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## Dynamics of η → π 0 π 0 π 0

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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
- 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

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

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

- 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 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 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

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.

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

- 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.

- 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:

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

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

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

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

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

Frascati 19 Luglio 2007

- 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 )

- 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.

After kinematic fit

After P(2) > 0.01

After E> 10 MeV

After EVCL

After 320 MeV < Erad < 400 MeV

Afterg > 18°

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

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

Status report on analysis

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

with a smearing of the photon energies, obtaining:

We have recovered the residual discrepancy

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

= 0.0301 ± 0.0035stat

The systematic uncertainty due to the resolution is obtained

considering the fluctuation in the RMSdata / RMS MC

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

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

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) %

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) %

Status report on analysis

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

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