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Hadronic 3-body B decays

Hadronic 3-body B decays. Hai-Yang Cheng Academia Sinica, Taipei. FPCP2008, Taipei, May 6, 2008. Introduction. Many three-body B decays have been observed with rates ~10 -5 useful for extracting CKM angles, CP violation

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Hadronic 3-body B decays

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  1. Hadronic 3-body B decays Hai-Yang Cheng Academia Sinica, Taipei FPCP2008, Taipei, May 6, 2008

  2. Introduction • Many three-body B decays have been observed with rates ~10-5 • useful for extracting CKM angles, CP violation • Most of quasi-2-body B decays (B→VP,SP) are extracted from Dalitz plot analysis of 3-body decays A(B→P1P2P3)= resonant + nonresonant (NR) • NR signal is less than 10% in D decays. Is NR component also small in B decays ? • There is no any theoretical study addressing both resonant and NR effects. Some works are based on flavor symmetry • Chua, Soni, and I (2007) have applied the factorization approach to study the dynamics of 3-body decays Gronau, Rosner focus on charmless B→PPP

  3. Two striking features: • Large NR fractions in penguin-dominated modes Nonresonant fraction (%) KKK:  90% K: 35-40% by Belle, 5% by BaBar K0: 12-15% :  14% NR contributions are essential in penguin-dominated B decays One of our goals is to identify the origin of NR signals

  4. NR amplitude in charm decays is usually treated as a constant over Dalitz plot. However, this is no longer true in B decays due to large energy release. Both BaBar & Belle employ the parametrization • to study the NR component in B→KKK decay, but differ in the NR analysis in B→K: BaBar adopted the LASS parametrization which is an effective range NR component + Breit-Wigner form for K0*(1430) • difficult to disentangle resonant & NR effects due to interference Recall that NR accounts for (95±7)% of D+→K-++in old experiments. With + included by E791, NR fraction is reduced to (8.6±0.8)%, confirmed recently by CLEO. David Asner (Friday): DP in D decays

  5. New broad scalar resonances fX(1550) & fX(1300) A broad scalar resonance fX(1500) [or X(1550) by BaBar] has been seen in K+K+K-, K+K-KS, K+K-- at energies ~1.5 GeV. It cannot be identified with f0(1500), otherwise it will decay to +- five times more frequently than to K+K-. Its nature is not clear. Production puzzle: The fraction of fX(1500) in K+K+K- is ~120% by BaBar and 63% by Belle, whereas it is  4% in K+K-KS by BaBar Belle BaBar B+→K+K+K- B0→K+K-K0 Likewise, fX(1300) was seen in K++- and K0+-.Its mass& width are consistent with f0(1500)

  6. Three factorizable amplitudes for B0→K+K-K0 • current-induced process: <B0→K0><0→K+K-> • transition process: <B0 →K-K0><0→K+> • annihilation process: <B0→0><0→K+K-K0> b→s b→u

  7. almost pure NR b→u • Early attempt: Apply HMChPT to evaluate form factors r and  Wise, Yan et al. Donoghue et al. (1992) Bajc,Fajfer,Oakes,Pham; Deandrea et al. (’99) K- K0 K- B0 +,r r B- B0 K0 K0 K- K0 +,-,r B0 B*0s B- r B0 B*0s K-

  8. NR rates for B→KKK,K,  will become too large For example, Br(B0→K+K-K0)NR=7710-6 larger than total BR=2510-6 ⇒HMChPT is applicable only to soft mesons ! • Ways of improving the use of HMChPT have been suggested before • We now propose to write NR amplitude as Fajfer et al. Yang, HYC,… -- HMChPT is recovered in soft meson limit, p2, p3→0 -- The parameter NR» 1/(2mB) is constrained from B-→+--

  9. b→s V=, , ,…, S=f0(980), f0(1370), f0(1500), fX(1500),… Decay constants for scalar mesons have been evaluated using QCDSR Chua,Yang,HYC

