1. Update of the Milano Dalitz Plot Analysis
Paolo Dini
Sandra Malvezzi
and ...
Because, you
know ….
...Luigi Moroni
E831-FOCUS meeting - Mar 19-20th 2000

2. Talk outline
The K-Matrix formalism for the coupled channel scalars ( f o(980) a o (980) ).
A better background parameterization: polynomial + Breit - Wigner
Further generalization of the analysis code:
arbitrary number of resonances in the model
arbitrary number of resonances in the background
Update results on :
Ds p-p+p and D p-p+p+
Ds K-K+ p + and D K-K+ p+
D K- p + p +

3. What is the f o(980) problem ?
In the E687 Dalitz Plot analyses we used the f o(980) coupled channel measured by WA76. If one makes a comparison between the Dalitz Plot of Ds f o p+ obtained by E831 data and Mini MC data ( generated using wa76 model for the f o ) :
E831 Data
Mini MC Data
Narrow f o
Large f o

4. f o f o E831 data WA76 model scalar model f o is better described
by a simple BW !
f o
f o

5. f o described by a simple BW
f o described by WA76
Fit Fraction.:
NR = ( 26  5)%
f o = (112  6) %
-2 ln L = 2295
f o described by a simple BW
Fit Fraction.:
NR = ( 15  4)%
f o = ( 76  4) %
-2 ln L = 2275
NR seems to
compensate
the larger tails
of the WA76
model

6. How to solve the f o(980) problem ?
trying to use new values for the coupling costants gK e gp measured
by WA improvements in the quality of the fit and in -2 ln L.
(see the next slide )
searching a correct method that allows us to use our data to define the
best f o(980) model the K-MATRIX formalism

7. The Dalitz Plot fit formalism: coupled channel by WA76/102.
The partial widths G p and GK are defined as :
f0 coupled channel
We try to use for the coupling constants gp and gK
the value measured by WA76 ( used in E687
Dalitz Plot analyses) ...
…and the most recently values measured by WA102...

13. The scan of -2 ln L confirm these results.
A scan of -2 ln L has been
performed to establish the
best parameters of f o(980)
in the scalar model:
M = 975 MeV
G = 55 MeV
These results can be used as input in order to establish a good approximation for the
K-Matrix shifted mass and width:
Mo = 982 MeV
G o = 142 MeV
The scan of -2 ln L confirm these results.

14. f o described by K-Matrix
formalism
allows us to
optimize the
shape of f o
on E831 data
f o described by WA102
Fit Fraction.:
NR = ( 20  4)%
f o = ( 93  5) %
-2 ln L = 2279
f o described by K-Matrix
Fit Fraction.:
NR = ( 19  4)%
f o = ( 82  4) %
-2 ln L = BEST FIT!

15. New Background parameterization in the Dalitz analyses
There are evidences of resonant background contribution in KKp and ppp Dalitz Plot.
Until now we have used only a polynomial of 1o order and high S/N ratio for the
Dalitz Plot sample to reduce the bckg dependencies in the fit.
Now we use a polynomial of 2o order + of Breit-Wigner (efficiency weighted)
for the bckg resonances :
K*0 (892) and f (1020) in KKp bckg
f o(980) and r(770) in ppp bckg
since we are working with high S/N samples we do not expect great improvements
in Dalitz Plot fits.

16. Ds+ D+ Great improvement in -2 ln L in Side Band Fit for D+ and Ds+
strong evidence for f (1020)
from -2 ln L = to 552 for D +
from -2 ln L = to 552 for Ds+

17. D+
Ds+
Great improvement in -2 ln L in Side Band Fit for D+ (evidence for r(770) )
( from -2 ln L = 757 to 432 )
No improvement in -2 ln L in Side Band Fit for Ds+

18. D+ K-K+p+ (100% of the full sample)
Fit results
Fit frac Phase (Deg)
K*0 (892) ± (fixed)
K*0 (1430) ± ± 3
f (1020) ± ± 4
E687 published result
Fit frac Phase (Deg)
K*0 (892) ± (fixed)
K*0 (1430) ± ±7
f (1020) ± ±8
-2 ln L =
(was )

19. D+ K-K+p+ (semi log. scale)

22. Ds+ K-K+p+ (100% of the full sample)
Fit results
Fit frac Phase (Deg)
K*0 (892) ± (fixed)
f (1020) ± ± 4
f0 (980) ± ± 28
K*0 (1430) ± ±8
fj (1710) ± ± 6
a0 (980) ± ± 12
E687 published result
Fit frac Phase (Deg)
K*0 (892) ± (fixed)
K*0 (1430) ± ± 40
f (1020) ± ± 20
f0 (980) ± ± 22
fj (1710) ± ± 20
-2 ln L =
(was )
f o(980) by K-Matrix
is narrower than WA76, but KKp seems to prefers a scalar with large tails !
( such as a o (980) )

23. Ds+ K-K+p+ (semi log. scale)

26. Ds+ p-p+p+ Dalitz Plot from E831 Data (100% of the full sample)
Fit results
Fit frac Phase
NR ± ± 7
r (770) ± ± 40
f2 (1270) ± ± 8
f0 (980) ± (fixed)
S0 (1475) ± ± 6
r (1450) ± ± 2
E687 published result
Fit frac Phase
NR ± ± 22
r (770) ± ± 44
f2 (1270) ± ± 18
f0 (980) ± (fixed)
S0 (1475) ± ± 15
-2 ln L = 2266
f o(980) by K-Matrix
(was ,
f o(980) by WA102 )

27. Ds+ p-p+p+ Dalitz Plot from E831 Data (semi log. scale)

30. D + p-p+p+ Dalitz Plot from E831 Data (100% of the full sample)
NEW!
Fit results
Fit frac Phase
NR ± (fixed)
r (770) ± ± 14
f2 (1270) ± ± 15
f0 (980) ± ± 21
S0 (1475) ± ± 34
r (1450) ± ± 30
f0 (400) ± ± 16
f0 (1300) ± ± 80
Fit seems good but
far from E687 results
(fit fractions are not
far from E791)
E687 published result
Fit frac Phase
NR ± (fixed)
r (770) ± ± 14
f2 (1270) ± ± 17
f0 (980) ± ± 28

31. D + p-p+p+ Dalitz Plot from E831 Data (semi log. scale)

34. D+ K- p +p+ (100% of the full sample)
NEW!
D K- p +p+ (100% of the full sample)
Already
seen in E687
Fit results
Fit frac Phase (Deg)
NR ± (fixed)
K*0 (892) ± ±1
K*0 (1430) ± ±1
K*0 (1680) ± ±1
K*1 (1410) ± ±16
K*2 (1430) ± ±1
E687 published result
Fit frac Phase (Deg)
NR ± (fixed)
K*0 (892) ± ±2
K*0 (1430) ± ±2
K*0 (1680) ± ±4
Good agreement with
E687 results!

35. D+ K- p +p+ (100% of the full sample)

38. Conclusions
A new approach to the coupled scalar description (K-Matrix).
This allow us to model f o(980) on our data in a proper way (unitarity conservation)
trough the Likelihood scan method
We can obtain an improvement in -2ln L Ds p-p+p+ using this model
Ds K-K+ p + seems to prefer a scalar with large tails ( a0(980)? ) instead of the
f o(980) obtained by K-Matrix.
The scan method performed on this decay do not give us any information (no minimum) for f o(980)
Now we can work with a most general approach to Dalitz Plot analyses:
Arbitrary numbers of amplitudes for the model and bckg (the only limit is the
MINUIT numbers of parameters )
It allow us to parameterized the bckg in a proper way.
Extension to D0 should be trivial.
New Dalitz Plot analysis has been preliminary studied (D p-p+p+ and D K- p + p + )