1. Results on 30 and  + - 0 from KLOE
F.Ambrosino, T. Capussela, F.Perfetto
Università Federico II Napoli
INFN Sezione di Napoli
for the KLOE Collaboration
Ponza 05 une 2008

2. KLOE @ DAFNE Data taking ended on March 2006
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
DAFNE
Drift chamber (4 m Ø × 3.75 m)
Gas mixture 90% He + 10% C4H10
12582 stereo sense wires
dpt / pt < 0.4% (q>45°)
xy  150 m ; z  2 mm
Data taking ended on March 2006
2.5 fb-1 on s = Mf
(8109 f)  ~ 108   ~ 5 105 ‘
~ , 1018, 1023, 1030 MeV
MeV
Integrated luminosity:
2005: 1256 pb-1
2004: pb-1
2002: pb-1
2001: pb-1
Electromagnetic calorimeter
lead/scintillating fibers (1 mm ), 15 X0
98% solid angle coverage
sE / E = 5.7% / (E(GeV))
st = 57 ps / (E(GeV))  100 ps
PID capabilities

3. Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
KLOE
At KLOE  is produced in the process  rec (Eg = 363 MeV)
From data taking period, Lint = 418 pb-1
The final state for  +-0 is thus +-, and the final state for  000 is 7, both with almost no physical background.
N( )  17 Mevts.
+-0 selection:
2 track vertex + 3g candidates
Kinematic fit

4. h->3p @ KLOE 0 0 0 selection:
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
KLOE
At KLOE  is produced in the process  rec (Eg = 363 MeV)
From data taking period, Lint = 418 pb-1
The final state for  +-0 is thus +-, and the final state for  000 is 7, both with almost no physical background.
N( )  17 Mevts.
0 0 0 selection:
7 candidates
Kinematic fit
+-0 selection:
2 track vertex + 3g candidates
Kinematic fit

5. Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Dalitz plot expansion
The dynamics of the 3p0 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 + 2z
With:
Z  [ 0 , 1 ]
Ei = Energy of the i-th pion in the  rest frame.
 = Distance to the center of Dalitz plot.
max = Maximun value of .

6. Matching to s Recoil  is the most energetic cluster.
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Matching to s
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
= MeV
is obtained as function of photon energies

7. Energy resolution 8 April 2009 Frascati
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Energy resolution

8. Matching to s Cutting on: Minimum 2 value
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Matching to s
After pairing we perform kinematic fit with h and 0 mass constraint
Cutting on:
Minimum 2 value
2 between “best” and “second” combination
One can obtain samples with different purity-efficiency
LOW
Pur  75.4%
Eff  30.3 %
N  1.42 Mevts
MEDIUM
Pur  92%
Eff  13.6 %
N  0.65 Mevts
HIGH
Pur  97.6%
Eff  4.3 %
N  0.22 Mevts

9. Resolution & efficiency
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Resolution & efficiency
RMS
RMS
N eventi MC 24 Milioni

10. Fit procedure This procedure relies heavily on MC.
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Fit procedure
The fit is done using a binned likelihood approach
We obtain an extimate by minimizing
Where:
ni = recostructed events
i = 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  ztrue
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.

11. Comparison Data - MC 8 April 2009 Frascati
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Comparison Data - MC

12. Result  = 0.027 ± 0.004stat + 0.004-0.006 syst
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Result
KLOE preliminary arXiv
We give the preliminary result for the slope parameter a using evts with 92% purity.
Fitting the Z distribution in the range [0 0.7] we get:
 = 0.027 ± 0.004stat syst
To check systematics we used samples with purity ranging from 75 % to 98% corresponding to datasets going from 1.4 Mevts to 0.2 Mevts.

13. Result  = 0.027 ± 0.004stat + 0.004-0.006 syst
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Result
KLOE preliminary arXiv
We give the preliminary result for the slope parameter a using evts with 92% purity.
Fitting the Z distribution in the range [0 0.7] we get:
 = 0.027 ± 0.004stat syst
To check systematics we used samples with purity ranging from 75 % to 98% corresponding to datasets going from 1.4 Mevts to 0.2 Mevts.

