1. KLOE results on  decays
LNF Spring School “Bruno Touschek”
Frascati, 16–20 May 2005
F. Perfetto (Università di Napoli “Federico II”  INFN)
for the KLOE Collaboration
Dynamics of →  decay
BR of → 0

2. The → decay in PT
The amplitude of the →  decay occurs primarily due to
the d-u quark mass difference.
From lowest order Chiral Pertubation Theory:
with
and, at L.O. ,
A good understanding of M(s,t,u) can lead to a very accurate determination of Q:
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

3.  3 @ KLOE +-0 selection: 000 selection:
At KLOE  is produced in the process  .
N( )  17 Mevts.
The final state for  +-0 is thus +-, and the final state for  000 is 7, both with almost no physical background.
000 selection:
7 candidates
Kinematic fit
+-0 selection:
2 track vertex + 3 candidates
Kinematic fit
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

4. The → +-0 Dalitz plot
Dalitz shape
X(T+-T-) , YT0
“core”
Y = 0.027
“core”
X = 0.018
Efficiency  36% , almost flat
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

5. Fit to the → +-0 Dalitz plot
|A(X,Y)|2 = 1+aY+bY2+cX+dX2+eXY+fY3
c and e are C violating
KLOE Preliminary
Ndf
P2 (%) a b c d e f
147 60
 0.006
-0.007
+0.005
0.117  0.006 
0.047 0.006
-0.0060.008
0.13 0.01
1 63
 0.005
0.005
---
IN THIS TABLE WE SHOW THE RESULTS OF THE FIT TO THE DALITZ PLOT FOR DIFFERENT PARAMETRIZATION OF AMPLITUDE.
WE ARE SENSITIVE TO CUBIC SLOPE IN Y, NEVER MESURED BEFORE.
IN AGREEMENT TO C CONSERVATION THE C AND E PARAMETERS ARE CONSISTENT WITH ZERO.
FIXING THIS PARAMETERS TO ZERO WE OBTAIN THE SAME RESULTS.
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

6. Q evaluation
Using this preliminary KLOE result:
[B.V. Martemyanov and V.S. Sopov, PRD 71 (2005) ]
Q = 22.8 ± 0.4
This result is in agreement with:
Q = 22.0 ± [J.Donoghue and A.Perez, PRD 55 (1997) 7075]
[J.Bijnens and J.Prades, NPB 490 (1997) 239]
Q = 22.4 ± [J.Kambor., C.Wiesendanger and D.Whyler, NPB 465 (1996) 215]
Q = 22.7 ± [A.V.Anisovich and H.Leutwyler, PLB 375 (1997) 335]
The theoretical error is currently dominated by PDG error on (→ )
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

7. Asymmetries KLOE Preliminary 1 2 3 4 577741 577849
196104
196264
381585
381637
577741
577849
64082
304455
209204
209043
304930
63876
A = (  0.093)  10-2
Aq = (-0.02  0.09)  10-2
As = (0.07  0.09)  10-2
ASIMMETRY IS SENSITIVE TO I=0,1,2 C VIOLATING FINAL STATES
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

8. Dalitz plot expansion 
The Dalitz plot density for   000 ( |A|2 ) is specified by a single parameter:
|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 .
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

9. Matching  to 0 ‘s
A 2 like variable is built for each of the 15 combinations in order to find the correct matching of photons to 0 ‘s
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 0 ‘s
Best purity obtained is 98.5%
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

10. Results on MC Phase space Reconstructed Resolution
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

11. Preliminary result  = 0.014  0.004stat  0.005syst
We have analyzed 415 pb-1 of data and we find the preliminary result, on the high purity sample:
KLOE Preliminary
 = 0.014  0.004stat  0.005syst
 = 0.031 ± 0.004stat+syst
Cfr. current best measurement (Crystal Ball):
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

12. → 0: a window on p6 PT…8 p2
L2 contributions
at tree level:
= 0 (Q = 0)
Coupling proportional to the charges, zero also for tree level. 
+,K+
-,K- 0 8
1-loop contributions from L2 vertices, suppressed by G parity conservation and kaon mass suppression: p4
-loops = 0.84 ×10-3 eV
K-loops = 2.45 ×10-3 eV
THERE IS NO CONTRIBUTION AT THIS LEVEL.
AT NEXT ORDER THE CONTRIBUTION FROM PION-LOOP AND K-LOOP ARE VERY SMALL.
SO THE DOMINANT CONTRIBUTION COME FROM P6, AND THIS ARE THE RESULTS.
L6 coefficients determined by the meson propagator. Th. expectations:
6VMD = ( 0.42 ± 0.20 ) eV
6ENJL = ( 0.58 ± ) eV
6Ch unit = ( 0.47 ± 0.10 ) eV 
0, ,  0  8 a0 0  p6
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

