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Recent Results from FOCUS

Recent Results from FOCUS. Sandra Malvezzi I.N.F.N. Milano. QCD 2005 Conversano 16 -20 June 2005. How charm can still be charming. Charm physics is a paradigm of how precise measurements have led to a revival of the sector New Physics search: Mixing, CPV, rare and forbidden decays

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Recent Results from FOCUS

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  1. Recent Results from FOCUS Sandra Malvezzi I.N.F.N. Milano QCD 2005 Conversano 16 -20 June 2005

  2. How charm can still be charming • Charm physics is a paradigm of how • precise measurements have led to a revival of the sector • New Physics search: Mixing, CPV, rare and forbidden decays • Spectroscopy of high-mass states (“the renaissance of spectroscopy”) • sophisticated investigations (typical of a mature field, under study over various decades) • Dalitz plot analyses, Semileptonic Form-Factor measurements... have revealed limits in the “standard” approach precisely

  3. QCD effects in charm weak decays can complicate the analysis and the phenomenological interpretation of the results requiring a new direction/approach in the decay dynamics investigation • What experimentalists have learnt so far • Goals: • Proper tools for present/future precise high-statistics studies of charm and beauty hadrons • coherent description of FSI in Beauty - Charm decays and & Light hadron sector (hopefully) • Synergy between experimentalists and theorists • FOCUS has played a pioneering role in various analyses

  4. FOCUS role • Lifetime hep-ex/0504056 A Measurement of the Ds+ Lifetime • Mixing hep-ex/0501006D0-D0 hadronic mixing and DCS decays (the best charm mixing limit from a fixed-target exp) • Pentaquark hep-ex/0506013Pentaquark search (Null) • Rare & forbidden decays • Semileptonic • Hadronic decays (Dalitz plot) • Multi-body channels (4,5,6 bodies) • Charm Baryons • D* spectroscopy hep-ex/0406044-hep-ex/0312060

  5. Charm lifetimes tDs =0.5074  0.0055  0.0051 Bigi Uraltsev 1.00-1.07 (no WA/WX) 0.8-1.27 (different process interference) (*)FOCUS (○) PDG 2002

  6. Time evolution of wrong-sign D* decay 2 sigma hints of mixing at few percent level! (K)=409.4  1.34 ps (KK)=395.4  5.5 ps d CP lifetime comparisons Charm mixing circa 2000 Some intriguing results.....not conclusive!

  7. Mixing circa 2003 Things have come a long way since those heady days... B-factories are leading the game It will be interesting to see if mixing does occur at the percent level.

  8. 2004-2005: data continue.... hep-ex/0501006 Belle : hep-ex/0408125 Phys. Lett. B 618 - 23 FOCUS ....agrees better with BaBar & Belle than with the old CLEO contour The best mixing limit from a fixed-target experiment: a valuable check More and more stringent limits! FOCUS has the world’s most accurate lifetime measurements and excellent lifetime-resolution.

  9. Decay dynamics investigation • .....The semileptonic sector

  10. New results on Our Kp spectrum looks like 100% K*(892) This has been known for about 20 years ...but a funny thing happened when we tried to measure the form factor ratios by fitting the angular distributions

  11. Decay is very accessible to theory Assuming the Kp spectrum contains nothing but K*, the decay rate is straight-foreward

  12. forward-backward asymmetry in cos below the K* pole but almost none above the pole A 4-body decay requires 5 kinematics variables: 3 angles and 2 masses An unexpected asymmetry in the K* decay matches model -15 % F-B asymmetry Sounds like QM interference

  13. Try an interfering spin-0 amplitude Phys.Lett.B535,43,2002 (plus mass terms) will produce 3 interference terms H0(q2), H+(q2), H-(q2) are helicity-basis form factors computable by LQCD...

  14. F-B asymmetry • K* mn interferes with S- wave Kp and creates a forward-backward asymmetry in the K* decay angle with a mass variation due to the varying BW phase • The S-wave amplitude is about 7% of the K* BW with a 45o relative phase • D+ Kpmnis the natural place to study the Kp system in the absence • of interactions with other hadrons. Due to Watson’s theorem the • observed Kp phase shift should be the same as those measured in • elastic scattering

  15. The S & P waves from LASS • Most information on K-p+ scattering comes from the LASS experiment (SLAC, E135) Aston et al., Nucl. Phys. B296 (1988) 493 PWA by LASS 892 MeV/c2 The phase difference between S & P waveat K*(892) pole from LASSis ~ 45degrees!.

  16. cos qv weighted M(Kp), GeV/c2 A broad Breit-Wigner amplitude ( the controversial k(900))? k(900)with no fsi phase shift and with a 100 degree phase shift. hep-ex/0503043Hadronic Mass Spectrum Analysis of D+Kpmn Decay and Measurementof the K*(892)0 Mass and Width in FOCUS Additional checks: k(900)is not required

  17. D+ s d u u Nominal spectroscopic pole masses d Form Factors The vector and axial form factors are generally parametrized by a pole dominance form Two numbers parameterize the decay

  18. Phys.Lett.B 544(2002) 89 • Our analysis is the first to include the effects on the acceptance due to changes in the angular distribution brought about by the S-wave interference • The inclusion of the S-wave amplitude dramatically improved the quality of the • Form-FactorFit • Form -factor lattice calculation(Damir Becirevic ICHEP02)RV = 1.55  0.11is remarkably close tothe FOCUS result.

  19. Decay dynamics investigation ..cont’d • .....The hadronic sector • Dalitz-plot analysis of D decays

  20. Dalitz Analysis of Heavy Flavour Decays • Powerful tool! • It provides a “complete observation” of the decay • Everything could be in principle measured • from the dynamical features of the HF decay mechanism • Relative importance of non-spectator processes • up to the CP-violating phases, mixing, etc • Just recall  from Bo and g(f3) from B  D(*)K • We have already learnt a lot about charm

  21. Recent articles (the Dalitz-plot revenge) • hep-ex/0503052Searches for CP violation and pp S-wave in the Dalitz Plot analysis of D0p+p+p0(CLEO) • hep-ex/0503045 Search for D0 - D0 Mixing in the Dalitz Plot Analysis of D0 KS0p+p-(CLEO) • hep-ex/0504039 Measurement of g in B  D(*)K decays with a Dalitz analysis of D  KS0p+p-(BaBar) • hep-ex/0504013Measurement of f3 with Dalitz Plot Analysis of B  D(*)KDecay(Belle) • hep-ex/0408099Measurement of CP-Violating Asymmetries in B0 (rp)0 Using a Time-Dependent Dalitz Plot Analysis(BaBar) Sophisticated studies both in charm & beauty

  22. I will • Address key issues of the Heavy Flavour Dalitz analysis • Formalization problems • Failure of the traditional “isobar” model • Need for the K-matrix approach • Implications for the future Dalitz analyses in the B-sector • Discuss these issues in the context of the recent Ds+,D++-+ Dalitz analysis we performed in FOCUS

  23. 2 3 3 r r | 1 2 1 Formalization Problems • The problem is to write the propagator for the resonance r • For a well-defined wave with specific isospin and spin (IJ) characterized by narrow and well-isolated resonances, we know how.

  24. Spin 0 Spin 1 Spin 2 • the propagator is of the simple Breit-Wigner type • the decay amplitude is • the decay matrix element traditional isobar model

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

  26. E.P.Wigner, Phys. Rev. 70 (1946) 15 What is K-matrix? S.U. Chung et al. Ann. Physik 4 (1995) 404 • It follows from S-matrix and, because of S-matrix unitarity, it is real • Viceversa, any real K-matrix would generate an unitary S-matrix • This is the real advantage of the K-matrix approach: • It (heavily) simplifies the formalization of any scattering problem since the unitarity of S is automatically respected.

  27. From Scattering to Production • Thanks to I.J.R. Aitchison (Nucl. Phys. A189 (1972) 514), the K-matrix approach can be extended to production processes • In technical language, • From • To • The P-vector describes the coupling at the production with each channel involved in the process • In our case the production is the D decay

  28. Describes coupling of resonances to D Known from Scattering Data K-Matrix Picture of D++-+ Beside restoring the proper dynamical features of the resonances, it allows for the inclusion of all the knowledge coming from scattering experiments: enormous amount of results and science!

  29. Add BW Add K The Unitarity circle • For a single pole problem, far away of any threshold, K-matrix amplitude reducesto the standard BW formula • The two descriptions are equivalent • In all the other cases, the BW representation is not anymore valid (limit of the traditional isobar model!!!) • The most severe problem is that it does not respectunitarity Add BW • Adding BWs ala “traditional Isobar Model” • Breaks the Unitarity • Heavily modify the phase motion! Add K

  30. Summarizing The decay amplitude may be written, in general, as a coherent sum of BW terms for waves with well-isolated resonances plus K-matrix terms for waves with overlapping resonances. Can safely say that in general K-matrix formalization is just required by scalars (J=0), whose general form is

  31. pp-  KKn : * GAMS ppp0p0n,hhn, hh’n, |t|0.2 (GeV/c2) CERN-Munich * GAMS ppp0p0n, 0.30|t|1.0 (GeV/c2) * BNL pp  p0p0p0, p0p0h , p0hh pp  p0p0p0, p0p0h * p+p-  p+p- At rest, from liquid * Crystal Barrel pp  p+p-p0, K+K-p0, KsKsp0, K+Ksp- * Crystal Barrel At rest, from gaseous * Crystal Barrel At rest, from liquid np  p0p0p-, p-p-p+, KsK-p0, KsKsp- * Crystal Barrel At rest, from liquid E852 * p-pp0p0n, 0|t|1.5 (GeV/c2) Where can we get a reliable S-wave scattering parametrization from? • In other words, we need to know K to proceed. • A global fit to (all) the available data has been performed “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

  32. is a 5x5 matrix (i,j=1,2,3,4,5) 1=pp, 5= 4= 2= 3=4p An impressive amount of data is well described in terms of 5 poles A&S is the coupling constant of the bare state a tothe meson channel describe a smooth part of the K-matrix elements and suppresses the false kinematical singularity at s = 0 near the pp threshold

  33. A&S T-matrix poles and couplings • This set of poles and couplings coherently describes the pp scattering. • as object is already included ....as very well known it is not a simple narrow BW Can we fit our D data??

  34. FOCUS D+ p +p +p - analysis Yield D+ = 1527 51 S/N D+ = 3.64 Sideband Signal PLB 585 (2004) 200

  35. decay channel phase (deg) fit fractions (%) K-matrix fit results C.L fit 7.7 % High mass projection Low mass projection Reasonable fit with no retuning of the A&S K-matrix. No new ingredient (resonance) required not present in the scattering!

  36. C.L.~ 7.5% C.L.~ 10-6 Isobar analysis of D+ p +p +p would instead require a new scalar meson: s m = 442.6± 27.0 MeV/c G= 340.4 ± 65.5 MeV/c Withs Withouts

  37. What about -meson then? • Can conclude that • Do not need anything more than what is already in the  S-wave phase-shift to explain the main feature of D  3  Dalitz plot Or, if you prefer, • Any -like object in the D decay should be consistent with the same -like object measured in the  scattering. • Note: B  D(*)K Dalitz plot analysis • The model used for the D0Ksp+p- decay is one of the main sources of systematics • Two “ad hoc” scalar states s1and s2 to describe excess of events not reproduced by “established” resonances.

  38. FOCUS D s+ p +p +p -analysis • Observe: • f0(980) • f2(1270) • f0(1500) Sideband Signal Yield Ds+ = 1475 50 S/N Ds+ = 3.41 PLB 585 (2004) 200

  39. Low mass projection High mass projection decay channel phase (deg) fit fractions (%) K-matrix fit results C.L fit 3 % No three-body non-resonant contribution

  40. Even more: from P to Q-vector • Just by a simple insertion of KK-1 in the decay amplitude F • We can view the decay as consisting of an initial production of the five virtual states pp, KK, hh, hh’and 4p,which then scatter via the physical T-matrix into the final state. • The Q-vector contains the production amplitude of each virtual channel in the decay

  41. Q-vector for Ds • S-wave dominated by an initial production of hh, hhand KK-bar states Ratio of moduli of Q-vector amplitudes The normalizing pp modulus The two peaks of the ratios correspond to the two dipsof thepp normalizing modulus, while the two peaks due to the K-matrixsingularities, visible in the normalization plot, cancel out in the ratios.

  42. Q-vector for D+ • The same! • s-wave dominated by an initial production of hh, hhand KK-bar states

  43. The resulting picture • The S-wave decay amplitude primarily arises from a ss-bar contribution such as that produced by • Cabibbo favored weak diagram for Ds • One of the two possible singly Cabibbo suppressed diagram for D+. For the D+. the ss-bar contribution competes with a dd-bar contribution.. • The measured fit fractions seems to confirm this picture • S-wave decay fraction, 87% for Ds and only 56% for D+ • The dd-barcontribution in D+ case evidently prefers to couple to a vector state like (770), that alone accounts for about 30% of the decay.

  44. Conclusions • Systematic investigation of charm decay dynamics is giving interesting results in both semileptonic and hadronic sectors • Dalitz plot analysis is and will be a crucial tool to extract physics from the HF decays • Nevertheless, to fully exploit this unlimited potential a systematic revision of the amplitude formalization is required • FOCUShas applied the K-matrix approach for the first time to the HF sector • Its application has been decisive in clearing up a situation which recently became quite fuzzy and confusing: new “ad hoc” resonances were required to understand data • K-matrix allows for a rigorous coupled-channel analysis • This will be the further step in the Dalitz analysis of HF decays • D+, D+s f0p amplitudes can feed both 3p and KKp

  45. Conclusions...cont’d • Strong dynamics effects in D-decays now seem under control and fully consistent with those measured by light-quark experiments. • The new scenario is very promising for the future measurements of the CP violating phases in the B sector, where a proper description of the different amplitudes is essential. • FOCUS is now sudying the D+K-p+p+ • High statistics sample –Test of the model • Quasi two-body process or multi-body process ?

  46. The first charm Dalitz analysis – MK1 (1977) D+K (GeV2) “...consistent with a phase space Dalitz distribution.” FOCUS D+K-p+p+ (GeV2) 50000 events High momentum pp combination Low momentum pp combination

  47. 2 nodes! 1 node The future We can learn even about D* states !!

  48. BACKUP SLIDES • My backup

  49. broad states Isobar model: Add up BW’s with angular factors What do you learn from Dalitz plots? • Bands indicate resonance contributions • For spinless parents, the number of nodes in the band give you the resonance spin • Look at the f band • Interference pattern gives relative phases and amplitudes • Look at the D+ K* band pattern of asymmetry Nearly all charm analyses use the isobar model:

  50. Atot= g1M1eid1 + g2M2eid2 CP conjugate Atot= g1M1eid1 + g2M2eid2 * * 2Im(g2 g1*) sin(d1-d2)M1M2 |Atot|2- |Atot|2 aCP= = |Atot|2+ |Atot|2 |g1|2M12+|g2|2M22+2Re(g2 g1*)cos(d1-d2)M1M2 CP violation on the Dalitz plot di= strong phase • For a two-body decay CP asymmetry: strong phase-shift 2 different amplitudes

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