KLKS Regeneration in KLOE

Simona S. Bocchetta

XII Frascati Spring School “Bruno Touschek”May 17th, 2007

2

About strange particles…

Neutral K mesons: see P. Franzini lectures

The quark eigenstates are:

The CP eigenstates are:2

KKK ,

2

KKK

00

2

00

1

00 K ,K

M. Gell-Mann A. Pais

3

A particle mixture?Suggestion for experimental check: Pais and Piccioni 1955

O. Piccioni

Pure K0:K1 and K2 mixture, with mean lifetimes 2>>1

K1(t)

K2(t)

Regeneration prediction!

4

The Regeneration Phenomenon

The state out of the material will be:

2

KKK

00

L

Consider a KL beam impinging on a thickness of material:

For regeneration: ~ 10-3 « 1 (indirect CP), suppose negligible:

SL00 K )(f-)f(

2

1K )(f)f(

2

1K )(fK )f(

2

1ψ θ

f(), f(): scattering amplitudes of K0 and K0

: scattering angle

If f()≠f(), the state out of the material

will have a regeneration component.

N)(K σN)K( σ 00 N)(K σN)K( σ 00 )(f)f( )(f)f( regeneration

incoherentcoherentDepends on:density and size of the material momentum of the incident K

in KLOE the incoherent regeneration has the main effect in the detector!

5

The KLOE experimentThe KLOE experiment

(e+e-) = 3.1 b

BR(KS KL) = 34 %

BR(KS + -) = 69.2 %

pL,S = 110 MeV

L,S = 0.22

S = 6 mm

L = 3.4 m

Our DATA sample: 328 pb-1Our DATA sample: 328 pb-1

KLOE 2001-2002: 1,21 108 events

decay length

6

Regenerating surfaces in KLOERegenerating surfaces in KLOE

• DC cylinder-shape - 750 mm of C - 150 mm of Al

• BP sphere-shape - 62% Be - 38% Al thickness: 500 m

• Be cylinder-shape thickness: 50 m

25 cm

Drift Chamber (DC)

4.3 cm

10 c

mBeam Pipe (BP)

Z axis

Beryllium (Be)

e+ e-

beam line

7

KL tag: after the KS identification cutting on kinematic variables, look for the KL in the other side of the detector:Reconstruction: evaluation of tracking and

vertexing efficiencies for the region of the regenerating surface (DC and BP-Be)KL decays: identification via kinematic variablesSignal selection: sample enriched of regeneration events cutting on kinematic variablesFit in the vertex coordinates: extraction of the events number and the cross sectionComparison with expectations and existing measurements

The analysis guidelines

SL KK ppp tag

8sinθ 22 ryxρ

LL KK

x

KKLL reconstruction reconstruction• using from KS and the interaction point, we get the line of flight of KL

• search 2 tracks of opposite sign which originates near the KL line of flight• request of vertex reconstruction with 2 tracks

tag

LKp

KS line of flight KL line of flight

+

-, , e

, , e

0,

LKx222

LLL KKK zyxr

KL vertex coordinates:

vtxtrkrec εεε vtxtrkrec εεε

DC: 21<<30 cm rec = 71.0 ± 0.5 % BP-Be: 0<<15 cm rec = 70.0 ± 0.7 %

9

2tot

2tot

2inv |P|EM

INVARIANT MASS:

To select a regeneration-enriched sample we need 2 kinematic variables:

0πππ

ppP tot

2π

22π

2tot mpmpE

For regeneration events:Minv ≈ MKL

So we select:492.5<Minv<502.5 MeV

Regeneration kinematic variablesRegeneration kinematic variables

10

Regeneration kinematic variablesRegeneration kinematic variables

DELTA P:

ppppΔLK

tag

tag

LKp

p ,p

KL momentum (from tagging)

tracks momenta from KL

For regeneration events:|p| ≈ 0

So we select:-10 < |p| < 20 MeV

11

Detector x-ray, extraction of NDetector x-ray, extraction of Nregreg

Spatial distribution of KL vertex after the selections in Minv and in |p|:

Y versus X versus Z

Transverse radius (cm) Radius r (cm)

extract the number of

regeneration events by

fitting the distributions in

r, for each regenerating

surface.

extract the number of

regeneration events by

fitting the distributions in

r, for each regenerating

surface.

obsregN

DCBP

Be

12

BP-Be: 0 < < 15 cm |z| < 15 cmDC: 21 < < 30 cm |z| < 120 cm

Selection of the regeneration region:

• Fit in variable for DC: MC shapes for background; 2 gaussians for the peak.• Matched fit in r & variables for BP-Be: MC shapes for background; 2 gaussians for the peak in the orthogonal coordinate to the surface; change of variables = r sin for the other peak, including angular distribution of KL ~ sin2.

