Highlights on rare kaon decays from NA48/2 Monica Pepe INFN Perugia on behalf of the NA48/2 Collaboration Cambridge, CERN, Chicago, Dubna, Edinburgh, Ferrara,

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


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


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


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)


1. The decay K± Results based on a sub-sample of 2003

data (~30 % of all)


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*


W distributions for IB, DE, INT

IB and DE contributions are well separated in W

IB INTDE


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)%


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


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


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


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)


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


•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


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


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


2. K± e±K+-

e4Preliminary results based on 30 days in 2003


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


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 +....


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


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:


Results: F, G, H

No overall normalization from Branching Ratio quote relative form factors

Preliminary

Se (M2e) dependence measurement consistent

with 0


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


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


3. K± e±K00

e4Preliminary results based on 2003+2004 data


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


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


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


4. Cusp effect in

Results based on 2003 data – Phys. Lett. B633 (2006)


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)


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 .......)


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:


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

Documents

Highlights on rare kaon decays from NA48/2 Monica Pepe INFN Perugia on behalf of the NA48/2 Collaboration Cambridge, CERN, Chicago, Dubna, Edinburgh, Ferrara,