)


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


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


1 entryper event

4m+2

CUSP STRUCTUREMUCH LESS VISIBLE

THAN IN K±→ ± DECAY

87,950,601 events (3 entries per event)

Cusp in KL →


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

K+ → + , KL→ comparison


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

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.