measurement of pp scattering lengths in kaon decays by na48/2

1

Measurement of Measurement of scattering lengths in Kaon scattering lengths in Kaon

decays by NA48/2decays by NA48/2EPS-HEP 2007

Manchester 19-25 july 2007

Gianluca LamannaGianluca Lamanna (Università & INFN di Pisa)(Università & INFN di Pisa)

on behalf of NA48/2 collaborationon behalf of NA48/2 collaboration

2 Gianluca Lamanna – HEP07 19.07.2007

OutlineOutline Introduction

Ke4 (K±→ e±)

Form factors and pion scattering lengths

Data 2003: Preliminary results

Cusp (in K±→±)

A new method to extract pion scattering lengths through the strong rescattering process →

Data 2003+2004: Preliminary results

Conclusions


Experimental setup:The BeamsExperimental setup:The Beams

K+

K−

BM

PK spectra, 603 GeV/c

54 60 66

Width ~ 5mm

K+/K- ~ 1mm

SPS protons @ 400 GeV

Simultaneus, unseparated, focused beams


NA48/2 detectorNA48/2 detectorSpectrometer:Spectrometer:

σσpp/p = 1.0% + 0.044% p [p in /p = 1.0% + 0.044% p [p in GeV/GeV/cc]]

LKR calorimeter:LKR calorimeter:

σσEE/E = 3.2%/√E + 9%/E + 0.42% [E /E = 3.2%/√E + 9%/E + 0.42% [E in GeV]in GeV]

CHODCHOD, , HACHAC,,MUVMUV,, vetos vetos

KabesKabes

Beam MonitorBeam Monitor

Only the spectrometer and LKr are involved in the analysis.

The CHOD is used at the trigger level.


NA48/2 data & resultsNA48/2 data & results

20032003 run: run: ~ 50 days~ 50 days

20042004 run: run: ~ 60 days~ 60 days

Total statisticsTotal statistics 2 years: 2 years:

KK±±→→±±0000: : ~1·10~1·1088

KK±±→→±±++--:: ~3·10~3·1099

Greatest amount ofGreatest amount of KK→3 →3 everever collectedcollected

u

v Beam Beam PipePipe

The main goal of NA48/2 was to measure the CP violationCP violation in charged kaon decays through the study of the asymmetry in three pion decays

The goal to reach a precision of 10-4 in the CP violation parameters Ag has been obtained after 2 years of data taking (2003 and 2004)

No signal of CP violation outside the SM at our level of precision

AAgg=(-=(-1.5+1.51.5+1.5statstat+0.9+0.9trigtrig+1.1+1.1systsyst))··1010-4-4

AAgg00=(1.8+1.7=(1.8+1.7statstat+0.5+0.5systsyst))··1010-4-4

AAgg=(-=(-1.5+1.51.5+1.5statstat+0.9+0.9trigtrig+1.1+1.1systsyst))··1010-4-4

AAgg00=(1.8+1.7=(1.8+1.7statstat+0.5+0.5systsyst))··1010-4-4Phys.Lett.B 634:474-Phys.Lett.B 634:474-

482,2006 Phys.Lett.B 482,2006 Phys.Lett.B 638:22-29,2006 638:22-29,2006 CERN-PH-EP-2007-021CERN-PH-EP-2007-021


KKe4e4: formalism: formalism The Ke4 dynamics is fully described

by 5 (Cabibbo-Maksymovicz) variables: MM

22, M, Mee22, cos, cos, cos, cosee and and

In the partial wave expansion the amplitude can be written using 2 axial and 1 vector form factors (the axial form factor R is suppressed in Ke4 but accessible in K4):

F=Fseis+Fpeipcos

G=Gpeip

H=Hpeip

The form factors can be expansed as a function of M

2 and Me2:

F (Fp,Fs), G, H and =p-s will be used as fit parameters

Fs=fs+fs’q2+fs’’q4+fe’(Me2/4m

2)+...

Fp=fp+fp’q2+...

Gp=gp+gp’q2+...

Hp=hp+hp’q2+...q2=(M

2/4m2)-1


KKe4e4: selection & background: selection & backgroundSelection:Selection:

3 tracks

Missing energy and missing Pt

LKr/DCH energy to

electron PID 677500 decays

The background is studied using the electron “wrong” sign events (we assume Q=S and total charge ±1) and cross check with MC. The total bkg is at level of 0.5%.

