1. 1 E831-FOCUS Stato dell’analisi e prospettive Sandra Malvezzi INFN-Milano

2. 2 Over 1 million reconstructed!! Successor to E687. Designed to study charm particles produced by ~200 GeV 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 , K2 , K3  FOCUS Spectrometer

3. 3 La collaborazione FOCUS Univ. of California-Davis, CBPF-Rio de Janeiro, CINVESTAV Mexico City, Univ. Colorado-Boulder, FERMILAB, Laboratori Nazionali di Frascati, Univ. of Illinois-Urbana-Champaign, Indiana Univ.-Bloomington, Korea Univ.-Seoul, INFN and Univ.-Milano, Univ. of North Carolina-Asheville, INFN and Univ.-Pavia, Univ. of Puerto Rico Mayaguez, Univ. of South Carolina-Columbia, Univ. of Tennessee-Knoxville, Vanderbilt Univ.-Nashville, Univ. of Wisconsin-Madison, Yonsei Univ.-Seoul

4. 4 Cronologia E831-FOCUS 1996-1997 Presa dati 1998 Completata la ricostruzione di piu`di 6 Miliardi di eventi 1999  ora Sub-skim Ottimizzazione MC Analisi Presentazioni a conferenze Pubblicazioni risultati di fisica

5. 5 Attività 2003 Analisi: - Presentazioni a conferenze - Articoli su riviste Frascati – Spettroscopia degli stati eccitati (L=1) del mesone D Milano – Studio dei mesoni con charm Pavia – Studio dei barioni con charm

6. 6 Stato dell’analisi e prospettive Nel periodo Giugno 2002-Giugno 2003 sono stati pubblicati 20 articoli su riviste internazionali (di cui 13 su Physics Letters B) Entro la fine del 2004 sono previste altre 20 pubblicazioni Fondamentale contributo alla fisica del charm Lifetimes Semileptonic decays Hadronic decays Rare decays

7. 7 An important lesson from for the B physics and CP studies “The advantages of high-statistics for the interpretation of Heavy-Flavour hadronic-decay dynamics will vanish without a strategy for controlling strong effects among particles involved in weak-decay processes ”

8. 8 Complication for Dalitz plot analysis had to face the problem of dealing with light scalar particles populating charm meson hadronic decays, such as D , D  Require understanding of light-quark hadronic physics including the riddle of  and   (i.e,  and  states produced close to threshold), whose existence and nature is still controversial

9. 9 A bridge of language, knowledge and measurements between the two worlds of Light Mesons and Heavy Flavours is necessary S-matrix and its representations Two-body unitarity Analyticity Limits of the Breit-Wigner approximation etc..

10. 10 Analysis techniques CAN and MUST be improved now in view of extensive application in high-statistics experiments (Cleo-c, Babar, Belle, BTeV, LHC-b etc...) for precision studies of CP and reliable New Physics measurements Pioneering work performed by

11. 11 An instructive example from FOCUS Milano group analogy with operatively : complete Dalitz plot analysis (time-dependent) to deal with all interference with other (  )  intermediate channels crucial for determination of the angle  of the SM unitarity triangle

12. 12 For a well-defined wave with specific isospin and spin (IJ) characterized by narrow and well-isolated resonances, we know how. the propagator is of the simple Breit-Wigner type and the amplitude is How can we formulate the problem? | 1 2 3 The problem is to write the propagator for the resonance r r r 3 1 2 traditional isobar model

13. 13 when the specific IJ–wave is characterized by broad and heavily overlapping resonances (just like scalars!), the problem is not so simple. where K is the matrix for the scattering of particles 1 and 2. In this case it can be demonstrated on very general grounds that, in the context of the K-matrix approach, the propagator may be written as Indeed, it is very easy to realize that propagation is no longer dominated by a single resonance, but is the result of complicated interplay among resonances. i.e., to write down the propagator we need the scattering matrix In contrast

14. 14 Based on “first principles” of S-matrix scattering theory The K-matrix formalism E.P.Wigner, Phys. Rev. 70 (1946) 15 S.U. Chung et al. Ann. Physik 4 (1995) 404 S scattering matrix  = phase space

15. 15 From T to F From scattering to production: the P-vector approach I.J.R. Aitchison Nucl. Phys. A189 (1972) 514 known from scattering data describes coupling of resonances to D

16. 16 K-matrix advantages An elegant and direct way of incorporating the two-body unitarity constraint Proper handling of overlapping and wide resonances Straightforward inclusion of already known physics and disadvantages requires translation into T-matrix to get the “physics”

17. 17 *  p    0 n,  n,  ’n, |t|  0.2 (GeV/c 2 ) GAMS *  p     n, 0.30  |t|  1.0 (GeV/c 2 ) GAMS * BNL *  p -  KKn CERN-Munich :         * Crystal Barrel * * * pp             pp       ,     ,    pp         K + K -  , K s K s  , K +  s   np       -,        K s K -  , K s K s  -  - p    0 n, 0  |t|  1.5 (GeV/c 2 ) E852 * At rest, from liquid At rest, from gaseous At rest, from liquid “ K-matrix analysis of the 00++-wave in the mass region below 1900 MeV’’ V.V Anisovich and A.V.Sarantsev Eur.Phys.J.A16 (2003) 229 A description of the scattering... A global fit to all the available data has been performed!

18. 18 FOCUS D s +   +  +  - analysis Observe: f 0 (980) f 2 (1270) f 0 (1500) Sideband Signal Yield D s + = 1475  50 S/N D s + = 3.41

19. 19 First fits to charm Dalitz plots in the K-matrix approach! C.L fit 3 % Low mass projection High mass projection decay channel phase (deg) fit fractions (%)

20. 20    No significant direct three-body- decay component No significant  (770)  contribution     Marginal role of annihilation in charm hadronic decays But need more data!

21. 21 Yield D + = 1527  51 S/N D + = 3.64 FOCUS D +   +  +  - analysis Sideband Signal

22. 22 C.L fit 6.8 % K-matrix fit results Low mass projection High mass projection decay channel phase (deg) fit fractions (%) No new ingredient (resonance) required not present in the scattering!

23. 23 With  Without  C.L. ~ 7.5% Isobar analysis of D +   +  +  would instead require a new scalar meson:  C.L. ~ 10 -6 m = 442.6± 27.0 MeV/c  = 340.4 ± 65.5 MeV/c

24. 24 A.D. Polosa: “ Hadronic pollution in B  ”? J.A. Oller: “On the resonant and non-resonant contributions to B  ” CKM03  in B  

25. 25 Conclusions The K-matrix approach has been applied to charm decays for the first time Such a result was not at all obvious! Full application to forthcoming high-statistics charm and beauty experiments for precision studies and search of New Physics ! The same K-matrix description gives a coherent picture of Two-body scattering measurements Light-quark spectroscopy experiments Charm-decay data

26. 26 Slides for questions

27. 27 m = 1473.0  8.8 MeV/c  = 109.5  16.3 MeV/c K-matrix coupled-channel parametrization FOCUS fit results single channel Breit-Wigner FOCUS fit results K-matrix mass and width dimensionless normalized coupling constants to  and KK channels  and KK phase space Preliminary 2 2 MeV/c 2 2 PDG does not help us! Large uncertainties in scalar-resonance paramenters

28. 28 f 2 (1270) f 0 (980) f 2 (1270) S 0 (1475) Isobar approach results Preliminary decay channel amplitude coefficient phase (deg) fit fractions (%) C.L. Fit 7.2%

29. 29 f 0 (1500) PDG m = 1507  5 MeV  = 109  7 MeV Preliminary if then fit fractions: C.L.  2% Instability depending on the 1500 MeV region parametrization !

30. 30 Resonances in K-matrix formalism where S.U. Chung et al. Ann.Physik 4(1995) 404 E.P.Wigner, Phys.Rev.70 (1946) 15

31. 31... from scattering to production: the P-vector approach  (complex) carries the production information I.J.R. Aitchison Nucl.Phys. A189 (1972) 514 known from scattering data

32. 32 is the coupling constant of the bare state  to the meson channel describe a smooth part of the K-matrix elements suppresses the false kinematical singularity at s = 0 near the  threshold and is a 5x5 matrix (i,j=1,2,3,4,5) 1=  2= 3=4  4= 5= A&S

33. 33 A&S K-matrix poles, couplings etc.

34. 34 A&S T-matrix poles and couplings A&S fit does not need a  as measured in the isobar fit