Measurement of FCNC decays
K±→π±l+l– by NA48/2 at CERN
Evgueni Goudzovski(University of Birmingham)

on behalf of the NA48/2 collaboration(Cambridge, CERN, Chicago, Dubna, Edinburgh, Ferrara, Florence, Mainz,Northwestern, Perugia, Pisa, Saclay, Siegen, Turin, Vienna)

Outline:1) Beams, detector and data taking in 2003/04;
2) K±→π±e+e− analysis: NA48/2 final results;
3) K±→π±μ+μ– analysis: analysis status and prospects;4) Summary.

Kaon 2009 conference
Tsukuba, Japan • June 9, 2008

1NA48/NA62 experiments
1997: ε’/ε run KL+KS
1998: KL+KS

NA48

NA48/1
NA48/2

1999: KL+KS

KS HI

2000: KL onlyKS HI

2001: KL+KS

KS HI

2002: KS/hyperons HI

NA48/NA62: a series of experiments,present-day CERN kaon physics programme
The presented results are based on 2003/04 data

Jura mountains
France2003: K+/K–

NA48/NA62
2004: K+/K–

SPS

NA62

(phase I)

NA62(phase II)

2007: K±e2/K±μ2

tests

2008: K±e2/K±μ2

tests

2006–2010:
design & construction
2011:
start of K+→π+νν run

E. Goudzovski / Kaon09, 9 June 2009

LHCSwitzerland

Geneva airport2NKaon momentumspectrum

2-3M K/spill (π/K~10),
π decay products stay in pipe.
Flux ratio: K+/K– ≈ 1.8

PK spectra,
60±3 GeV/c5460

NA48/2: kaon beam line
Simultaneous K+ and K− beams:
large charge symmetrization ofexperimental conditions
magnet66

K+
K+
Be targetK−~7⋅1011 ppp,
400 GeVBMbeam pipe

K−

Front-end
achromat• Momentum
selectionz

focusing beams

Secondachromat• Cleaning
Quadrupole • Beam spectrometer
quadruplet(momentumresolution ~0.7%)• Focusing• μ sweepingBeams coincide within ~1mm
all along 114m decay volumevacuumtank

1cm
E. Goudzovski / Kaon09, 9 June 2009

He tank+ spectrometer10 cm

not to scale

50100200

3250 mThe NA48 detector
Main detector components:• Magnetic spectrometer (4 DCHs):
4 views/DCH: redundancy ⇒efficiency;
used in trigger logic;
Δp/p = 1.0% + 0.044%*p [GeV/c].
• Hodoscope
fast trigger;
precise track time measurement (150ps).
• Liquid Krypton EM calorimeter (LKr)
Beam pipe
High granularity, quasi-homogenious;
σE/E = 3.2%/E1/2 + 9%/E + 0.42% [GeV];σx=σy=0.42/E1/2 + 0.6mm (1.5mm@10GeV).
Used for γ detection and particle ID.
• Hadron calorimeter, muon veto counters,photon vetoes.
E. Goudzovski / Kaon09, 9 June 2009

He filled tank@atmospheric pressure

K± beams

4

NA48/2 data taking: completed
A view of the NA48/2 beam line

2003 run: ~ 50 days
2004 run: ~ 60 days
K3π statistics in 2 years:
K± → π−π+π±: ~4·109
K± → π0π0π±: ~1·108
Rare K± decays:
BRs down to 10–9
can be measured>200 TB of data recorded
5E. Goudzovski / Kaon09, 9 June 2009

Kπll: motivation & theory
K± → π±γ* → π±l+l–: suppressed FCNC processproceeding through single virtual photon exchange.
Information on weak interactions at low energy.

dΓπee/dz ~ P(z)·|W(z)|2 z=(Mee/MK)2, P(z) is a phase space factor
Considered models for the form factor:(1) polynomial:W(z) = GFMK2·f0·(1+δz)
W(z) = GFMK2·(a++b+z) + Wππ(z)(2) ChPT O(p6):
G. D’Ambrosio et al., JHEP 9808 (1998) 4(3) ChPT, large-Nc QCD: W(z) = W(w, β, z)