Main background sources:Main background sources:

+ →e

with misidentified

or +(Dalitz) +e misidentified and s outside the LKr

e

K

Kaon momentum

GeV/c


KKe4e4: Fitting procedure: Fitting procedure The form factors (F,G,H and ) are extracted minimizing a log-likehood estimator in

each of 10(M)x5(Me)x5(cose)x5(cos)x12()=15000 equi-populated bins. In each bin the correlation between the 4+1 parameters is taken into account.

Data MC

K+ evts 43565429

10.0 M667

Evts/bin

K- evts 24185616

5.6 M373

Evts/bin

The form factors structure is studied in 10 bins of M, assuming constant form factors in each bins

A 2D fit (M, Me) is used to study the Fs expansion

All the results are given wrt to Fs(q=0) constant term, due to the unspecified overall normalization (BR is not measured)

M

● Data

▬ MC


KKe4e4: Fitting procedure and results: Fitting procedure and results

Fp(q

2)

Fs(q

2)

Gp

(q2)

Hp(q

2)

Fs is quadratic in q2 First measurement of Fp≠0

Linear in q2 No linear term (hp’)


KKe4e4: form factors result: form factors result

f’s/fs = 0.165±0.011±0.006

f’’s/fs= -0.092±0.011±0.007

f’e/fs = 0.081±0.011±0.008

fp/fs = -0.048±0.004±0.004

gp/fs = 0.873±0.013±0.012

g’p/fs = 0.081±0.022±0.014

hp/fs = -0.411±0.019±0.007

f’s/fs = 0.165±0.011±0.006

f’’s/fs= -0.092±0.011±0.007

f’e/fs = 0.081±0.011±0.008

fp/fs = -0.048±0.004±0.004

gp/fs = 0.873±0.013±0.012

g’p/fs = 0.081±0.022±0.014

hp/fs = -0.411±0.019±0.007 All the Form factors are measured

relatively to fs

first evidence of fp≠0 and fe’≠0

The f.f. are measured at level of <5% of precision while the slopes at ~15% (factor 2 or 3 improvement wrt previous measurements)

Separately measured on K+ and K- and then combined (different statistical error)

Systematics checks:Systematics checks:

Acceptance

Background

PID

Radiative corrections

Evaluation of the sensitivity of the form factors on the Medependence of the normalization

Prelimina

ry (2003

data)


KKe4e4:: dependence dependence The extraction of the pion scattering lengths from the =s-p phase shift needs

external theoretical and experimental data inputs .

The Roy equations, for instance, provide this relation between and a0,a2 near threshold, extrapolating from the M>0.8 GeV region. The precision of these data defines the width of the Universal Band in the (a0,a2) plane.

The fit of the experimental points using the Roy equations in the universal band allows to extract the a0 and a2 values


KKe4e4: (a: (a00,a,a22) plane: result and comparison) plane: result and comparison

Minimizing the 2 in the 2D fit it’s possible to identify the favoured solution (and the corresponding ellipse)

The E865 and NA48/2 results agreement is marginal (manly due to the last point in E865) (work ongoing (see Gasser talk at Kaon07) )

The correlation between a0 and a2 is ~96% (similar for both experiment)


KKe4e4: “neutral”: “neutral”Selection:Selection: one electron track in the DCH , 4 photons in the LKr, 0 mass constraints, missing Pt. 9642 events in 2003 (previous exp. 216 events) ~30000 events in 2004

Background:Background: with a misidentified , ke3+1 accidental ~ 3% in 2003 (276 events) ~ 2% in 2004

Due to the symmetry only the s-wave is present (fs’, fs’’)

f’e has been measured consistent with 0 within the present statistics

BR(Ke400)prel=

(2.587±0.026stat±0.019syst±0.029ext)·10-5

f’s/fs=0.129±0.036±0.020

f’’s/fs=-0.040±0.034±0.020

f’s/fs=0.129±0.036±0.020

f’’s/fs=-0.040±0.034±0.020

Preliminar

y


Cusp: KCusp: K±±→→±± selection selection Offline selectionOffline selection: among all the possible pairings, the

couple for which is smallest is selected

The K-decay vertex is the average between the two decay vertices

After associating a charged track to the 2 0s the compatibility with the PDG kaon mass is requested to be ± 6 MeV.

