Euridice Midterm Meeting

1
Study of h? ppp Dalitz plot at KLOE
F.Ambrosino Università e Sezione INFN, Napoli for
the KLOE collaboration

• Motivations
• h? pp-p0
• h? p0p0p0
• Conclusions and outlook

2
h?3p in chiral theory
The decay h ? 3 p occours primarily on account
of the d-u quark mass differences and the result
arising from lowest order chiral pertubation
theory is well known

And, at l.o.
With
A good understanding of M(s,t,u) can in principle
lead to a very accurate determination of Q
3
and its open questions

• Still there are some intriguing questions for
  this decay
• Why is it experimental width so large (270 eV)
  w.r.t theoretical calculation ? (Tree level 66
  eV (!!!) 1 loop 160 eV ) Possible answers
• Final state interaction
• Scalar intermediate states
• Violation of Dashen theorem
• Is the dynamics of the decay correctly described
  by theoretical calculations ?

4
Dalitz plot expansion
The usual expansion of square modulus of the
decay amplitude about the center of the Dalitz
plot is A(s,t,u)2 1 aY
bY2 cX dX2 eXY Where
5
Dalitz expansion theory vs experiment
1 Gasser,J. and Leutwyler, H., Nucl.
Phys. B 250, 539 (1985) 2 Kambor, J.,
Wiesendanger, C. and Wyler, D., Nucl. Phys. B
465, 215 (1996)
Tabella sperimentale di Bijnens
6
h ?3p at KLOE
At KLOE h is produced in the process f? hg . The
final state for h ?pp-p0 is thus ??-???, and
the final state for h ?p0p0p0 is 7g, both with
almost no physical background.

• Selection
• 2 track vertex3 g candidates
• Kinematic fit

7
Resolutions and efficiency
core sY 0.027
Efficiency almost flat, and ? 36
8
Comparison Data-MC p

9
Comparison Data-MC p-

10
Signal
B/S ? 0.8

11
Fitting function

• The analysis has been applied on 450 pb1
  corresponding to
• N(????-?0) 1,425,131
• events in the Dalitz plot, fitted with function
• fit is stable
• but the model seems not to fit adeguately data
  (BAD Pc2).
• We have added the cubic terms

A(X,Y)2 1aYbY2cXdX2eXY

A(X,Y)2 1aYbY2cXdX2eXYfY3gX3hX2YlXY2
12
Fit stability

13
Results

A(X,Y)2 1aYbY2cXdX2eXYfY3
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Results (II)
A(X,Y)2 1-1.072 Y0.117 Y20.047 X20.13Y3
Using preliminary KLOE results shown at ICHEP 04
B.V. Martemyanov and V.S. Sopov
(hep-ph\0502023) have extracted
Q 22.8 0.4 against Qdashen 24.2

(as already argued for example in J. Bijnens and
J. Prades, Nucl. Phys. B490, 239 (1997)
15
h ? 3p0 Dalitz plot expansion
The dynamics of the h ? p0 p0 p0 decay can be
studied analysing the Dalitz plot distribution.
The Dalitz plot density ( A2 ) is specified by
a single parameter A2 ? 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 ?.
16
Dalitz expansion theory vs experiment
1 Gasser,J. and Leutwyler, H., Nucl.
Phys. B 250, 539 (1985) 2 Kambor, J.,
Wiesendanger, C. and Wyler, D., Nucl. Phys. B
465, 215 (1996)
17
Photons pairing
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
134.98 MeV
is obtained as function of photon energies
18
Combination selection

• Cutting on
• Minimum ?2 value
• ??2 between best and second combination
• One can obtain samples with different
  purity-efficiency
• Purity Fraction of events with all photons
  correctly matched to p0 s
  
  

19
The problem of resolution

MC reconstructed
Phase space
Resolution
Efficiency
20
Results on MC
21
Results on MC
22
Results on MC
23
Comparison Data - MC
The agreement is good on all spectra
24
Fitting Data
Low purity
Medium purity
High purity
Systematics are at the same level of the
statistical error
25
Conclusions

• KLOE is analyzing an unprecedented statistics of
  h?3p decays with negligible background
• For pp-p0 channel the analysis is almost
  completed and finds evidence for an unexpected
  large y3 term
• 3 p0 analysis is much harder, we expect to
  provide soon a result at the same level of the
  Crystal Ball one.

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SPARE SLIDES
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Kinematic fit with no mass constrains

28
Tests of the fit procedure on MC
Generator slopes in MC rad-04 a -1.04 b
0.14 c 0. d 0.06 e 0. KLOE measure (100
pb-1)

29
Comparison Data-MC

? data ? MC
A.U.
30
Comparison Data-MC Ych Y0

Shift ? 1.33 MeV
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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.

32
Comparison Data-MC X Y

33
Goodness of fit
Comparison between efficiency corrected data and
fitted function as function of the bin
number. The structure observed is due to the Y
distribution for X slices
P(?2 ? ?02) ? 60
34
Asymmetries
-

As (0.07 ? 0.09) ? 10-2
A (-0.009 ? 0.093) ? 10-2
Aq (-0.02 ? 0.09) ? 10-2

35
h? pp-p0(g)
We have tested the effect of radiative
corrections to the Dalitz plot density.
The ratio of the two plots has been fitted with
the usual expansion corrections to parameters
are compatible with zero
36
h? pp-p0 time stability
To check stability wrt data taking conditions we
fit the integrated Dalitz plot in samples of 4
pb-1 each
37
Check on cubic term
Fitted function is actually
Assume
No cubic dependence in A(X,Y)2 A(X,Y)2 1
aY bY2 dX2 with a ? -1. Can evaluate a
such as to mimic the cubic term.

38
MC
MC weighted
p
MC
MC weighted
p-
39
Sample selection

• The cuts used to select h ? p0 p0 p0 are
• 7 and only 7 prompt neutral clusters with 21 lt
  ?? lt 159
• and E? gt 10 MeV
• opening angle between each couple of photons gt
  18
• Kinematic Fit with no mass constraint
• 320 MeV lt E?rad lt 400 MeV
• P(?2) gt 0.01

40

41
Second kinematic fit
Once a combination has been selected, one can do
a second kinematic fit imposing ?0 mass for each
couple of photons.
42
Doing it the hard way..
Still we minimize
But now
ni recostructed events ?i from each single MC
recostructed event weighted with the
theoretical function
43
Comparison Data MC (II)
The center of Dalitz plot correspond to 3 pions
with the same energy (Ei M?/3 182.4 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
44
Comparison Data MC (II)
Eg1 - Eg2
Vs. Ep