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Dynamics of η → π 0 π 0 π 0. F. Ambrosino T. Capussela F. Perfetto. OUTLINE. KLOE Memo n. 359 α = − 0.027 ± 0.004 stat ± 0.006 syst ( blessed 19/07/2007; KLOE preliminary arXiv 0707.4137) Selection scheme & fit procedure & systematics evaluations

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slide1

Dynamics of η → π0π0π0

F. Ambrosino T. Capussela F. Perfetto

outline
OUTLINE
  • KLOE Memo n. 359
  • α = − 0.027 ± 0.004 stat ± 0.006 syst
  • (blessed 19/07/2007; KLOE preliminary arXiv 0707.4137)
  • Selection scheme & fit procedure & systematics evaluations
  • Introduction of a new selection scheme: NEW approach
  • NEW or OLD approach ?
  • KLOE Memo n. 359 + x
  • Update on the measurement using different samples
  • Final results
dalitz plot expansion
Dalitz plot expansion

The decay η → 3π violates iso-spin invariance and itis induced dominantly by the strong interaction via the u−d quark mass difference.

The Dalitz plot density corresponding to the intrinsic η→ π0 π0 π0 decay amplitude is approximately described by

|A|2 ∝1 + 2αz

With:

Z ∈ [ 0 , 1 ]

Ei = Energy of the i-th pion in the ηrest frame.

ρ = Distance to the center of Dalitz plot.

ρmax = Maximun value of ρ.

η−>3π @ KLOE

theory vs experiment
Theory vs Experiment

Calculations for α:

J.Kambor et al. (1996): −0.007 or −0.0014

B.Borasoy et al. (2005): −0.031 ± 0.003

J.Bijnens et al. (2007): 0.013 ± 0.032

Experimental results for α:

GAMS-2000 (1984): −0.022 ± 0.023

CBarrel at LEAR (1998): −0.052 ± 0.017 ± 0.010

CBall at AGS (2001): −0.031 ± 0.004

KLOE (prelim.2005): −0.013 ± 0.004 ± 0.005

CELSIUS-WASA (2007): −0.026 ± 0.010 ± 0.010

KLOE (prelim.2007): −0.027 ± 0.004 ± 0.005

CBall at MAMI-B (2009): −0.032 ± 0.002 ± 0.002

CBall at MAMI-C (2009): −0.032 ± 0.003

  • Experiment: α = −0.031 ± 0.004
  • KLOE, CBall and WASA consistent
  • ChPT LO: α = 0
  • ChPT one and two loop: α > 0
  • Quark masses from η → π0π0π0?
  • [ DeAndrea, Nehme, Talavera PRD78(2008)034032 ]

η−>3π @ KLOE

sample selection
Sample selection
  • The cuts used to select:η → π0 π0 π0are:
  • 7 and only 7 prompt neutral clusters with 21°<θγ<159°
  • and Eγ> 10 MeV
  • Opening angle between each couple of photons > 18°
  • Kinematic Fit with no mass constraint
  • P(χ2) > 0.01
  • 320 MeV < Eγrec < 400 MeV (after kin fit)
  • The overall common selection efficiency (trigger, reconstruction, EVCL) is ε = (30.30 ± 0.01)%

With these cuts the expected contribution from events other than the signal is < 0.1%

Frascati 19 Luglio 2007

matching to 0 s
Matching γ to π0 s
  • In order to select the best π0 π0 π0 pairing, we introduce a pseudo−χ2 variable for each of the 15 possible pairs,
  • cutting on:
  • Minimum χ2 value
  • Δχ2 between “best” and “second” combination
  • one can obtain samples with different purity-efficiency

Δχ2

Δχ2

min χ2

min χ2

matching to 0 s1
Matching γ to π0 s
  • In order to select the best π0 π0 π0 pairing, we introduce a pseudo- χ2 variable for each of the 15 possible pairs,
  • cutting on:
  • Minimum χ2 value
  • Δχ2 between “best” and “second” combination
  • one can obtain samples with different purity-efficiency

