Dynamics of η→πππ

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

η−π@ KLOE

The decay η→π 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→πππ decay amplitude is approximately described by |A|2 ∝ 1 + 2αzWith:

Z ∈ [ 0 , 1 ]

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

Theory vs Experiment

η−π@ KLOE

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→πππ? [ DeAndrea, Nehme, Talavera PRD78(2008)034032 ]

Frascati 19 Luglio 2007

Sample selectionThe cuts used to select: η→π0π0π0are:

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%

Matching γto πs In order to select the best πππpairing, we introduce a pseudo−χ2 variable for each of the 15 possible pairs, cutting on: • Minimum χ2 value • Δχ2 between “best” and “second” combinationone can obtain samples with different purity-efficiency

Δχ2Δχ2minχ2 minχ2

Matching γto πs In order to select the best πππ pairing, we introduce a pseudo- χ2 variable for each of the 15 possible pairs, cutting on: • Minimum χ2 value • Δχ2 between “best” and “second” combinationone can obtain samples with different purity-efficiency

Δχ2

After pairing we perform kinematic fit with ηandπmass constraintηmass: MMC = 547.30 MeV /c2 MData = 547.822 MeV/c2

Δχ2

Samples

LOW MED I MED II MED III HIGH

min χ NO CUT < 10 < 5 < 3 < 2

Δχ NO CUT > 1.2 > 3 > 4 > 7

PUR 75.4 % 84.5 % 92 % 94.8 % 97.6 %

RES 0.2003 0.1663 0.1287 0.1099 0.0871

ε 30.3 % 22 % 13.6 % 9.2 % 4.3 %

Δεε 8 % 14 % 21 % 25 % 26 %

N(Mevts) 1.418 1.029 0.6459 0.4453 0.2123

ni = recostructed eventsνi = 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 α ztrue Weight the event with the fraction of combinatorial background, for the signal (bkg) if it has correct (wrong) pairing

Where:

We obtain an extimate by minimizing

The fit is done using a binned likelihood approach

This procedure relies heavily on MC.

Fit procedure

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.)

Low Med I Med II Med III High

α −0.0009 ± 0.0019 0.0002 ± 0.0021 0.0008 ± 0.0026

0.0022 ± 0.0030 0.0029 ± 0.0044

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 αand then we have compared the two procedures.

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 αand then we have compared the two procedures.

•Parameter scan:

Range α α−

α−

α−

α−

α−

α−

α−

0 − 1 10−15 % 25% 16% 40% 21% 12% 13% 8 %

0 − 0.9 10−8 % 84% 75% 78% 59% 41% 26% 18%

0 – 0.8 10−7% 73% 64% 67% 52% 35% 23% 17%

0 – 0.7 10−6 % 85% 83% 83% 71% 73% 54% 78%

0 – 0.6 10−6 % 94% 93% 95% 88% 89% 83% 78%

Frascati 19 Luglio 2007

Mean 134.2RMS 11.83

Mean 134.2RMS 11.99

Systematic checks

Systematic check

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

vs

Systematic check

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

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

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

Systematic check

Idea, try to fit the WPf on DATA.

To check procedure, we fit the WPf on MC:

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) %

WPf(MC) = 24.6 %WPf(MC fit) = (24.6 ± 0.2) %

Systematic checkOn DATA:

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) %

WPf (MC) = 24.6 % WPf (DATA) = (26.45 ± 0.26) %

Frascati 19 Luglio 2007

Systematic check

Results

α = − 0.027 ± 0.004stat ± 0.006 syst

χ2/ndf = 13.72 / 17.