S. Friot, D. Greynat, E. de Rafael, PLB 595 (2004) 301(4) “Mesonic” ChPT:

W(z) = W(Ma, Mρ, z)

A.Z. Dubnickova et al., Phys. Part. Nucl. Lett. 5 (2008) 76 [hep-ph/0611175]

Goals: 1) dΓ/dz and model-independent BR in kinematic range z>0.08;
2) parameters of the models + BRs in the full kinematic range;3) upper limit for CPV charge asymmetry of decay rates.
6
E. Goudzovski / Kaon09, 9 June 2009

Principal selection criteria
The K±→π±e+e– is measured normalizing to K±→π±π0D→π±e+e–γ.
Thus particle ID efficiencies cancel in the first order.
Common selection criteria:
3-track vertex [consistent in space/time],
one π candidate, two opposite sign electron candidates.
Electron (pion) ID based on E deposition : E/p>0.95 (E/p<0.85).
Signal selection:
Kinematic suppression of π±π0D
background: Mee>140MeV/c2.
Limitations on reconstructed
π±e+e– invariant mass,
total & transverse momentum

Normalization selection:
Selection of good γ candidate.
Limitations on reconstructede+e–γ and π±e+e–γ masses,
total & transverse momentum.
7E. Goudzovski / Kaon09, 9 June 2009

Signal & normalisation samples
700

K±→π±e+e–DataMC

EventsEventsTotal kaon decays in fiducial volume (2003+2004): NK=1.7×1011
106105Data

K±→π±π0D

600500104400300

10200

Radiative tailsimulation: Photos

10000.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53M(π±e+e-), GeV/c27253 candidates

Background/Signal = 1.0%(K±→π±π0D, K±→π0De±ν + particle misID,
two e+e– pairs: π0D(D), γ conversions).

Subtracted with same-sign lepton candidates.

3102

K μ3D0.42

K 2πD

0.44

0.46

0.48

0.5

0.52 0.54 0.56M(π±π0D), GeV/c212.12 mln candidates

Background/Signal = 0.15%(K±→π0Dμ±ν, subtracted with simulation)
8E. Goudzovski / Kaon09, 9 June 2009

The accessible Mee region
All analysis cuts except the Mee cut are appliedh20102

201287
Entries 9796
0.09448
Mean 0.1255
0.04283

Normal and same-sign events

gg

Entries
MeanRMS

Analysis cut:z>0.08, or Mee>140MeV/c2

800
700

900

K±→π±π0DD subtracted

800700K±→π±π0D600

191491
0.09209
0.04346

normal – 2×(same-sign)

RMS 0.01496

900600500

5002×(same-sign events):
K±→π±π0DD process

400300200K±→π±e+e– (7.3K)

10000.05

hEntries
MeanRMS

Mee

0.1

0.15

0.2

0.25

0.3

0.35

Mee, GeV/c2

400300π0→e+e– peak (~0.5K):
BR=0.6×10–7200
10000.05

0.1

0.15

0.2

0.25

0.3

0.35

Mee, GeV/c2• The region Mee<140MeV/c2 is dominated by background and not accessible;• Subtraction of the K±→π±π0DD reveals the π0→e+e– signal (~500 events).
9E. Goudzovski / Kaon09, 9 June 2009

Eventsz=(Mee/MK)2600

EventsKinematic variables: (z, cosθeπ)
300

500

250

400

200

300

150

200

100

1000

Background ×5M(2π)

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
zz distribution is sensitive to the form-factor
and contains the dynamical information:dΓ/dz ~ P(z) × |W(z)|2.

DataMCcosθeπ

500-1 -0.8 -0.6 -0.4 -0.2 00.2 0.4 0.6 0.8 1cosθeπDecay via one photon exchange:dΓ/dθ ~ sin2θ = (1–cos2θ),θ = angle between (e+,π) in (e+,e–) frame.
No dynamical information in this projection.

