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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