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

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 +

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

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

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

How to solve the f o(980) problem ? trying to use new values for the coupling costants gK e gp measured by WA102 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

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...

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.

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 = 2266 BEST FIT!

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.

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 = 1993 to 552 for D + from -2 ln L = 1700 to 552 for Ds+

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+

D+ K-K+p+ (100% of the full sample) Fit results Fit frac. Phase (Deg) K*0 (892) 0.30 ± 0.01 0 (fixed) K*0 (1430) 0.38 ± 0.01 65 ± 3 f (1020) 0.28 ± 0.01 -179 ± 4 E687 published result Fit frac. Phase (Deg) K*0 (892) 0.30 ± 0.02 0 (fixed) K*0 (1430) 0.37 ± 0.04 70 ±7 f (1020) 0.29 ± 0.03 -159 ±8 -2 ln L = - 6999 (was - 6972 )

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

Ds+ K-K+p+ (100% of the full sample) Fit results Fit frac. Phase (Deg) K*0 (892) 0.44 ± 0.02 0.0 (fixed) f (1020) 0.45 ± 0.02 140 ± 4 f0 (980) 0.04 ± 0.03 241 ± 28 K*0 (1430) 0.10 ± 0.01 116 ±8 fj (1710) 0.03 ± 0.01 109 ± 6 a0 (980) 0.25 ± 0.06 114 ± 12 E687 published result Fit frac. Phase (Deg) K*0 (892) 0.48 ± 0.05 0.0 (fixed) K*0 (1430) 0.09 ± 0.03 152 ± 40 f (1020) 0.40 ± 0.03 178 ± 20 f0 (980) 0.11 ± 0.04 159 ± 22 fj (1710) 0.03 ± 0.02 110 ± 20 -2 ln L = - 13637 (was - 13586 ) 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) )

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

Ds+ p-p+p+ Dalitz Plot from E831 Data (100% of the full sample) Fit results Fit frac. Phase NR 0.20 ± 0.04 233 ± 7 r (770) 0.02 ± 0.01 39 ± 40 f2 (1270) 0.09 ± 0.01 152 ± 8 f0 (980) 0.83 ± 0.04 0 (fixed) S0 (1475) 0.24 ± 0.04 254 ± 6 r (1450) 0.04 ± 0.01 210 ± 2 E687 published result Fit frac. Phase NR 0.12 ± 0.12 235 ± 22 r (770) 0.02 ± 0.03 53 ± 44 f2 (1270) 0.12 ± 0.06 100 ± 18 f0 (980) 1.07 ± 0.14 0 (fixed) S0 (1475) 0.27 ± 0.11 234 ± 15 -2 ln L = 2266 f o(980) by K-Matrix (was 2279, f o(980) by WA102 )

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

D + p-p+p+ Dalitz Plot from E831 Data (100% of the full sample) NEW! Fit results Fit frac. Phase NR 0.10 ± 0.08 0 (fixed) r (770) 0.34 ± 0.04 84 ± 14 f2 (1270) 0.11 ± 0.02 171 ± 15 f0 (980) 0.06 ± 0.02 238 ± 21 S0 (1475) 0.01 ± 0.01 273 ± 34 r (1450) 0.04 ± 0.01 0 ± 30 f0 (400) 0.26 ± 0.01 -64 ± 16 f0 (1300) 0.01 ± 0.01 -19 ± 80 Fit seems good but far from E687 results (fit fractions are not far from E791) E687 published result Fit frac. Phase NR 0.59 ± 0.11 0 (fixed) r (770) 0.29 ± 0.06 27 ± 14 f2 (1270) 0.05 ± 0.03 207 ± 17 f0 (980) 0.03 ± 0.03 197 ± 28

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

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 0.96 ± 0.02 0.0 (fixed) K*0 (892) 0.12 ± 0.01 50 ±1 K*0 (1430) 0.30 ± 0.01 58 ±1 K*0 (1680) 0.03 ± 0.01 70 ±1 K*1 (1410) 0.01 ± 0.01 -44 ±16 K*2 (1430) 0.01 ± 0.01 37 ±1 E687 published result Fit frac. Phase (Deg) NR 1.00 ± 0.02 0.0 (fixed) K*0 (892) 0.14 ± 0.01 48 ±2 K*0 (1430) 0.28 ± 0.01 63 ±2 K*0 (1680) 0.05 ± 0.01 73 ±4 Good agreement with E687 results!

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

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 + )