14. Result: Theory vs. experiment
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Result: Theory vs. experiment a
Tree
One-Loop
NNLO
Dispersive
Tree dispersive
Abs. dispersive
Unitary approach
0.000
0.013 
-0.006
-0.007
-0.031
J. Bijnens, K.Ghorbani JHEP11(2007)030

15. Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
h->p+p-p0 dynamics
We expand the decay amplitude about the center of
Dalitz plot as :
|A(X,Y)|2 = 1+aY+bY2+cX+dX2+eXY+fY3
Where:

16. Resolution & Efficiency
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Resolution & Efficiency
“core”
sX =
0.018
“core”
sY =
0.020

17. Resolution & Efficiency
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Resolution & Efficiency
“core”
sX =
0.018
Efficiency almost flat, and ≈35%
“core”
sY =
0.020

18. Background contamination
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Background contamination
The bkg depends on the cut value for the variable M
B/S ≈ 0.7 %
NO CUT
B/S ≈ 0.3 %
M  [110, 160]

19. Comparison Data – MC 8 April 2009 Frascati
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Comparison Data – MC

20. The fit procedure The fit is done using a binned 2 approach
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
The fit procedure
The fit is done using a binned 2 approach
i is for each bin: the efficiency as a function of Dalitz-plot.
Ni is for each bin: the number of events of Dalitz-plot.
i is the statistical error on the ratio Ni / I.
All the bins are included in the fit apart from the bins crossed by the Dalitz plot contour.

21. Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Results
Nobs = (1.377±0.001) 106
B/S 0.3 %
A(X,Y)2 ≈ 1 + aY + bY2 + cX + dX2 + eXY +fY3 + gX3 + hX2+lXY2
g, h, l consistent with zero.

22. Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Results
Nobs = (1.377±0.001) 106
B/S 0.3 %
A(X,Y)2 ≈ 1 + aY + bY2 + cX + dX2 + eXY +fY3 + gX3 + hX2Y + lXY2
g, h, l consistent with zero.

23. Results ndf P2 % a b c d e f 8 April 2009 Frascati
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Results
ndf
P2 % a b c d e f
147 73
1.090  0.005
0.124  0.006
0.002  0.003
0.057  0.006
0.006  0.007
0.14  0.01
149 74
---
150
< 106
1.069  0.005
0.104  0.005
0.13  0.01
< 108
1.041  0.003
0.145  0.006
0.050  0.006
151
1.026  0.003
0.125  0.006

24. Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Goodness of fit
Comparison between efficiency corrected data and fitted function as function of the bin number.

25. Systematic uncertainties
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Systematic uncertainties
1) The final evaluation for the slope parameters has been given for NbinX = NbinY = 16, (X=Y=0.13 much larger than the X and Y resolutions X = 0.020, Y = 0.019). The effect associated to this choice:
a=0.008/ b=0.006/ d= 0.007/0.001 f=0.02/0.02
2) Fitting the Dalitz plot distribution requiring or no the event selection procedure (EVCL) on a minimum bias sample, we quote:
a =  b = d =  f = 0.01
3) Changing the cut on Mgg in a wide range, corresponding to a background change from 0.7% to 0.2%, we find
a = 0.001/0.006 b = 0.008/0.006 d = 0.007/ f = -0.01

26. Results: Theory vs. Experiment
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Results: Theory vs. Experiment
|A(X,Y)|2 = 1+aY+bY2+cX+dX2+eXY+fY3
KLOE JHEP(05)
a b d f
Tree
One-loop
NNLO
Dispersive
Tree dispersive
Abs dispersive
J. Bijnens, K.Ghorbani JHEP11(2007)030