13. Analysis of → 0 @ KLOE}
 → 
0
5 final state
 ~ 8 pb BR = (7.2  1.4)  104
GAMS2000
Background candidates:
Process
 (pb)
e+e-→0, →0, 0→
450
→f0, f0→00, 0→
300
→a0, a0→0, /0→
260
→, →
17000
→, →000
13000
Process
 (pb)
e+e-→0, →0, 0→
450
→f0, f0→00, 0→
300
→a0, a0→0, /0→
260
→, →
17000
→, →000
13000
Process
 (pb)
e+e-→0, →0, 0→
450
→f0, f0→00, 0→
300
→a0 a0→0, /0→
260
→, →
17000
→, →000
13000
Rejected with veto on additional -0-
Rejected with energy momentum conservation and likelihood technique to identify splitted/merged clusters
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

14. BR(→ 0) = ( 8.4 ± 2.7stat ± 1.4syst ) × 10-5
→ 0: BR evaluation
Fit of data with superposition of background and signal shape.
NDATA = 735
Nbkg = 667  36
Nsig = 68  23
N(30) = 2,288,882
THIS IS THE DISTRIBUTION OF INVARIANT MASS OF LESS ENERGETIC PHOTONS IN RED….
BR(→ 0) = ( 8.4 ± 2.7stat ± 1.4syst ) × 10-5
KLOE Preliminary
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

15. BR(→ 0: comparison with models
GAMS (1984)
Crystal Ball
(2004)
KLOE
…. THE MEASURE IS SMALLER BY A FACTOR 3 WITH RESPECT TO CRYSTALL BALL
KLOE 1
KLOE 2
KLOE 3
P6 calculations
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

16. Conclusions
We are analyzing an unprecedented statistics of 3 decays with negligible background and we have new and accurate values for the Dalitz plot slopes of both +-0 and 30 final states.
We measure a value of BR(0) smaller by factor 3 w.r.t. recent Crystal Ball value (and an order of magnitude smaller than PDG value) still significantly different from zero, and in agreement with PT p6 calculations.
KLOE as already published the best upper limit on C, P(C) violating decay ():
BR()  1.3  [PLB 606 (2005) 276]
BR()  1.6  [PLB 591 (2004) 49]
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

17. Spare slides
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

18. … and an experimental challenge!
p- + p ® h + n
(CERN, Brookhaven, GAMS, Crystal Ball)
p+ + d ® p + p + h (67)
p+ + p ® p+ + p +h (67,69)
K- + p ® L + h (70 AGS)
p+ + n ® h + p (71)
p- + n ® p- + n + h (80)
f ®hg (SND 01)
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

19. Fit to the → +-0 Dalitz plot
|A(X,Y)|2 = 1+aY+bY2+cX+dX2+eXY+fY3
c and e are C violating
KLOE Preliminary
Ndf
P2 (%) a b c d e f
147 60
 0.006
0.117  0.006 
0.047 0.006
0.008
0.13 0.01
150 63
 0.005
0.005
---
0.02
 0.004
0.006
0.100 0.005
0.120.01
 0.003
0.004
0.120  0.005
0.043 0.006
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

20. Dalitz expansion: theory vs experiment
Calculation
a b d
Tree
One-loop[1]
Dispersive[2]
Tree dispersive
Absolute dispersive
[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)
Measurement N
a b d
Layter
Gormley
Crystal Barrel
80884
30000
1077
3230
-1.08    0.031
-1.17    0.04
-0.94  0.27
-1.22   fixed
Tabella sperimentale di Bijnens
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

21. Fit stability
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

22. Dalitz expansion: theory vs experiment
Calculation 
Tree
One-loop[1]
Dispersive[2]
Tree dispersive
Absolute dispersive
0.00
0.0015 
-0.006
-0.007
[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)
Alde (1984)  0.023
Crystal Barrel (1998)  0.020
Crystal Ball (2001)  0.004
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005

23. 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
Francesco Perfetto LNF Spring School "Bruno Touschek" May 20, 2005