2

0

1ijjiij dEE

mZ

++0000 invariant mass, GeV/c invariant mass, GeV/c22

Resolution: 0.9 MeV/c2

MKPDG ± 6 MeV/c2

cut

contribution

LKr

z

dij

i

jZ(i,j)Z(k,l)

Vertex

22

2

Km

K

z

mz


Cusp: Dalitz plot distributionCusp: Dalitz plot distribution The high statistics and the good

resolution allow to see a “cusp” in the U (or M2

) distribution in the position of 2m

16.0 M events in 2003 + 43.6 M events in 2004 data taking

~65% of the whole statistics

M2

M2


Cusp: one loop rescatteringCusp: one loop rescattering

M

K±

±

=M0

K±

±

+M1

K±

±

+-

24 ms ||)(|| 2

12

02 MMM

24 ms 10

21

20

2 2)()(|| MMMMM

The M1 contribution is real below and immaginary above threshold

M0 = A0(1+g0u/2+h’u2/2+k’v2/2)

1– ( )2M1 = –2/3(a0–a2)m+M+

M00

2m+

Below the threshold the (negative) interference term gives a “depletion” in the mass distribution

The cusp is proportional to (a0-a2)

Cabibbo Phys. Rev. Lett. 93, 121801 (2004)

threshold

13% of depletion


Cusp: two loopsCusp: two loops

M

K± ±

=M0

K±±

+

M1

K±±

+

- K±

+ +...

Including 2-loops diagrams other terms appear in the amplitude

All the S-wave amplitudes (5 terms) can be expressed as linear combination of a0 and a2

The isosping breaking effect is taking in to account

The radiative correction (most relevant near threshold) are still missing

A deviation from the no rescattering amplitude behaviour appears also above threshold

Cabibbo,Isidori JHEP 0503 (2005) 21M2(00), (GeV/c2)2

0.074 0.076 0.078 0.080

Leading effect

Sub-Leading effect

No rescattering

Cusp


Cusp: fit procedure & resultCusp: fit procedure & result The detector acceptance

correction is obtained with a full GEANT simulation

The 1-D fit is performed excluding 7 bins7 bins around the threshold position

The excess of events in this region is interpreted as pioniumpionium signature Pionium : R=(K+A2)/(K+–) =

(1.820.21)10–5.

Prediction: R=0.810–5 (Silagadze, 94)

(a0–a2)m+= 0.261 0.006stat. 0.003syst. 0.0013ext

.

a2m+= –0.037 0.013stat. 0.009syst. 0.0018ext.

(a0–a2)m+= 0.261 0.006stat. 0.003syst. 0.0013ext

.

a2m+= –0.037 0.013stat. 0.009syst. 0.0018ext.

Using ChPt constraints [Colangelo et al., PRL 86 (2001) 5008] a2 = –0.0444 + 0.236(a0–0.22) – 0.61(a0–0.22)2

– 9.9(a0–0.22)3 (a0–a2)m+= 0.263 0.003stat. 0.0014syst. 0.0013ext

Using ChPt constraints [Colangelo et al., PRL 86 (2001) 5008] a2 = –0.0444 + 0.236(a0–0.22) – 0.61(a0–0.22)2

– 9.9(a0–0.22)3 (a0–a2)m+= 0.263 0.003stat. 0.0014syst. 0.0013ext

This result is fully compatible with our previous measurement on partial sample ((Phys.Lett. Phys.Lett. B633:173-283,2006B633:173-283,2006))

Preliminar

y


Cusp: systematics & “neutral” Cusp: systematics & “neutral” slopesslopesSystematic effectSystematic effect (a(a00––

aa22))101022

aa22101022 (a(a00–a–a22))

10102 2 ChPtChPtAnalysis technique ±0.10±0.10 ±0.20±0.20 ±0.08±0.08

Trigger inefficiency negl.negl. ±0.50±0.50 negl.negl.

Description of resolution ±0.06±0.06 ±0.11±0.11 ±0.06±0.06LKr non-linearity ±0.06±0.06 ±0.26±0.26 ±0.05±0.05Geometric acceptance ±0.02±0.02 ±0.01±0.01 ±0.02±0.02

MC sample ±0.03±0.03 ±0.21±0.21 ±0.06±0.06

Simulation of LKr showers ±0.17±0.17 ±0.50±0.50 ±0.04±0.04V-dependence of amplitude

±0.17±0.17 ±0.38±0.38 ±0.02±0.02

Total ±0.28±0.28 ±0.90±0.90 ±0.14±0.14

The external error comes from A00/A+-= 1.9750.015

A theoretical error of 0.013 (in a0-a2) have to applied to take in to account the still missed radiative correction and the high order terms

Standard expansion is not enough to describe the K→3dynamics

The slopes has been remeasured as (slightly different definition wrt to the PDG definition):

g = (64.9 0.3stat. 0.4syst. )% h’ = (–4.7 0.7stat 0.5syst.)%k’ = (0.970.03stat.0.08syst.)%

g = (64.9 0.3stat. 0.4syst. )% h’ = (–4.7 0.7stat 0.5syst.)%k’ = (0.970.03stat.0.08syst.)%

First evidence of k≠0

Preliminary


ConclusionsConclusions

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→: the scattering lengths are extracted from the study of rescattering contribution in the m 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

NA48/2 Ke4NA48/2 Cusp

DIRAC band (prel. 2007)

Isospin breaking corrections applied both in Cusp and in Ke4 (work ongoing (see Gasser talk at Kaon07) )


SparesSpares


MeMe slope: 2D fit slope: 2D fit

Fs=fs+fs’q2+fs’’q4+fe’(Me2/4m

2)+...

f’’s f’s

f’s -0.96 0.03

f’’s -0.06 In the 1D fit a residual variation is observed with respect to Me

2D in (M, Me

) performed

Linear depence with Me

f’e/fs = 0.081±0.011±0.008


Ke4: isospin breaking correctionKe4: isospin breaking correction

See Gasser’s talk @ Kaon 2007Kaon 2007

Thanks to the indipendent bin analysis the correction can be applied also to old data coming from previous experiment

The results become compatible with the cusp’s results


Fit resultsFit results

K-

K+


Cusp fit (in 2003)Cusp fit (in 2003)

420/148420/148

155/146155/146

149/145149/145

145/139145/139

One loop

Two loops

Pionium

Excluding 7 bins

Standard Dalitz plot parameterization

=(data-fit)/data

|M(u,v)|2 ~1+gu+hu2+kv2+...


Dirac experimentDirac experiment The |a0-a2| quantity can be extracted from the

measurement of the lifetime of pionic atoms in a model independent way

The ionized exotic atoms are produced in a fixed target

Lifetime in the order of 3 fs

ChPt predicts with high accuracy this lifetime

p is the 0 momentum and corrections

Physics Letters B 619 (2005) 50

|a0-a2|=0.264+0.033-0.020

expected error in 2007: +7.4%, -4.2%

)1(||9

21 220

3

aap


Spectrometer alignmentSpectrometer alignment

P = P0∙(1+β)∙(1+qbP0)

B signKaon sign

Raw momentum

Eq. Sensitivity (on DCH4):

M/x 1.5 keV/m

The kaon mass depends from the time variation of the spectrometer alignment

The mis-alignment gives a mis-measurement of the charged pion momentum

The reconstructed invariant K mass is used to fine tune the spectrometer by imposing (correction ) : MK+ =MK-

The non-perfect field alternation is tuned by imposing ( correction): MK+-=MKpdg


Beam movementsBeam movements

DCH1DCH1(upstream magnet)(upstream magnet)

K+ K

X, cm

Large time scale movement: the beam positions change every run

Acceptance largely defined by central beam hole edge (~10 cm radius)

The cut is defined around the actual beam position obtained with the c.o.g. measured run by run, for both charges as a function of the K momentum (“virtual pipe” cut)

Short time scale movement: the beam moves during the SPS spill

Monitored with an high resolution beam monitor on the beams

The 2 beam movement is “coherent”

No effect in the 4-uple ratio


““blue field”blue field”

The Earth field (Blue Field) was directly measured and used at the vertex recostruction level. The residual

systematics is ΔΔ<10<10-5-5

P kick(stray field)P kick(spectrometer) 1010

-4-4

measurement of pp scattering lengths in kaon decays by na48/2

Documents

form factors f

p pen form factors

constant form factors

form factors resultfsfs

hpeidpthe form factors

form factors structure

vector form

level of ke4