10E. Goudzovski / Kaon09, 9 June 2009

Fit results (1)dΓ/dz, GeV/c 2

×10-24(4)
60 (2)(3)50

Model parameterswith their statistical errors
and correlation coefficients:

Measured dΓ/dz
The models can not be distinguishedwith the available data set

(1)

(1)

f0 = 0.531±0.012
δ = 2.32±0.15
ρ(δ, f0) = –0.962(2)

a+ = –0.578±0.012
b+ = –0.779±0.053
ρ(a+, b+) = –0.913(3)w = 0.057±0.005
β = 3.45±0.24
ρ(w, β) = 0.999

4030
20
10

Model (1): χ2/ndf=22.7/19
Model (2): χ2/ndf=32.1/19
Model (3): χ2/ndf=27.7/19
Model (4): χ2/ndf=36.9/19

00 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5z (4)Model-independent BR (integral of dΓ/dz):
BRmi(z>0.08)=(2.28±0.03)×10–7

E. Goudzovski / Kaon09, 9 June 2009

Ma = (0.951±0.028) GeVMρ = (0.705±0.010) GeV
ρ(Ma, Mρ) = 0.998
11Fit results (2)|W(z)|2 / |W(0)|2Squared form factors
normalised by |W(0)|2=1
4.5
4(2)

3.5
3(1)

(4)

2.5
2(3)

1.5
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5z
E. Goudzovski / Kaon09, 9 June 200912

2.7(|f0|, δ)

2.6

Fit results (3)-0.65(a+, b+)-0.7
2.5

68% CL
contours

-0.75

2.4
2.3

-0.8

2.2-0.85
2.1
20.5
4
3.9

0.51 0.52

0.53

0.54

0.55

(w, β)

-0.9
-0.6
0.56
0.74

-0.59

-0.58

-0.57

-0.56

-0.55

(Ma, Mρ)
0.73

3.8
3.7

0.72

3.6
3.5

0.71

3.4
3.3

0.7

3.2
3.1
3
0.045

0.05

0.055

0.06

0.065

0.69
0.07 0.92 0.94

13
0.96

0.98

1

1.02

1.04

Fit results (4)BRmi×107 =2.28 ±
f0 = 0.531 ±δ=
2.32 ±
BR1×107 =3.05 ±
a+ = –0.578 ±b+ = –0.779 ±BR2×107 =3.14 ±
w = 0.057 ±β=3.45 ±
BR3×107 =3.13 ±
Ma = 0.974 ±Mρ = 0.716 ±BR4×107 =3.18 ±

0.03stat ± 0.04syst ±0.012stat ± 0.008syst ±0.15stat ± 0.09syst
0.04stat ± 0.05syst ±0.012stat ± 0.008syst ±0.053stat ± 0.036syst ±0.04stat ± 0.05syst ±0.005stat ± 0.004syst ±0.24stat ± 0.17syst ±0.04stat ± 0.05syst ±0.030stat ± 0.019syst ±0.011stat ± 0.007syst ±0.04stat ± 0.05syst ±2.28 ± 0.08
0.06ext =0.007ext = 0.531 ± 0.016=
2.32 ± 0.18
3.05 ± 0.10
0.08ext =0.007ext = –0.578 ± 0.016
0.017ext = –0.779 ± 0.066
3.14 ± 0.100.08ext =0.001ext = 0.057 ± 0.007
3.45 ± 0.300.05ext =3.13 ± 0.100.08ext =0.002ext = 0.974 ± 0.035 [GeV/c]
0.002ext = 0.716 ± 0.014 [GeV/c]
3.18 ± 0.100.08ext =Including uncertainty due to the model dependence,

BR = (3.11±0.04stat±0.05syst±0.08ext± 0.07model)×10–7 = (3.11±0.12)×10–7
CPV parameter (first measurement; only uncorrelated K+/K– uncertainties):

Δ(K±πee) = (BR+–BR–) / (BR++BR–) = (–2.1±1.5stat±0.6syst)×10–2
E. Goudzovski / Kaon09, 9 June 200914