After pairing we perform kinematic fit with η andπ0 mass constraint

η mass:MMC = 547.30 MeV /c2 MData = 547.822 MeV/c2

Δχ2

Δχ2

slide9

Fit procedure

The fit is done using a binned likelihood approach

We obtain an extimate by minimizing

Where:

  • ni= recostructed events
  • νi= 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 + 2αztrue
  • Weight the event with the fraction of combinatorial

background, for the signal (bkg) if it has correct (wrong)

pairing

This procedure relies heavily on MC.

slide10

Test on fit procedure (I)

  • We have tested the fit procedure in different ways:
  • Looking at the result of our fit on MC (αMC = 0.)
slide11

Test on fit procedure (II)

  • We have tested the fit procedure in different ways:
  • Looking at the result of our fit on MC (αMC = 0.)
  • Using hit or miss and our reweighting we have generated
  • samples with different values of α and then we have
  • compared the two procedures.
slide12

Test on fit procedure (III)

  • We have tested the fit procedure in different ways:
  • Looking at the result of our fit on MC pure phase space(αMC = 0.)
  • Using hit or miss and the fit procedure we have generated samples with different values of α and then we have compared the two procedures.
  • Parameter scan:
slide13

Systematic checks

Mean 134.2

RMS 11.83

Mean 134.2

RMS 11.99

Frascati 19 Luglio 2007

slide14

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

Systematic check

vs

slide15

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

A data MC discrepancy at level of 1÷2 % is observed.

Thus we fit filling a histo with:

z’rec = zgen + η(zrec− zgen ).

Systematic check

slide16

Systematic checks

N2/N1 exp. = 0.7263 ± 0.0002

N3/N1 exp. = 0.4497 ± 0.0002

N4/N1 exp. = 0.3048 ± 0.0002

N5/N1 exp. = 0.1431 ± 0.0001

N2/N1 obs = 0.7258 ± 0.0004

N3/N1 obs. = 0.4556 ± 0.0004

N4/N1 obs. = 0.3140 ± 0.0004

N5/N1 obs. = 0.1498 ± 0.0003

slide17

Idea, try to fit the WPf on DATA.

To check procedure, we fit the WPf on MC:

WPf(MC) = 24.6 %

WPf(MC fit) = (24.6 ± 0.2) %

WPf(MC) = 15.5 %

WPf(MC fit) = (15.5 ± 0.2) %

WPf (MC) = 8.0 %

WPf (MC fit) = (7.9 ± 0.3) %

WPf (MC) = 5.2 %

WPf (MC fit) = (5.2 ± 0.3) %

WPf (MC) = 2.4 %

WPf (MC fit) = (2.4 ± 0.4) %

Systematic check

slide18

On DATA:

WPf (MC) = 24.6 %

WPf (DATA) = (26.45 ± 0.26) %

WPf (MC) = 15.5 %

WPf (DATA) = (16.6 ± 0.28) %

WPf (MC) = 8.0 %

WPf (DATA) = (8.90 ± 0.37) %

WPf (MC) = 5.2 %

WPf (DATA) = (6.0 ± 0.45) %

WPf (MC) = 2.4 %

WPf (DATA) = (3.25 ± 1.00) %

Systematic check

slide19

Systematic check

Frascati 19 Luglio 2007

slide20

α= − 0.027 ± 0.004stat ± 0.006 syst

Results

χ2/ndf = 13.72 / 17.

slide21

NEW approach:

  • 7 and only 7 pnc with
  • 21° < θγ< 159°and Eγ> 10 MeV
  • θγγ > 18°
  • Kin Fit with η mass constraint
  • (onDATAMη= 547.822 MeV/c2 )
  • P(χ2) > 0.01
  • 320 MeV < Eγrad < 400 MeV
  • AFTER PHOTON’S PAIRING
  • Kinematic Fit with π0mass
  • constraint

Dalitz plot expansion

  • OLD approach:
  • 7 and only 7 pnc with
  • 21° < θγ< 159° and Eγ > 10 MeV
  • θγγ > 18°
  • Kin Fit with no mass constraint
  • P(χ2) > 0.01
  • 320 MeV < Eγrad < 400 MeV
  • AFTER PHOTON’S PAIRING
  • Kinematic Fit with η and π0 mass constraints (on DATA Mη = 547.822 MeV/c2 )
slide24

NEW or OLD ?

NEW APPROACH

OLD APPROACH

……OLD APPROACH !!

slide26

Dalitz plot expansion

  • Now we have updated the measurement of a using:
  • Before the kinematic fit : qgg > 9°
  • In the kinematic fit on data : Mh = 547.874± 0.007 ±0.031MeV/c2
  • MC sample generated according to a = -0.027
  • New samples with different purity - efficiency
  • A correction of about 2% to the photon energies in the p0 rest frame.
slide27

qgg > 9°

After kinematic fit

After P(2) > 0.01

After E> 10 MeV

After EVCL

After 320 MeV < Erad < 400 MeV

Afterg > 18°

slide29

qgg > 9°

Low

Med

High

slide30

qgg > 9°

Low

Med

High

slide31

New MC sample

We have generated MC samples with different a values in input and we have fitted a on data:

  • We’ll use MC generated with:
  • = - 0.027.

On this MC sample:

  • a = - 0.027  0.002

Status report on  analysis

Ponza 05 June 2008

slide32

3 new samples

We have fix the cut on min c2< 5 obtaining:

LOW

Dc2 > 2.5

Pur  90.4%

e 21%

De / e 11%

Res  0.1335

N = 948471

MEDIUM

Dc2> 5

Pur  95%

e 14%

De / e 10%

Res 0.1108

N = 614663

HIGH

Dc2 > 9

Pur  97.3%

e 7%

De / e  10%

Res 0.096

N = 333493

slide33

Resolution & efficiency

Status report on analysis

slide34

Correction

We have corrected the Data / MC discrepancy (at level of 1.5 %)

with a smearing of the photon energies, obtaining:

slide35

Correction

We have recovered the residual discrepancy

(Low: h’ = 0.; Med: h’= 0.6%; High: h’ =0.9%),obtaining

slide36

Residuals in [0 – 0.7]

=  0.0301 ± 0.0035stat

slide40

Systematic checks: Resolution

The systematic uncertainty due to the resolution is obtained

considering the fluctuation in the RMSdata / RMS MC

slide41

Systematic checks: Efficiency

DATA

NHigh / Nlow = 0.3516 ± 0.0007

NMedium / Nlow = 0.6481 ± 0.0011

MC

NHigh / Nlow = 0.3511 ± 0.0003

NMedium / Nlow = 0.6461± 0.0005

slide42

Systematic checks: Efficiency

Correction to the photon efficiency is applied weighting the Montecarlo

events with a Fermi Dirac function obtained fitting the photon energy spectrum Data/MC discrepancy

slide44

Systematic checks: WPF

On DATA:

Wrong pair fraction (MC) = 9.59 %

Wrong pairfraction (DATA) = (10.01 ± 0.45) %

Wrong pairfraction (MC) = 5 %

Wrong pairfraction (DATA) = (5.51 ± 0.68) %

Wrong pair fraction (MC) = 2.7 %

Wrong pairfraction (DATA) = (3.31 ± 0.90) %

slide46

Systematic checks: WPF

On DATA:

Wrong pair fraction (MC) = 9.59 %

Wrong pairfraction (DATA) = (10.01 ± 0.45) %

Wrong pairfraction (MC) = 5 %

Wrong pairfraction (DATA) = (5.51 ± 0.68) %

Wrong pair fraction (MC) = 2.7 %

Wrong pairfraction (DATA) = (3.31 ± 0.90) %

slide47

Final results 10-4

Status report on analysis

slide48

Conclusion

2005: we have published this preliminary result:

= 0.013 ± 0.004stat ± 0.005 syst

2007: we have published this preliminary results:

= 0.027 ± 0.004stat ± 0.006 syst

2009: we found this result:

= 0.0301 ± 0.0035stat - 0.0036 syst + 0.0022 syst

This result is compatible with the published Crystal Ball result:

= 0.031 ± 0.004

And the calculations from the +- analysis using only the  -  rescattering in the final state.

= 0.038 ± 0.003stat +0.012-0.008syst