Dalitz plot expansionNEW approach:

7 and only 7 pnc with 21° < θγ < 159° and Eγ > 10 MeV

θγγ > 18° Kin Fit with η mass constraint

(on DATA Mη= 547.822 MeV/c2 ) P(χ2) > 0.01 320 MeV < Eγrad < 400 MeV

AFTER PHOTON’S PAIRING

Kinematic Fit with πmass constraint

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 ηand π0 mass

constraints (on DATA Mη = 547.822 MeV/c2 )

NEW vs OLD

Pur %New

Pur %Old

RmsNew

RmsOld

Δε %New

Δε %Old

Data/Mcwpf

NewData/Mcwpf

Old

Low 82.2 75.4 .1864 .2003 12.4 8 1.11 1.07

MedI

89.4 84.5 .1465 .1663 15.8 14 1.22 1.07

MedII

95.1 92.1 .1141 .1287 21.9 21 1.53 1.12

Med III

97.1 94.8 .097 .1099 27.6 25 1.97 1.15

High 99.0 97.6 .080 .0871 26.7 26Not

converge1.35

Results OLD vs NEW

RangeLow· 10−3

Medium I · 10−3

Medium II· 10−3

Medium III· 10−3

High· 10−3

(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

(0, 1) − 36 ± 2 − 37 ± 2 − 37 ± 2 − 35 ± 3

(0, 0.8) − 36 ± 2 − 37 ± 2 − 34 ± 3 − 32 ± 3

(0, 0.7) − 38 ± 2 − 40 ± 3 − 36 ± 3 − 33 ± 3

(0, 0.6) − 44 ± 3 − 48 ± 4 − 42 ± 4 − 37 ± 4

NEW APPROACHOLD APPROACH

NEW or OLD ?

……OLD APPROACH !!

II Part MEMO 359 + x

Dalitz plot expansionNow we have updated the measurement of α using:

• Before the kinematic fit : θγγ

• In the kinematic fit on data : Mη = 547.874 ± 0.007 ±0.031MeV/c2

• MC sample generated according to α = -0.027

• New samples with different purity - efficiency

• A correction of about 2% to the photon energies in the π0 rest frame.

θγγ > 9°

After kinematic fit After P(χ2) > 0.01

After EVCL

After θγγ > 18°

After Eγ > 10 MeV

After 320 MeV < Eγrad < 400 MeV

θγγ > 9°

θγγ > 9°

θγγ >18°

> 15° > 12° > 9° > 6°

= 0°

PUR % 91 90.7 90.6 90.5 90.4 90.3

Δε % 18.4 15.6 12.4 10.7 9.9 9.6

PUR % 95.4 95.3 95.2 95.1 95 95

Δε% 22 18 12.6 10.3 10 8.8

PUR % 97.6 97.5 97.4 97.3 97.2 97.1

Δε% 16 13 12 10 9.6 8

Low

Med

High

θγγ > 9°

θγγ >18°

> 15° > 12° > 9° > 6°

= 0°

PUR % 91 90.7 90.6 90.5 90.4 90.3

Δε % 18.4 15.6 12.4 10.7 9.9 9.6

PUR % 95.4 95.3 95.2 95.1 95 95

Δε% 22 18 12.6 10.3 10 8.8

PUR % 97.6 97.5 97.4 97.3 97.1 97.1

Δε% 16 13 12 10 8 8

Low

Med

High

Ponza 05 June 2008

Status report on ηπanalysis

α input MC α fit on data0 -0.028 0.004

-0.026 -0.026 0.004

-0.028 -0.028 0.004

-0.030 -0.027 0.004

-0.032 -0.027 0.004

-0.034 -0.027 0.004

-0.036 -0.027 0.004

-0.038 -0.027 0.004

-0.040 -0.027 0.004

-0.042 -0.027 0.004

-0.044 -0.027 0.004

-0.046 -0.027 0.004

-0.048 -0.027 0.004

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

On this MC sample:α- 0.027 0.002

New MC sample We have generated MC samples with different α values in input and we have fitted αon data

LOWΔχ2 > 2.5Pur 90.4%

ε 21%

Δεε 11%Res 0.1335N = 948471

MEDIUMΔχ> 5Pur 95%

ε 14%

Δεε 10%Res 0.1108N = 614663

HIGHΔχ> 9Pur 97.3%

ε 7%

Δεε 10%Res 0.096N = 333493

3 new samples

We have fix the cut on min χ2< 5 obtaining:

Status report on ηπanalysis

Resolution & efficiency

CorrectionWe have corrected the Data / MC discrepancy (at level of We have corrected the Data / MC discrepancy (at level of 1.5 %)with a smearing of the photon energies, obtaining:with a smearing of the photon energies, obtaining:

CorrectionWe have recovered the residual discrepancy We have recovered the residual discrepancy (Low: (Low: ηη’ = 0.; Med: ’ = 0.; Med: ηη’= 0.6%; High: ’= 0.6%; High: ηη’ =0.9%)’ =0.9%),, obtainingobtaining

RangeLow

· 104Medium

· 104High

· 104

(0, 1) 288 ± 22 281 ± 26 289 ± 34

(0, 0.8) 313 ± 26 288 ± 31 295 ± 42

(0, 0.7) 319 ± 29 301 ± 35 308 ± 47

(0, 0.6) 348 ± 31 330 ± 44 343 ± 60

Residuals in [0 – 0.7] = 0.0301 ± 0.0035stat

Systematic checks: Resolution

Systematic checks: Resolution

Systematic checks: Resolution

Systematic checks: ResolutionThe systematic uncertainty due to the resolution is obtained The systematic uncertainty due to the resolution is obtained considering the fluctuation in the RMSdata / RMS MC considering the fluctuation in the RMSdata / RMS MC

EffectLOW

· 104

MEDIUM

· 104

HIGH

· 104

Res -4 +4 -4 +4 -2 +2

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

Systematic checks: Efficiency

Correction to the photon efficiency is applied weighting the Montecarloevents with a Fermi Dirac function obtained fitting the photon energy spectrum Data/MC discrepancy

Systematic checks: Efficiency

HighHigh MediumMedium

LowLow EffectLOW

· 104

MEDIUM

· 104

HIGH

· 104

Low Eγ -5 -3 -5

On DATA:

Wrong pair fraction (MC) = 5 %Wrong pair fraction (DATA) = (5.51 ± 0.68) %

Wrong pair fraction (MC) = 2.7 %Wrong pair fraction (DATA) = (3.31 ± 0.90) %

Wrong pair fraction (MC) = 9.59 % Wrong pair fraction (DATA) = (10.01 ± 0.45) %

Systematic checks: WPF

Systematic checks: WPF

On DATA:

Wrong pair fraction (MC) = 5 %Wrong pair fraction (DATA) = (5.51 ± 0.68) %

Wrong pair fraction (MC) = 2.7 %Wrong pair fraction (DATA) = (3.31 ± 0.90) %

Wrong pair fraction (MC) = 9.59 % Wrong pair fraction (DATA) = (10.01 ± 0.45) %

Systematic checks: WPF

EffectLOW

· 104

MEDIUM

· 104

HIGH

· 104

Bkg -7 +5 -6 +5 -16 +17

Status report on ηπanalysis

RangeLow

· 104Medium

· 104High

· 104

(0, 1) 288 ± 22 281 ± 26 289 ± 34

(0, 0.8) 313 ± 26 288 ± 31 295 ± 42

(0, 0.7) 319 ± 29 301 ± 35 308 ± 47

(0, 0.6) 348 ± 31 330 ± 44 343 ± 60

EffectLOW

· 104

MEDIUM

· 104

HIGH

· 104

Res -4 +4 -4 +4 -2 +2

Low Eγ -5 -3 -5

Bkg -7 +5 -6 +5 -16 +17

Mη -6 +5 -2 +6 -1 +5

Range -29 +31 -29 +20 35 +19

Purity +15 -18 4 +11

Tot -31 +35 -36 +22 -40 +28

Final results 10-4

Conclusion

= 0.0301 ± 0.0035stat - 0.0036 syst + 0.0022 syst

2005: we have published this preliminary result:

= 0.027 ± 0.004stat ± 0.006 syst

2009: we found this result:

2007: we have published this preliminary results:

= 0.013 ± 0.004stat ± 0.005 syst

This result is compatible with the published Crystal Ball result: = 0.031 ± 0.004

And the calculations from the ηπ+π-π analysis using only the π - π rescattering in the final state.

= 0.038 ± 0.003stat +0.012

-0.008 syst