27. Asymmetries In agreement with the null value
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Asymmetries
Left – Right C
Quadrant C (DI =2)
Sextant C (DI =1)
ALR = (0.09 ± ) ·10-2
AQ = (0.05 ± ) ·10-2
AS = (0.08 ± ) ·10-2
In agreement with the null value
of the c and e parameters in our
fit, we find no evidence for C
violation in the h->p+p-p0 decay.
ALR = (0.09 ± 0.17) ·10-2
AQ = (-0.17 ± 0.17) ·10-2
AS = (0.18 ± 0.17) ·10-2
PDG 08

28. Alternative parametrization (I)
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Alternative parametrization (I)
Since strong interactions are expected to mix the two isospin I = 1 final states of the h->3p decay, it is possible to introduce a unique rescattering matrix R which mixes the corresponding decay amplitudes [1]:
where
and
The complete amplitudes, keeping the expansion in powers of x and y
up to quadratic terms, are:
[1] G.D’Ambrosio, G.Isidori,A.Pugliese, N.Paver Phys.Rev D50 (1994) 5767
h->3p Dalitz plot analysis

29. Alternative parametrization (II)
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Alternative parametrization (II)
Using the above parametrization to fit the Dalitz plot we obtain:
CL 74%
and:
In agreement with the PDG average a = 0.031± and
the KLOE result a = 0.027±

30. Conclusions The h30 analysis is quite complex, but looks
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Conclusions
The h30 analysis is quite complex, but looks
also quite solid in the fitting procedure.
We are reducing the systematic uncertainties on a.
New accurate results have been pubblished
(JHEP05(2008)006) for both Dalitz plot and
asymmetries in h->p+p-p0.
Fitting the h->p+p-p0 Dalitz plot with a different parametrization we obtained a prediction for the h30 slope which is consistent with the PDG average

31. Spare

32. Cusp effect
Looking at the cusps effects in 92% purity ( e  14%):
Nh30 =  Mevts Lint = 2.2 fb-1 ( KLOE)
Nh30 =  Mevts Lint = 418 pb-1 ( KLOE)
Nh30 =  Mevts Lint = 20 fb ( KLOE – 2 )
s(min pp mass)
 18 MeV/c2

33. Cusp effect
Nevts per 2 MeV/c2
1 s
Nevts per 2 MeV/c2
1 s
1 s
1 s

34. h->3p in chiral theory
The decay violates iso-spin invariance and itis induced dominantly by the strong interaction via the u, d quark mass difference. To lowest order in the chiral expansion:
With :
and, at l.o
A good understanding of M(s,t,u) can in principle lead to a very
accurate determination of Q:
Need to check the description
of the dynamics for both p+p-p0
and 3p0 final states

35. Dalitz plot expansion

36. Resolution vs. purity RMS = 0.2003 RMS = 0.1864 RMS = 0.1287
Low purity
RMS =
RMS =
RMS =
Medium II purity
RMS =
RMS = 0.080
High purity

37. Linearity of DATA / MC ratio
Idea: check linearity of DATA/MCreco using for MC pure phase space…
low purity = High statistics…

38. 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 ?

39. A toy MC
To understand the effect we used a toy MC to generate events with different eta masses:
Sample 1 : M = MeV
Sample 2 : M = 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 = MeV to build the “z” variable for sample 2 big deviations are observed……..
Z2(547.8)/Z1(547.3)

40. A toy MC Z2(547.3)/Z1(547.3) Z2(547.8)/Z1(547.3)
To understand the effect we used a toy MC to generate events with different eta masses:
Sample 1 : M = MeV
Sample 2 : M = 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 = MeV to build the “z” variable for sample 2 big deviations are observed……..
Z2(547.3)/Z1(547.3)
Z2(547.8)/Z1(547.3)

41. Linearity
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)
@ Low purity

42. Results of fit on MC This procedure relies heavily 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:
This procedure relies heavily on MC.

43. Comparison Data MC
A first check on resolution is from pion mass distribution

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

45. Fitting the combinatorial background
On DATA:
Wrong pair fraction (MC) = 24.6 %
Wrong pair fraction (DATA) = (26.45 ± 0.26) %
Wrong pair fraction (MC) = 15.5 %
Wrong pair fraction (DATA) = (16.7 ± 0.28) %
Wrong pair fraction (MC) = 7.9 %
Wrong pair fraction (DATA) = (8.98 ± 0.37) %
Wrong pair fraction (MC) = 5.2 %
Wrong pair fraction (DATA) = (5.2 ± 0.45) %
the correction used in the fit are for Low…. High
Wrong pair fraction (MC) = 2.4 %
Wrong pair fraction (DATA) = (3.47 ± 1.00) %

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

47. Resolution
A further check can be done comparing the energies of the two photons in the pion rest frame as function of pion energy
dalle slice in bin di Epio abbiamo preso le RMS di Eg1 -Eg2
A data MC discrepancy at level of 12 % is observed.
Thus we fit filling a histo with:
z’rec = zgen + (zrec  zgen ).

48. Background
Background composition, Medium II purity sample

49. Mh evaluation
M (MC) = MeV
M (PDG) =  MeV
M (Data) =  (stat) MeV
For the same events no shift in the peak value of the  invariant mass is observed.

50. Mgg

51. Systematic uncertainties
Joint Collaborations Meeting on 3 decays
8 April 2009 Frascati
DAfNE h->3p0 h->p+p-p0 Conclusions
Systematic uncertainties
The systematic error due to bkg subtraction
M (MeV/c2)
P2 (%) a b d f
B/S (%)
 [80, 190] 82
1.084  0.005
0.116  0.006
0.050  0.006
0.14  0.01
0.4
 [90, 180]
1.086  0.005
0.117  0.006
0.052  0.006
 [100, 170] 75
1.087  0.005
0.118  0.006
0.053  0.006
0.3
 [110, 160] 74
1.090  0.005
0.124  0.006
0.057  0.006
 [115, 155] 71
1.091  0.005
0.128  0.006
0.060  0.006
0.2
 [120, 150] 58
1.089  0.006
0.130  0.006
0.064  0.006
0.13  0.01

52. Selection efficiency We use   +0 control sample VERTEX TRACKING
+ MC
+ Data
VERTEX
TRACKING

53. Cluster efficiency
In the simplest approach we obtain directly a correction to the photon efficiency by weighting the Montecarlo events with a Fermi-Dirac function obtained fitting the photon energy spectrum Data-MC discrepancy. Other corrections to photon efficiency give slightly different absolute scales but very similar effects in X&Y.
The visible effect is negligigle for the parameters evaluation

54. Radiative correction
To include the radiative correction in the MC simulation we have used a generator   +0 .
The ratio of the two plots has been fitted with the usual expansion: corrections to parameters are compatible with zero.

55. Time stability
To check stability wrt data taking conditions we fit the integrated Dalitz plot in samples of 4 pb1 each

56. Alternative parametrization
The rescattering phases depend on the x and y variables as:
Where a0=0.18, a0’’ =-0.11 ,b0 =0.06, b0 ’ =-0.022,
are obtained from [1], after rescaling from kaon to h mass.
Note that now, x = (u – t) / m2 and y = (s - s0) / m2.
[1] G.D’Ambrosio, G.Isidori,A.Pugliese, N.Paver Phys.Rev D50 (1994) 5767

57. Correlations a b d f 1
-0.226
-0.405
-0.795
0.358
0.261
0.113

58. Correlation new rab = 0.058 , rac= -0.865, rbc = -0.046
Introduction Theoretical Tools Analysis Conclusions
Correlation new
rab = , rac= , rbc =
h->3p Dalitz plot analysis
Flavianet Kaon Workshop Anacapri June 2008

59. Residuals distribution

60. Goodness of fit Comparison between efficiency corrected data and
fitted function in X and Y projections

61. Q2 Using preliminary KLOE results
|A(X,Y)|2 = Y+0.117Y X2+0.13Y3
B.V. Martemyanov and V.S. Sopov (hep-ph\ ) have extracted:
Q = 22.8 ± against QDashen= 24.2
Remember: