D Meson Dalitz fit from Focus Sandra Malvezzi

D Meson Dalitz fit from Focus Sandra Malvezzi INFN Milano for E 831/Focus Collaboration Outline • FOCUS experiment • Hadronic decays and Dalitz analyses • Amplitude Formalism • Preliminary results from FOCUS • Conclusions 24 May 2000 Sandra Malvezzi CIPANP 2000 1

FOCUS Spectrometer Over 1 million reconstructed!! Successor to E 687. Designed to study charm particles produced by ~200 Ge. V photons using a fixed target spectrometer with upgraded Vertexing, Cerenkov, E+M Calorimetry, and Muon id capabilities. Includes groups from USA, Italy, Brazil, Mexico, Korea 1 million charm particles reconstructed into D K , K 2 , K 3 24 May 2000 Sandra Malvezzi CIPANP 2000 2

Dalitz analyses & charm hadronic decays • The Past: inclusive studies • establishment of lifetime hierarchy of charmed particles difference in their hadronic decay rate • The Present and the Future: exclusive studies • two body final states interference between isospin amplitudes and FSI • three or four body final states (dominated by quasi-two-body resonant states) interference between amplitudes for the various resonant channels, phase-shift measurements and FSI 24 May 2000 Sandra Malvezzi CIPANP 2000 3

D E 687 E 831 Ds+ : YIELD S/N (D+ : YIELD S/N = 1288 47 = 4. 34 0. 30 = 1800 60 = 3. 08 0. 16) E 687 Ds+ : YIELD = 98 12 S/N = 4. 22 0. 85 (D+ : YIELD = 236 20 S/N = 7. 47 1. ) 24 May 2000 Sandra Malvezzi CIPANP 2000 4

- + + processes D s+ Annihilation through a resonance Annihilation Spectator Interesting: and KK states with resonances coupling to and KK! 24 May 2000 Sandra Malvezzi CIPANP 2000 5

Preliminary Focus Results Ds Dalitz plot Observe: • f 0(980) • f 2(1270) • f 0 (1500) • Dominated by weird resonances with simultaneous KK and couplings 24 May 2000 Sandra Malvezzi CIPANP 2000 6

Amplitude Formalism Each decay can be visualized as a Feynman diagram: D r ( ) Vertex Form Factor Legendre Polynomial Relativistic Breit-Wigner +3 q 13 Each decay function is multiplied by a constant complex amplitude factor to give 1 +2 r A non-zero phase shift implies FSI according to Watson’s Theorem 24 May 2000 Sandra Malvezzi CIPANP 2000 7

The f parametrization 0 • `Regular resonance`: relativistic Breit-Wigner with J=0 for a scalar state as the f 0 • Flatte`coupled-channel formula according to WA 76 experiment 24 May 2000 Sandra Malvezzi CIPANP 2000 8

Ds Dalitz plot WA 76 parametrization for f 0 Fit results Fit frac. NR r (770) f 2 (1270) f 0 (980) S 0 (1475) 0. 17 ± 0. 04 0. 03 ± 0. 01 0. 15 ± 0. 02 1. 07 ± 0. 04 0. 18 ± 0. 03 Phase 4. 19 ± 0. 08 1. 00 ± 0. 24 2. 05 ± 0. 10 0. 0 (fixed) 3. 89 ± 0. 09 E 687 published result Fit frac. NR r (770) f 2 (1270) f 0 (980) S 0 (1475) 24 May 2000 Sandra Malvezzi CIPANP 2000 0. 12 ± 0. 12 0. 02 ± 0. 03 0. 12 ± 0. 06 1. 07 ± 0. 14 0. 27 ± 0. 11 Phase 4. 10 ± 0. 38 0. 93 ± 0. 76 1. 74 ± 0. 31 0. 0 (fixed) 4. 08 ± 0. 26 9

D s+ K -K + + WA 76 parametrization for f 0 Fit results K*0 (892) K*0 (1430) f (1020) f 0 (980) fj (1710) Fit frac. Phase (Deg) 0. 44 ± 0. 01 0. 06 ± 0. 01 0. 45 ± 0. 01 0. 16 ± 0. 01 0. 04 ± 0. 01 0. 0 (fixed) 114 ± 5 148 ± 4 135 ± 4 106 ± 8 E 687 published result K*0 (892) K*0 (1430) f (1020) f 0 (980) fj (1710) 24 May 2000 Sandra Malvezzi CIPANP 2000 Fit frac. Phase (Deg) 0. 48 ± 0. 05 0. 09 ± 0. 03 0. 40 ± 0. 03 0. 11 ± 0. 04 0. 03 ± 0. 02 0. 0 (fixed) 152 ± 40 178 ± 20 159 ± 22 110 ± 20 10

D+ K -K + + Fit results K*0 (892) K*0 (1430) f (1020) Fit frac. Phase (Deg) 0. 31 ± 0. 01 0. 37 ± 0. 01 0. 29 ± 0. 01 0 (fixed) 69 ± 2 -171 ± 3 E 687 published result K*0 (892) K*0 (1430) f (1020) 24 May 2000 Sandra Malvezzi CIPANP 2000 Fit frac. Phase (Deg) 0. 30 ± 0. 02 0. 37 ± 0. 04 0. 29 ± 0. 03 0 (fixed) 70 ± 7 -159 ± 8 11

The Role of Final State Interaction The KK Dalitz plots are instructive to understand the role of FSI. The lobe asymmety in D+ is due to interference effect with a broad spinless resonance Bare amplitudes are real (d=0 or 180): asymmetry can be caused only by FSI 24 May 2000 Sandra Malvezzi CIPANP 2000 12

What is the f o(980) problem ? Comparison between the Dalitz Plot of Ds+ f o + obtained by E 831 data and Mini MC data ( generated using WA 76 model for the f o ) : E 831 Data Mini MC Data Narrow f o Large f o We can use Focus Ds 3 data to fix the f parametrization and then fit the Ds KK ! 0 24 May 2000 Sandra Malvezzi CIPANP 2000 13

E 831 data WA 76 model scalar model f o is better described by a simple BW ! fo fo 24 May 2000 Sandra Malvezzi CIPANP 2000 14

The K-matrix • Resonances are associated with poles of the S-matrix • The transition operator T is associated with the scattering operator S through S =I +2 i. T • The K operator is defined as K-1 =T-1 +ir ¨ K is Hermitian (K=K†) ¨ From the time-reversal invariance of S and T , K must be symmetric The K-matrix may be chosen to be real and symmetric 24 May 2000 Sandra Malvezzi CIPANP 2000 15

The f 0 resonance in the K-matrix – Consider the isovector S-wave scattering with the f 0 coupling to the (channel 1) and KK (channel 2) final states. The elements of the invariant K-matrix are ; ; the normalized couplings are: and the T-matrix is g 12 + g 22 =1 At first approximation: Assuming mr=975 Me. V and Gr=55 Me. V we get m 0 =982 Me. V and G 0=142 Me. V 24 May 2000 Sandra Malvezzi CIPANP 2000 16

A scan of -2 ln L has been performed to establish the best parameters for the f o(980) in the scalar model: • M = 975 Me. V 2000 • G 24 =May 55 Me. V These results can be used as input in order to establish a good approximation for the K-Matrix shifted mass and width: • Mo = 982 Me. V • G o = 142 Me. V Sandra Malvezzi 17 The scan of -2 ln L confirms these results. CIPANP 2000

f o described by WA 76 Fit Fraction. : NR = ( 26 5)% f o = (112 6) % -2 ln L = 2295 24 May 2000 K-Matrix formalism allows us to optimize the shape of f o data aaaa on E 831 Sandra Malvezzi CIPANP 2000 f o described by K-Matrix Fit Fraction. : NR = ( 19 4)% f o = ( 82 4) % BEST FIT! 18 -2 ln L = 2266

Ds+ - + + preliminary results K-matrix f 0 Fit results Fit frac. NR r (770) f 2 (1270) f 0 (980) S 0 (1475) r (1450) 24 May 2000 Sandra Malvezzi CIPANP 2000 0. 19 ± 0. 04 0. 02 ± 0. 01 0. 09 ± 0. 01 0. 82 ± 0. 04 0. 24 ± 0. 04 ± 0. 01 Phase 233 ± 7 39 ± 40 152 ± 8 0 (fixed) 254 ± 6 210 ± 2 19

D+ - + + preliminary results Fit frac. NR r (770) f 2 (1270) f 0 (980) S 0 (1475) r (1450) f 0 (400) f 0 (1300) 0. 10 ± 0. 08 0. 34 ± 0. 04 0. 11 ± 0. 02 0. 06 ± 0. 02 0. 01 ± 0. 01 0. 04 ± 0. 01 0. 26 ± 0. 01 Phase 0 (fixed) 84 ± 14 171 ± 15 238 ± 21 273 ± 34 0 ± 30 -64 ± 16 -19 ± 80 K-matrix f 0 24 May 2000 Sandra Malvezzi CIPANP 2000 20

D s+ K -K + + Fit results K*0 (892) f (1020) f 0 (980) K*0 (1430) fj (1710) a 0 (980) f o(980) by K-Matrix is narrower than that from WA 76, but KK seems to prefers a scalar with large tails ! a o (980) KK 24 May 2000 Sandra Malvezzi CIPANP 2000 Fit frac. Phase (Deg) 0. 44 ± 0. 02 0. 45 ± 0. 02 0. 04 ± 0. 03 0. 10 ± 0. 01 0. 03 ± 0. 01 0. 25 ± 0. 06 0. 0 (fixed) 140 ± 4 241 ± 28 116 ± 8 109 ± 6 114 ± 12 E 687 published result K*0 (892) K*0 (1430) f (1020) f 0 (980) fj (1710) Fit frac. Phase (Deg) 0. 48 ± 0. 05 0. 09 ± 0. 03 0. 40 ± 0. 03 0. 11 ± 0. 04 0. 03 ± 0. 02 0. 0 (fixed) 152 ± 40 178 ± 20 159 ± 22 110 ± 20 21

Conclusions Exciting physics ! • The K-matrix formalism has been applied to parametrize coupledchannel resonances ( f 0 and a 0). • Improved fit has been obtained on Ds 3 decay where the f 0 dominates. • A study is in progress on Ds and D+ KK decays to evaluate the f 0 and a 0 roles. • The Dalitz studies may provide new handles to measure CP violation in charm hadronic decays • New analyses: • D 0 Ks. K+K • D+ K+ K+ K • D+ K+ + 24 May 2000 Sandra Malvezzi CIPANP 2000 22

PRELIMINARY D 0 Ks K+ K- Dalitz plot D 0 -> Ks K+ K_ Too many kaons Here we have only an s u u d quarks in the final state yet three kaons appear! 2 spectator diagrams with resonances which couple to ’s and K’s a 0(980) f(1020)? ~50% FOCUS aaaaaaaaaaa a 0(980)? m²K+K- Y=520 25 S/N=15 f 0(980)? f(1020) We use D* tagging to determine strangeness of K°s 24 May 2000 Sandra Malvezzi CIPANP 2000 m²K+Ko 23

First Observation of D+ K+K K+ f squared mass Preliminary !! Y(D+ ) = 73. 1± 13 Y(Ds+ ) = 64. 5± 13 24 May 2000 Sandra Malvezzi CIPANP 2000 24