Introduction Analysis Results Conclusions Frascati 12 March 2008 Status of analysis F. Ambrosino T. Capussela F. Perfetto Status of analysis

Introduction Analysis Results Conclusions

Frascati 12 March 2008

Status of analysis

F. Ambrosino T. Capussela F. Perfetto

Status of analysis

Status of analysisFrascati 12 March 2008

Outline

Repeat the analysis with mass constraint before photon’s pairing

Review the correction to the photon efficiency

Look at Data /MC comparison for min2


Sample selection

OLD approach:

7 and only 7 pnc with 21° < < 159° and E > 10 MeV > 18° Kin Fit with no mass constraint P(2) > 0.01 320 MeV < Erad < 400 MeV AFTER PHOTON’S PAIRINGKinematic Fit with and mass

constraints (on DATA M=547.822

MeV/c2 )

NEW approach:

7 and only 7 pnc with 21° < < 159° and E > 10 MeV > 18° Kin Fit with mass constraint

(on DATA M= 547.822 MeV/c2 ) P(2) > 0.01 320 MeV < Erad < 400 MeV AFTER PHOTON’S PAIRINGKinematic Fit with mass constraint


OLD - NEW

Using the same cuts on min and

Pur 75.4%

Pur 84.5%

Pur 92%

Pur 94.8%

Pur 97.6%

Pur 82.2%

Pur 99%

Pur 98%

Pur 96.3%

Pur 91%

Low purity

Medium I purity

Medium II purity

Medium III purity

High purity


OLD - NEW

The slope in the efficiency shapes

8%

14%

21%

25%

26%

Low purity

Medium I purity

Medium II purity

Medium III purity

High purity

8%

14.6%

22.3%

25.3%

26%


OLD - NEW

RMS = 0.1169

RMS = 0.1632


Efficiency

Correction to the photon efficiency is applied weighting the Montecarloevents for the Data/MC photon efficiency ratio ≈ 1 exp(E/8.1)



Efficiency (I)


Low purity

Medium II purity

High purity

P1 = 0.001258

P1 = 0.001692

P1 = 0.002014 P1 = 0.001876

P1 = 0.001601

P1 = 0.001623



Photons pairing

m0

j

m ioj

j2

m i

0j M

0

m0

j

i1

3

2

Recoil is the most energetic cluster.In order to match every couple of photon to the right 0 we build a 2-like variable for each of the 15 combinations:

With:

is the invariant mass of i0 for j-th combination

= 134.98 MeV

is obtained as function of photon energies

M 0



Energy resolution

EEp1 1 e

p2

E p3

Ep4

E

M

M

1

2

E1

E1

E2

E2



Data – MC RMS

A data MC discrepancy at level of 12 % is observed.

A further check can be done comparing the energies of the two photons in the pion rest frame as function of pion energy


Conclusions

We are ready to fit and to evaluate the systematical errors in the NEW approach.

We have to resolve the Data MC discrepancy onmin

2


Dalitz plot analysis of with the KLOE experimentFrascati 19 Luglio 2007

3in chiral theory

A s,t,u 1

Q2

mK2

m2m

2 mK2 M s,t,u

3 3F2

( 3 ) A2 Q 4

M (s,t,u)3s 4m

2

m2 m

2Q2 ms

2 m2

md2 mu

2

The decay occours primarily on account of the d-uquark mass differences and the result arising from lowestorder chiral perturbation theory is well known:

With:

A good understanding of M(s,t,u) can in principle lead to a very accurate determination of Q:

And, at l.o.



z 2

3(

3Ei m

m 3m 0i1

3

)2 2

max2

The dynamics of the decay can be studied analysing the Dalitz plot distribution.

The Dalitz plot density ( |A|2 ) is specified by a single quadratic slope :

|A|2 1 + 2z

with:

Ei = Energy of the i-th pion in the rest frame. = Distance to the center of Dalitz plot.max = Maximun value of .

Z [ 0 , 1 ]

Dalitz plot expansion

Introduction Theoretical tools Results Conclusions


Dalitz plot expansion



Dalitz expansion: theory vs experiment

Calculation Tree

One-loop[1]

Dispersive[2]

Tree dispersive

Absolute dispersive

Unitary[3]

0.00

0.0015

0.007 0.014

0.006

0.007

0.031 [1] Gasser,J. and Leutwyler, H., Nucl. Phys. B 250, 539 (1985) [2] Kambor, J., Wiesendanger, C. and Wyler, D., Nucl. Phys. B 465, 215 (1996) [3] Borosoy B., Niler R. hep-ph/0510384 v2 (2005)

Alde (1984) 0.022 ± 0.023

Crystal Barrel (1998) 0.052 ± 0.020

Crystal Ball (2001) 0.031 ± 0.004



Sample selection

The cuts used to select: 000are:

7 and only 7 prompt neutral clusters with 21° < <

159°

and E > 10 MeV Opening angle between each couple of photons > 18° Kinematic Fit with no mass constraint P(2) > 0.01 320 MeV < Erad < 400 MeV (after kin fit)

The overall common selection efficiency (trigger, reconstruction, EVCL) is = (30.30 0.01)%With these cuts the expected contribution from events other than the signal is < 0.1%



Sample selection



Photons pairing

m0

j

m ioj

j2

m i

0j M

0

m0

j

i1

3

2

Recoil is the most energetic cluster.In order to match every couple of photon to the right 0 we build a 2-like variable for each of the 15 combinations:

With:

is the invariant mass of i0 for j-th combination

= 134.98 MeV

is obtained as function of photon energies

M 0



Energy resolution

EEp1 1 e

p2

E p3

Ep4

E

M

M

1

2

E1

E1

E2

E2



Matching to s

Cutting on: Minimum 2 value 2 between “best” and “second” combination

One can obtain samples with different purity-efficiency

Purity = Fraction of events with all photons correctly matched to 0’s



Samples

Pur 84.5% Eff 22 %Pur 92 % Eff 13.6 %

Pur 94.8% Eff 9.2 %

Pur 97.6% Eff 4.3 %

Low purity

High purity

Medium purity III

Medium purity II

Pur 75.4% Eff 30.3 %

Medium purity I 2 < 10

2 > 1.2

2 < 5

2 > 3

2 < 3

2 > 4

2 < 2

2 > 7

No cut on 2 and 2



Efficiency

Low purity



Efficiency

Medium II purity



Efficiency

High purity

ReconstructedPhase space



The problem of resolution

Low Purity High Purity



Second kinematic fit

Once a combination has been selected, one can do a second kinematic fit imposing 0 mass for each couple of photons.



Fit procedure

ni log i i

We obtain an extimate by minimizingThe fit is done using a binned likelihood approach

Where:

ni = recostructed eventsi = for each MC event (according pure phase space):

Evaluate its ztrue and its zrec (if any!) Enter an histogram with the value of zrec

Weight the entry with 1 + 2 ztrue Weight the event with the fraction of combinatorial background, for the signal (bkg) if it has correct (wrong) pairing



Results on MC

We have tested the fit procedure on MC by generating samples with different values of the parameter and looking at the result of our fit for these samples:



Results on MC (Low Pur)

Fitted region (0,0.6)

Fitted region (0,1)





Results on MC (Medium II Pur)


Fitted region (0,1)





Results on MC (High Pur)


Fitted region (0,1)





Data sample

We have analyzed Lint = 418 pb1 of ee collisions collected in the 20012002 data taking period

N1 = 1.4179 0.0012 Mevts Low purity

N2 = 1.0292 0.0010 Mevts Medium I purity

N3 = 0.6459 0.0008 Mevts Medium II purity

N4 = 0.4453 0.0007 Mevts Medium III purity

N5 = 0.2123 0.0005 Mevts High purity



Analysis on data

Trying some more systematics checks on the fitting range we got in BIG trouble…

RangeLow

· 103

Medium I

· 103

Medium II

· 103

Medium III

· 103

High Pur

· 103

(0, 1) 18 ± 2 18 ± 2 18 ± 3 11 ± 3 8 ± 4

(0, 0.7) 31 ± 3 30 ± 2 26 ± 3 18 ± 4 18 ± 6



Linearity of DATA / MC ratio

Check linearity of DATA/MCreco using for MC pure phase space…

Nothing really strange @ high purity…



Linearity of DATA / MC ratio (II)

Idea: check linearity of DATA/MCreco using for MC pure phase space… But @ low purity = High statistics…



A possible explanation_

The edge of the flat part of the phase space depends in the value of the eta mass. What if its value on data is larger than the nominal one ?



A toy MC

To understand the effect we used a toy MC to generate 1200000 events with different eta masses:

Sample 1 : M = 547.30 MeVSample 2 : M = 547.822 MeV We observe that when the input mass value is used to build “z” variable the phase space shape does not change. But if one uses M = 547.30 MeV to build the “z” variable for sample 2 big deviations are observed……..

z 2

3(

3Ei m

m 3m 0i1

3

)2 2

max2

Z2(547.8)/Z1(547.3)



A toy MC

To understand the effect we used a toy MC to generate 1200000 events with different eta masses:

Sample 1 : M = 547.30 MeVSample 2 : M = 547.822 MeV We observe that when the input mass value is used to build “z” variable the phase space shape does not change. But if one uses M = 547.30 MeV to build the “z” variable for sample 2 big deviations are observed……..

z 2

3(

3Ei m

m 3m 0i1

3

)2 2

max2

Z2(547.8)/Z1(547.3)Z2(547.3)/Z1(547.3)



LinearityIf the effect is given by the eta mass, correcting for it now all sample should exhibit good linearity for the ratio DATA/MCrec (phase space)

@ Low purity



Linearity (II)If the effect is given by the eta mass, correcting for it now all sample should exhibit good linearity for the ratio DATA/MCrec (phase space)

@ High purity



Results on data

Let us look at what happens now…

Range Low

· 103

Medium I

· 103

Medium II

· 103

Medium III

· 103

High Pur

· 103

(0, 1) 33 ± 2 35 ± 2 33 ± 3 28 ± 3 25 ± 4

(0, 0.7) 33 ± 3

35 ± 3 32 ± 4 26 ± 4 25 ± 6

…..we gained greater stability with respect to the range and purity.



Third kinematic fit

We performed a kinematic fit constraining the mass

(M = 547.822 MeV)

RangeLow

· 103

Medium I

· 103

Medium II

· 103

Medium III

· 103

High

· 103

(0, 1) 30 ± 2 31 ± 2 31 ± 3 25 ± 3 26 ± 4

(0, 0.8) 26 ± 2 28 ± 2 28 ± 3 22 ± 4 22 ± 5

(0, 0.7) 26 ± 3 28 ± 3 27 ± 4 21 ± 4 23 ± 5

(0, 0.6) 30 ± 4 31 ± 4 31 ± 4 24 ± 5 20 ± 6

RangeLow

· 103

Medium I

· 103

Medium II

· 103

Medium III

· 103

High

· 103

(0, 1) 30 ± 2 31 ± 2 31 ± 3 25 ± 3 26 ± 4

(0, 0.8) 26 ± 2 28 ± 2 28 ± 3 22 ± 4 22 ± 5

(0, 0.7) 26 ± 3 28 ± 3 27 ± 4 21 ± 4 23 ± 5

(0, 0.6) 30 ± 4 31 ± 4 31 ± 4 24 ± 5 20 ± 6



The systematic check

This procedure relies heavily on MC.

The crucial checks for the analysis can be summarizedin three main questions:

I. Is MC correctly describing efficiencies ?II. Is MC correctly describing resolutions ?III. Is MC correctly estimating the “background” ?



Efficiency (I)




Efficiency (I)


Low purity

Medium II purity

High purity



Efficiency (II)

Further check is to look at the relative ratio between the different samples:

N2/N1 exp. = .7263 ± .0002

N3/N1 exp. = .4497 ± .0002

N4/N1 exp. = .3048 ± .0002

N5/N1 exp. = .1431 ± .0001

N2/N1 obs = .7258 ± 0.0004

N3/N1 obs. = .4556 ± 0.0004

N4/N1 obs. = .3140 ± 0.0004

N5/N1 obs. = .1498 ± 0.0003



Efficiency (III)



Resolution (I)

A first check on resolution is from pion mass distribution



Resolution (II)

The center of Dalitz plot correspond to 3 pions with the same energy (Ei = M/3 = 182.4 MeV). A good check of the MC performance in evaluating the energy resolution of 0 comes from the distribution of E0 Ei for z = 0

E1

E2

E



Resolution (III)


Vs.



Resolution (IV)

A data MC discrepancy at level of 12 % is observed.Thus we fit filling a histo with: z’rec = zgen + (zrec zgen ).




Fitting the combinatorial backgroundIdea, try to fit background composition on DATA.To check procedure, we fit background composition on MC:

Background fraction (MC) = 15.5 %Background fraction (MC fit) = (15.5 ± 0.2) %







Fitting the combinatorial background (II)

On DATA:

Background fraction (MC) = 15.5 %Background fraction (DATA) = (16.6 ± 0.28) %




Background fraction (MC) = 24.6 % Background fraction (DATA) = (26.45 ± 0.26) %



Background

Background composition, Medium II purity sample



Systematic uncertainties

EffectLow

· 103

Medium I

· 103

Medium II

· 103

Medium III

· 103

High

· 103

Res 9 6 4 3 3

Low E 1.6 1.9 1.6 1.3 1.4

Bkg 0. 0. 0. 1 1 +1

M 1 1 2 2 5

Range 4 3 4 4 3 +3

Purity 2 +5 +7 1 + 6 7 5 + 2

Tot 10 + 5 7 + 7 6 + 6 9 9 + 4

We take as milestone, for each sample, the fit in the range (0, 0.7)



Results

We give the final results for the slope parameter in corrispondence of the sample with 92% of purity:

This result is compatible with the published Crystal Ball result:

= 0.031 ± 0.004

And the calculations from the chiral unitary approach.

= 0.027 ± 0.004stat ± 0.006 syst



Fit residual

2/ndf = 13.72 / 17.



Effect of mass constraint in fit

Why did this effect not pop up in other experiments analyses? The reason is the effect is much less evident if you constrain in a kinematic fit the mass and then use the value you have constrainedd to build z….



Conclusions

If you bless this preliminary result we are ready to prepare a brief paper for LP07.

Otherwise…… . The MEMO is ready and Giorgio already gave

us his comments (This talk is partially upgrade one.)

Next step: to perform the kinematic fit imposing mass before the photon pairing, as asked by Giorgio.

And then? ……THE END!!!!!!!



Spare



Efficiency I

Medium I purity



Efficiency

Medium III purity



Results on MC (Medium I Pur)


Fitted region (0,1)





Results on MC (Medium III Pur)


Fitted region (0,1)





DATA MC comparison



DATA MC comparison



Outline



Outline



@ KLOE

At KLOE is produced in the process .N(2001-2002) 17 Mevts. The final state for is 7, with almost no physical background.

BR() = 3.910-3

Documents

Introduction Analysis Results Conclusions Frascati 12 March 2008 Status of analysis F. Ambrosino T. Capussela F. Perfetto Status of analysis