Comparison: FF slope δMeasurement

Process

ResultAlliegro et al., PRL 68 (1992) 278

K+→π+e+e–1.31±0.48

Appel et al. [E865], PRL 83 (1999) 4482

K+→π+e+e–2.14±0.20

Ma et al. [E865], PRL 84 (2000) 2580

K+→π+μ+μ–2.45+1.30–0.95

NA48/2, arXiv:0903:3130 (2009)

K±→π±e+e–2.32±0.18

χ2 / ndfδ

3.5p04.288 / 32.193 ± 0.1277

3NA48/22.5Æ A contradiction of the data to the meson
dominance models observed earlier isfurther confirmed;

new WA

21.51‘92

Æ NA48/2 measurement of δ is compatible
with the earlier results, has good precision;

‘99

‘00

‘08

VMD models [PRD60 (1999) 053007]

0.5Measurements
0 0.5 1 1.5 2 2.5 3 3.5
4 4.5 5
E. Goudzovski / Kaon09, 9 June 2009

Æ NA48/2 values of (f0,a+,b+,w, β) are inagreement with BNL E865 ones.
15

Comparison: BR in full z range
MeasurementSample

BR×107

Bloch et al., PL 56 (1975) B20141 (K+)

2.70±0.50

Alliegro et al., PRL 68 (1992) 278500 (K+)

2.75±0.26

Appel et al. [E865], PRL 83 (1999) 4482

10,300 (K+)

2.94±0.15

NA48/2, arXiv:0903:3130 (2009)

7,300 (K±)

3.11±0.12

3.6
3.4
3.2
3
2.8
2.6
2.4

2.259 / 33.001 ± 0.08676

p0

NA48/2

New “naïve” WA

BR×107

χ2 / ndf

‘75

‘92

‘99

‘08

2.2
20 0.5 1 1.5 2 2.5 3 Measurements
3.5 4 4.5 5
E. Goudzovski / Kaon09, 9 June 2009

Comparison of E865 vs NA48/2 results
taking into account correlated uncertainties(normalization and model dependence):
1.6σ difference.
The NA48/2 results are final and published:
CERN-PH-EP-2009-005, arXiv:0903:3130,
accepted by Physics Letters B.
16Events

π ±μ+ μ–106105Data

EventsK±→π±μ+μ– analysis (1)106105104104

31010210210MC Kπμμ101110-10.4

0.42

0.44

0.460.48

Data

310MC K3π

Same-sign muon candidates-10.5 0.52 0.54 100.4M(π±μ +μ -), GeV/c2MC K3π0.420.440.460.480.5 0.52 0.54M(π±μ +μ -), GeV/c2

NA48/2: N=3,100 K±→π±μ+μ– candidates with 3% background.
Background well described by both K3π MC and same-sign muon samples.
Cf. total world sample is ~700 events.
17
E. Goudzovski / Kaon09, 9 June 2009

K±→π±μ+μ– analysis (2)×10-24

Eventsz=(Mee/MK)2400

Measured dΓ/dz

25350

Fit to a linear FF

300

20250
15200
150
1005010Backgroundevaluated with SS events

0 0.2

0.25

0.3

0.35

50.4

0.45

00.5

0.2

0.25

0.3

0.35

0.40.450.5z

Analysis is well advanced,we aim to present the preliminary results in 2009.
E. Goudzovski / Kaon09, 9 June 200918

SummaryPrecise study of the K±→π±e+e– decay (BR~3×10–7):
Æ sample & precision comparable to world’s best ones;Æ (BR, FF) agree to theory and earlier measurements;
Æ first limit on the CPV charge asymmetry obtained;Æ final results published recently.
Precise study of the K±→π±μ+μ– decay (BR~0.8×10–7):
Æ NA48/2 sample ~4 times larger than total world sample;
Æ background is low and under control;
Æ aim at preliminary results in 2009 – stay tuned!
19

E. Goudzovski / Kaon09, 9 June 2009