Fit shapesFit shapes

13

Regeneration cross sectionsRegeneration cross sections

tt

regreg Δx n

Pσ

tt

regreg Δx n

Pσ

The cross section depends on the probability of regeneration and on thethickness of the regenerating surfaces:

selrec

obsreg

reg ε ε

NN

L

LL

λtagKK e NN

LK

regreg N

NP

LK

regreg N

NP

where:t

tAt A

ρNn

target density

target atomic weight

8tagK 101,21N

L

cm 343λL

sinθ

1ρ average length covered

from the KL until the regenerating surface

ii

ii

iAMtt t(%)

A

ρNΔxn

tΔx = target thickness

Main systematic error source:

surfaces thickness ~10%

mb 6.00.860.2σDCreg

syststat mb 6.00.860.2σDCreg

syststat DC:

mb 6.00.659.6σBPreg

syststat mb 6.00.659.6σBPreg

syststat BP: Be

Still to do…

14

Comparison with expectations & measurementsComparison with expectations & measurements

mbarn 7.755.1σBereg

He Be C Al

Reg

en

era

tion

cro

ss s

ecti

on

(m

barn

)

All the results as a function of the atomic weight A.

tt NNNt wwAA

where:N

tNN A

Δxρw t

t

Comparison with the calculation of R. Baldini - A.

Michetti (‘96)and the

Novosibirsk CMD-2 result (‘99),

only existing measurementat this momentum value:

For DC & BP average atomic weight:

THANK YOU!

15

BACK-UP SLIDES

16

Effetto coerente ed incoerenteEffetto coerente ed incoerente

Si definisce:2

)()()(

fffreg

ampiezza di rigenerazione nella direzione

Mezzo rigeneratore = distribuzione uniforme di centri scatteratori, l’azione complessiva di questi centri potrà risultare in un effetto coerente o incoerente, ciò dipende da: • densità e dimensioni del materiale• impulso dei K incidenti

I casi sono due:• Se d(pL-pScos)≤1 si ha un’addizione coerente delle ampiezze delle due onde di KS

• Se d(pL-pScos)»1 l’intensità del KS risulta in un contributo medio nullo: si ha la rigenerazione incoerente

1 2d

KS KS

KL

Consideriamo due centri scatteratori 1 e 2 distanti d.Le due onde uscenti di KS si possono scrivere così:

|1>S=exp(ipSd cos) freg() |KS>

|2>S=exp(ipLd) freg() |KS>

La probabilità di rigenerazione per il sistema dei due centri scatteratori è:|<KS|1+2>S|2 = 2 |freg()|2 {1 + cos[d (pL - pS cos)]}

In KLOE la rigenerazione incoerente è l’effetto di rigenerazione dominante nel rivelatore.

17

Data and MC samples, KData and MC samples, KLL tag tag

• 2001/2002 sample for Data & Monte Carlo (328 pb-1)• KL tag: same selection as for KL BR measurements Requests:

• the vertex reconstructed with two tracks of opposite charge must stay in the fiducial volume centered in the nominal position of

• the invariant mass of two tracks (in the hypothesis m=m) within 5 MeV from the KS mass:

• the KS momentum within 10 MeV of the nominal value

NKLtag ~ 1.2 · 108

= (x2+y2)1/2 < 10 cm |z| < 20 cm

492.7 < Minv < 502.7 MeV

After this selection we have:

18

Regenerating surfaces in KLOERegenerating surfaces in KLOE• DC cylinder-shape transverse radius 25 cm made of: -750 m of Carbon A=12 - 60% carbon fibers - 40% epoxy -150 m of Aluminium A=27 • BP sphere-shape radius 10 cm made of: - 62% Beryllium A=9 - 38% Aluminium A=27 thickness 500 m

• Be cylinder-shape transverse radius 4.3 cm thickness 50 m A=9

Drift Chamber (DC)

25 cm

4.3 cm 10 c

m

Beam Pipe (BP)

Z axis

Beryllium (Be)

e+ e-

19

Reconstruction efficiencyReconstruction efficiency

• DC: 21 < < 30 cm, |z| < 160 cm• BP-Be: 0 < < 15 cm, |z| < 15 cm

rec = 71.0 ± 0.5 %

rec = 70.0 ± 0.7 %

vtxtrkrec εεε vtxtrkrec εεε

Both these efficiencies were calculated from MC and corrected with check measurements using data; the efficiencies depend on:

The reconstruction efficiency depends on:• the tracking efficiency • the vertex reconstruction efficiency

• tracks momentum • decay region

Pions from KL semileptonic decays have the same momentum spectra of pions from regenerated KS

Selection of a pure sample (95%) of Ke3 decays using calorimeter variables.

Reconstruction efficiency values:

20

KKLL charged decays analysis charged decays analysis

Study of kinematic variables:

• missing momentum:

• squared missing mass: hypotesis: pion mass

pppPtag

KmissL

2

miss2miss

2miss PEM

2missM 2

missM

Pm

iss

Pm

iss

data

MonteCarlo

MeV2 MeV2

MeV

MeV

Ke3

K3

+-0reg

semileptonic: CPV:

+-0:

regeneration:

0M2miss

2

π

2miss 0mM

1/22missmiss MP

0Emiss

0M2miss 0Pmiss 0Emiss

CPV

21

Regeneration kinematic variablesRegeneration kinematic variables

Regeneration event features:

To select a regeneration-enriched sample we need 2 kinematic variables:

ppP tot

2π

22π

2tot mpmpE

2tot

2tot

2inv |P|EM

INVARIANT MASS:

• Minv ≈ MKL • |p|≈0• angular distribution (more study in future)

• Minv ≈ MKL • |p|≈0• angular distribution (more study in future)

KL→+-, too

DELTA P:

ppppΔLK

tag

tag

LKp

p ,p

KL momentum (from tagging)

tracks momenta from KL

KL→+-, too

22

Signal selection: MSignal selection: Minvinv

2tot

2tot

2inv |P|EM

2tot

2tot

2inv |P|EM

below the peak: semileptonic background + regeneration + CPV

0πππ

MeV 502.5M492.5 inv

559,023 evs

if we choose:

survive

23

Signal selection: Signal selection: ||pp||

ppppΔLK ppppΔ

LKbelow the peak:

semileptonic background + regeneration + CPV

symmetricpeakasymmetric

peak(the KL gives a small fraction of its momentum to the target nucleus)

if we choose:

MeV 20pΔ10-

272,958 evs

pΔ survive

24

Detector x-ray, extraction of NDetector x-ray, extraction of Nregreg

Spatial distribution of KL vertex after the selections in Minv and in |p|:

Y versus X versus Z

Transverse radius (cm) Radius r (cm)

extract the number of

regeneration events by fitting the

distributions in r, foreach regenerating

surface.

extract the number of

regeneration events by fitting the

distributions in r, foreach regenerating

surface.

obsregN

DCBP

Be

25

Regeneration cross sectionRegeneration cross section

tt

regreg Δx n

Pσ

tt

regreg Δx n

Pσ

The cross section depends on the probability of regeneration and on thethickness of the regenerating surfaces:

biastagselrec

ossreg

reg ε ε ε

NN

L

LL

λtagKK e NN

LK

regreg N

NP

LK

regreg N

NP

where:t

tAt A

ρNn

target density

target atomic weight

tΔx = target thickness

4120,907,26NtagKL

cm 343λL

sinθ

1ρ average length covered

from the KL until the regenerating surface

ossregN to take out from fit

recεto estimateselεalready evaluated

26

Fit shapesFit shapes

BP-Be: 0 < < 15 cm |z| < 15 cmDC: 21 < < 30 cm |z| < 120 cm

Selection of the regeneration region

• Fit in variable for DC: MC shapes for background; 2 gaussians for the peak.• Matched fit in r & variables for BP-Be: MC shapes for background; 2 gaussians for the peak in the orthogonal coordinate to the surface; change of variables = r sinfor the other peak, including angular distribution of KL ~ sin2

27

Selection variation ISelection variation IVariation of cuts in the invariant mass

M1: 495.0 < Minv < 500.0 MeVM2: 492.5 < Minv < 502.5 MeVM3: 490.0 < Minv < 505.0 MeVM4: 487.5 < Minv < 507.5 MeVM5: 485.0 < Minv < 510.0 MeV

28

-5 < |p| < 10 MeV -10 < |p| < 20 MeV-20 < |p| < 30 MeV-30 < |p| < 40 MeV-40 < |p| < 50 MeV

25 fit foreach regenerating surface (DC & BP-Be) matching the cuts, we expect an asymptotic trend of the number of regeneration events which points to the true number.

In the region 0<r<15 cm the matched fit on the Be gives not the same results of the fit in the only transverse radius

We need a further study for the layer of Beryllium

up to now only DC & BP

Variation of cuts in |p|

Selection variation IISelection variation II

BUT:

29

Tig

hter cu

t in p

|Fit results, not yet corrected with Fit results, not yet corrected with

We can see the asymptotic trend, the results from fit must be corrected with the selection efficiencies, calculated in MC and corrected with data.

DRIFT CHAMBER

30 25 20

103

30 25 2030 25 2030 25 2030 25 20

BEAM PIPE

15

15

15

15

15

20

20

20

20

20

103

Tighter cut in Minv Tighter cut in Minv

N r

egen

era

tio

n e

ven

ts

N r

egen

era

tio

n e

ven

ts

30

Our selection efficiencyOur selection efficiency

pΔMsel εεε pΔMsel εεε The total selection efficiency depends on the selection efficiency of the single cut:

To estimate we’ve built the distributions in Minv and p of regeneration events in data:

• use a regeneration-enriched sample by selecting a region around the regenerating surfaces:

23 < < 28 cm for DC 7 < r < 13 cm for BP

• CP violating events are rejected by requesting There is superimposition of peaks in both the distributions. • Request of the cut 492.5 < Minv < 502.5 MeV for the |p| distribution, to reject the

further semileptonic background.

MeV 10pEQ 2miss

2missmiss

MC

bckg) fitted(data

ε

εc

By subtracting to the fit results the semileptonic background, we can calculate the efficiencies for the regeneration events in data. We have applied the same method on the MC events. Finally, we correct the MC efficiencies with the ratio:

31

Fit in the invariant mass & Fit in the invariant mass & |p||p|

DataFit

RegenKe3K3bckg

DataFit

RegenKe3K3CPV

INVARIANT MASS (DC) |p| (DC)

MeV MeV

The |p| peak shape is badly reproduced by the MC, but the efficiency calculation is not affected because only the fitted background shapes are taken from MC.

The invariant mass fit with a large cut in the regeneration regions provides us also a cross check for the number of regeneration events on the DC (not for BP):

38,043 ± 354 evs, compatible with the measurements obtained from the fit.

32

38

38

38

38

38

36

36

36

36

36

Number corrected for the efficienciesNumber corrected for the efficiencies

The measurement is reasonably stable, we choose a measurement foreach regenerating surface:

DC: Nobs = (37,175 ± 469) eventsBP: Nobs = (24,388 ± 176) events

DRIFT CHAMBER BEAM PIPE103 103

26

26

26

26

26

24

24

24

24

24

N r

egen

era

tio

n e

ven

ts

N r

egen

era

tio

n e

ven

ts

33

Probability & cross sectionProbability & cross section

48

rec

selobsreg

λtagK

DCreg 100.06)(4.72

0.71

175 37

0.9180101.21

1

ε

εN

e N

1P

L

L

48

rec

selobsreg

λtagK

BPreg 100.02)(2.97

0.70

388 24

0.9713101.21

1

ε

εN

e N

1P

L

L

mbarn 0.8)(60.2Δx n

Pσ

DCtt

DCregDC

reg mbarn 0.8)(60.2Δx n

Pσ

DCtt

DCregDC

reg mbarn 0.4)(59.6Δx n

Pσ

BPtt

BPregBP

reg mbarn 0.4)(59.6Δx n

Pσ

BPtt

BPregBP

reg

DRIFT CHAMBERDRIFT CHAMBER BEAM PIPEBEAM PIPE

221Cepoxy

epoxy

epoxyCF

CF

CFAl

Al

AlADCtt cm 106.67t(%)

A

ρ(%)

A

ρt

A

ρNΔxn

221BPBe

Be

BeAl

Al

AlABPtt cm 104.98t(%)

A

ρ(%)

A

ρNΔxn

where:

34

Systematic errorsSystematic errors

surfaces thickness 10%

error on the selection efficiencies: 2% BP 1.5% DC

error on the reconstruction efficiencies: about 1%

nuclear interactions contamination: negligible

fit shapes: negligible

tails of the invariant mass distribution: about 2%

~10%

We need further studies to find the right thickness of the regenerating surfaces, the idea is to use the energy loss of charged particles in the matter.

We need further studies to find the right thickness of the regenerating surfaces, the idea is to use the energy loss of charged particles in the matter.

We can directly measure the thickness of beam pipe!

35

From fit preliminary results we find a cross section comparatively large for the Beryllium.

So a value of about 75 mbarn for Be would imply a small cross section on Aluminium

as predicted from calculations of R. Baldini & A. Michetti (1996).

ResultsResults

mbarn 6.00.860.2σDCreg

syststat mbarn 6.00.860.2σDCreg

syststat

mbarn 6.00.459.6σBPreg

syststat mbarn 6.00.459.6σBPreg

syststat

DC:

BP:

Cross section on Aluminium (mbarn)

Cro

ss s

ectio

n on

Be,

C (

mba

rn)

Since the cross section on the Be is unknown, we can find variation bands for the cross

sections on Be and C versus the cross sectionof the Aluminium.

BerylliumCarbon

36

Comparison with expectations & measurementsComparison with expectations & measurements

mbarn 7.755.1σBereg

13.1A 14.0A BPDC

He Be C Al

Reg

ener

atio

n c

ross

sec

tio

n (

mb

arn

)

All the results as a function of the atomic weight A.

tt NNNt wwAA

where:N

tNN A

Δxρw t

t

Comparison with the Novosibirsk CMD-2 result (‘99),

only existing measurementat this momentum value:

For DC & BP average atomic weight: