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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: