1 / 37

CPV in three-body decays: the Dalitz plot analysis

CPV in three-body decays: the Dalitz plot analysis. DIF06 LNF - February 28 –March 3. Sandra Malvezzi INFN Milano. Outline. The power of the Dalitz plot analysis CPV and Dalitz plot Recent applications of the Dalitz technique in the beauty sector Results

aram
Download Presentation

CPV in three-body decays: the Dalitz plot analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CPV in three-body decays: theDalitz plot analysis DIF06 LNF - February 28 –March 3 Sandra Malvezzi INFN Milano

  2. Outline • The power of the Dalitz plot analysis • CPV and Dalitz plot • Recent applications of the Dalitz technique in the beauty sector • Results • Problems/complications • Some guidance from charm • D mesons and FSI • A pioneering anlysis in D ppp • Conclusions

  3. Dalitz plot in the last few years • SPIRESsearch for “Dalitz and date after 1999” 91 entries after 2004 29 entries • Experiments: FOCUS, E791, CLEO, BaBar-Belle • From D to B decays • From decay dynamics to CPV to New Physics new millennium

  4. Dalitz plot: the revenge • The experimentalist’s struggle! “When the going gets tough, the tough getgoing” • for the younger in the auditurium: the analysis is certainly complex but not impossible • if you survive, you might understand how QM works!

  5. The power of the Dalitz plot • Dalitz plot analysis allows for determination of a complete set of decay parameters, i.e. amplitudesandphases • CP is a matter of phase • Exploit interference and make use of formalisms with explicit CKM phases. • B  rp a angle • B  D(*)K (*)g angle ...promising

  6. CPV and Dalitz plot • Promising and complementary approach • Independent measurements to over determine the unitarity triangle provide a non-trivial test of the Standard Model. • Comparing the results in various channels and via different analysis techniques will allow us to find possible inconsistency... the way toNew Physics.

  7. Some pilot Dalitz-plot analyses in the beauty sector Results and complications

  8. B rp • A theoretically clean way to extract a is via atime-dependent Dalitz plot analysis of B rp • Snyder - Quinn formalism Phys. Rev. D48, 2139 (1993) • from the operative point of view B p+p-p0 (all charge combinations) with all possible resonant structuresand interferences. • A full Dalitz analysis from BaBar a = (113+27-17± 6)° • 213 ML BB hep-ex/0408099 (ICHEP04) • A “partial’’ Dalitz analysis from Belle • Selecting distinct bands in the p+p-p0 Dalitz Plot a = (102 ± 11 ± 15)° • 152 ML BB hep-ex/0408003 Phys.Rev.Lett. 94, 121801 (2005)

  9. B  rr (not Dalitz) • This decay has recently received attention: small theoretical uncertainty • Potentiallyhighly complicated • Three possible helicity states for the decay • Helicity 0 is CP-even • Helicity ±1 are not CP eigenstates • BaBar a=(100 ± 13)° fL = 0.978 ± 0.014+0.021-0.029 • 232 MLBB hep-ex/0503049 Phys. Rev. Lett. 95, 041805 (2005) • Belle a= (88 ± 17)°fL = 0.941+0.034-0.040 ± 0.030 • 275 MLBB hep-ex/0601024

  10. Some complications to gofrom Bppp toB  rp from Bpppp toB  rr means selecting and filtering the desired states among the possible contributions, e.g. sp, f0(980)p, sr, ss, rpp... • How to deal with the underlying strong dynamics effects? • The pp S-wave is characterized by broad, overlapping states: unitarity is notexplicitly guaranteed by a simple sum of Breit -Wigner (BW) functions • Independently of the nature of s(genuine resonance or a strong dynamics structure), it is not a simple BW • f0(980) is a Flatté-like function, coupling to KK and pp

  11. BDK • Possibility of observing CP violation in BDK decays • B+ D(*)K(*)+can produce neutral D mesons of both flavors • D0 and D0 mesons can decay into a common final state u b u K(*)+ s D(*)0 c b c B+ s B+ D(*)0 K(*)+ u u u u Relative phase q+=d+g is the sum of strong and weak interaction phases q-=d-g for charge conjugate mode

  12. Dalitz plot andthe g angle Dalitz plot analysis to extract g • Originally: interference of Cabibbo-favored D0 K+p-p0 and doubly Cabibbo-suppressed D0 K+p-p0 • Recently: interference D0, D0  KSp+p- (both CF decays) • Belle - 275 ML BB g=(64 ±15)° for B± DK ± ( 137 – 139 events ) g=(75 ±25)° for B± D*K ± ( 34 - 35 events ) combinedsamples hep-ex 0506033

  13. Dalitz plot andthe g angle (II) • BaBar - 227 ML BB Phys.Rev.Lett. 95 (2005) 121802 • A model for D0 decay is needed • Dominating source of systematic error hep-ex/0504039

  14. Somecomplications • Model assumptions .... • Set of 15 two-body amplitudes (Kp)p K*(892)p, K*(1430)p, K2*(1430)p, K*(1680)p • (plus doubly Cabibbo-suppressed partners for each of these states) Ks(pp)Ksr, Ksv, Ksf0(980), Ksf2(1270), Ksf0(1370), KSs1,KSs2 s1 and s2 are “ad hoc” resonances introduced to describe excess of events at pp threshold and at 1.1 GeV2 Ms1 = 539 ± 9 MeV Gs1= 453 ± 16 MeV Ms2= 1048 ± 7 MeV Gs1= 109 ± 11 MeV

  15. A word of caution • Some questions • Do wereally understandthe systematics? • Are weconfidentof controlling strongdynamics effects in the analysis? • Where can we look for directions? • Charm: we have already come across parametrization and formalism issues • Low and intermediate energy processes • Hadron spectroscopy • Scattering

  16. A way to proceed ... • BaBar • Implemented the K-matrix formalism to describe the pp S-wave component in D0,D0 KSp+p- • Benefiting from charm expertise and work • FOCUS three-pion Dalitz plot analysis • No ad “ad hoc” resonances needed • tried to quote a preliminary, reliable, systematic error on the g angle: 3°(hep-ex/0507101) • The right track to pursue ... promising!

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

  18. Add BW Add K The Unitarity circle • For a single-pole problem, far away from any threshold, a K-matrix amplitude reducesto the standard BW formula • The two descriptions are equivalent • In all the other cases,the BW representationis no longer valid • The most severe problem is that it does not respectunitarity Add BW • Adding BWs ala “traditional Isobar Model” • Breaks Unitarity • Heavily modify thephase motion! Add K

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

  20. 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 ingredients (resonances), not present in the scattering, required !

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

  22. 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

  23. 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

  24. The effort continues, grows and matures....

  25. B  DK* • Statistical accuracy of the g extraction can be improved by adding excited K states to the analysis Belle • B  DK* (hep-ex/0504013) • 253 fb-1 56 signal candidates B  DK* g = ( 112 359  11  8 )° BaBar • B  DK* and B  D(*)K* (hep-ex/0507101) g = ( 67 28  13  11 )° (D Ksp+p-) non-resonant B  DKSp

  26. Dalitz Analysis of B  Khh Belle hep-ex/05100059 • 140 fb-1 B+ K+p+p- and B+ K+K+K- • 357 fb-1 B0 K0p+p- • Already mentioned complications due to pp states • KK final state can come from f0(980), f0(1300), f0(1500) – coupled-channel parametrization • CP asymmetry is predicted very small in B+ K*0(892) p+ • window to NP • Kp model is needed.

  27. Dalitz Analysis of B  hhh BaBar • 210 fb-1 B±p±p±p hep-ex/0507025 Phys. Rev. D72, 052002 (2005) • 205.4 fb-1 B±K±p±p hep-ex/0507004 Phys. Rev. D72, 072003 (2005) • 230 fb-1 B0K+K-KS0 hep-ex/0507094

  28. Dalitz plot and B  fKs Promising way to search for New Physics • A reliable SM prediction exists for sin2b(BdJ/yKs)  sin2b(BdfKs) • BaBar/Belle average for 2005 • sin2b(BdJ/yKs) = 0.685 ± 0.032 • sin2b(BdfKs) = = 0.50 ± 0.25 +0.07–0.04 BaBar = 0.44 ± 0.27 ± 0.05 Belle • How do other resonant (e.g. f0(980)) and non-resonant KK components underneath f affect the measurement? • It is mandatory to measure various contributions and related interference via a Dalitz plot analysis.

  29. First set of conclusions • Dalitz plot analysis represents a powerful, unique and promising tool to study CP violation in the beauty sector • The analysis is challenging but there are no shortcuts to perform precise studies (New Physics) • There is a new vigorous effort to perform amplitude analyses • more robust formalism implemented • many different channels analysed • beauty community can benefit from charm experience and expertise but need to go on..

  30. Beauty and charm relationship... • B rp • B pppD ppp • B D(*)K(*) Kspp  Kpp0 • B  KppD Kpp from charm we can learn something for beauty .... but not only ...

  31. CPV in charm • In the SM, the D system is not as sensitive to CPas the K and B mesons. • The small effects predicted could leave open a window onto NP • Charm is unique (I. Bigi): • non-Standard-Model effects might exhibit very different patterns for the up and down classes of quarks • Charm decays are the only up-type decays that afford a probe of such physics • Important to measure it! • Asymmetry in decay rates are already measured, also in three-body decays • Alternative approaches are worth being exploited ... (DKK p )

  32. Dalitz plot analysis and CPV in the charm sector • FOCUS D+K+K–p+(ICHEP 02) • BaBarD0K0K+K–hep-ex/050702 Phys. Rev. D72, 052008 (2005) • CLEO • D0 p+ p- p0 hep-ex/0503052 Phys.Rev. D70, 031102 (2005) • D0 KSp+ p- hep-ex/0311033 Phys.Rev.D70, 091101 (2004) No statistically significant asymmetries reported ... improve accuracy!

  33. 2 Yield D+ = 7106 92 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 2250 0.2 2000 2.0 1.9 1.8 1.7 3 2 2.5 1.5 3.5 1 1750 GeV 2 1500 2 1250 m(KK)(GeV) 1000 2 750 2 m(Kp)(GeV) 500 2.1 250 0 D+K–K+p+ is (would be) a good candidate • Two amplitudes (spectator CSD - penguin) • Good yield and S/N ratio • Strong phases present D+ ,Ds KK

  34. Measured phase: q =d+f CP violating f =-f d = d CP conserving q =d-f CP conjugate Simple idea ... look at D+/D– • Measure coefficient and phasefor each amplitude • Look for possible local asymmetry in D+/D–parametrs • Complications in the final state (KK) (Kp) treatment • f0(980)/a0(980) coupled-channel lineshape • Higher mass f0(1370)-f0(1500) ... • Broad K*0(1430) ...

  35. D+/D- split samples ICHEP2002 • Fit based on BW formalism • preliminary and tentative • No CPV but a more reliable parametrization needed • Start studying scattering S-matrix (K-matrix) Coefficients: D±,D+,D- Phases:D±,D+,D-

  36. Hadronic physics • The other perspective The hadronic physics challenge ... • very clean samples of HF decays offer an unprecedented opportunity to investigate light meson physics • enriching, testing and finding consistency with the already available measurements from low-intermediate energy experiments ... • BES, BaBar, Belle, Cleo-c have (and/or) will have clean, high-statistics samples to provide phase-shift behaviour, measuring resonance parameters ... etc. ...

  37. Conclusions • Dalitz plot analysis will definitely keep us company over the next few years • Some complications have already emerged • expecially in the charm field others (unexpected) will only become clearer when we delve deeper into the beauty sector • Bs will be a new chapter (hep-ph/0602207 Bs Kpp, Bs KKp) • There will be a lot of work for both theorists and experimentalists • Synergy invaluable! The are no shortcuts toward ambitious and high-precision studies and NP search

More Related