  10. <K+K-|qq|0> is related to the kaon’s e.m. form factors ch, x1, x2 fitted from kaon e.m. data Chua,Hou,Shiau,Tsai motivated by asymptotic constraint from QCD counting rules Brodsky, Farrar NR NR is constrained by KSKSKS rate and K+K- mass spectrum

  11. B0→K+K-K0 BaBar: PRL, 99, 161802 (2007) NR rates: 88% from b→s (via <KK|ss|0>) and 3% from b→u transitions

  12. BaBar: PRD, 74, 032003 (2006) Belle: PRD, 71, 092003 (2005) B-→K+K-K- BR(10-6) 1st theory error: NR 2nd theory error: ms, NR, form factors 3rd theory error:  • The predicted NR rate agrees with Belle • The large fraction of X0(1550), 121% by BaBar and 63% by Belle, is entirely unexpected, recalling that it is only 4% in K+K-K0

  13. B-→K-+- Evidence for direct CP violation in B→0K: ACP=(30±11+11-5)% by Belle, PRL 96, 251803 (2006) ACP=(44±10+6-14)% by BaBar, arXiv:0803.4451 9.3±1.0+6.9-1.7 BaBar & Belle have very different results for NR fractions: ~4.5% by BaBar, ~34% by Belle calculable for the first time BaBar Belle • K0*(1430): LASS parametrization Relativistic Breit-Wigner K0*(1430) resonance with an effective range NR component • NR: phase space (constant amplitude) exponential total nonres= NR(p.s.)+NR(LASS) arXiv: 0803.4451

  14. Difficulties for extracting NR component by BaBar: • Substantial mixing of NR & K0*(1430) due to LASS shape • Part of LASS is really NR and should be added to phase-space NR piece Total NR=NR(LASS) + NR(p.s.) This leads to a better agreement with Belle, NR fraction is enhanced from 4.5% to 17.5% No perfect agreement due to different models for NR K mass shape

  15. Why is NR rate large in K++- ? • SU(3) symmetry ⇒ • ⇒ similar NR rates are expected in K++- and in KKK. • Why is NR fraction ~ 40% in K-+- but ~ 90% in K+K-K- ? resonant poles in KKK: , f0(980),… resonances in K: K*, K*0(1430), , f0(980),… ⇒ K has a total rate larger than KKK by a factor  2

  16. BaBar: arXiv:0711.4417 Belle: PLB, 599, 148 (2004) B0→K-+0 BaBar: LASS + nonres Belle: performed with simplified technique for DP; interference between quasi-two-body amplitudes was not taken into account Just as DP analysis of B-→K-+-, it is necessary to include NR(LASS) to get total nonres for BaBar.

  17. Tree dominated B→KK, 

  18. B-→K+K-- dominated by b→u tree and b→d penguin Decay rate is small and consistent with the limits set by BaBar & Belle. Recently, BaBar [PRL 99, 221801 (2007)]obtained Br(B+→K+K-+)=(5.0±0.5±0.5)10-6 • broad peak at ~1.5 GeV in KK mass • no peak at ~ 1 GeV due to 

  19. B→ • dominated by intermediate  mesons • Since <|qq|0> is suppressed by penguin Wilson coefficients, NR amplitude arises mainly from B→ transition⇒ NR is suppressed ⇒ can be used to fix the NR parameter +-- B→+-0 is predicted to have a rate (Br=26.3£10-6) larger than +-- as it receives +, - and 0 resonant contributions

  20. Quasi-two-body B decays We compute B→P1P2P3 and then apply narrow width approximation (B→ RP3; R￫P1P2)=(B→RP3) Br(R→P1P2) R: V,S and to determine the rates of quasi-two-body B decays: B→VP,SP

  21. VP modes Br(-++-+)=24.0±2.5 Br(-++-+)=24.0±2.5 • QCDF predictions are from Beneke and Neubert • Unless specified, expt’l BRs are extracted from 3-body Dalitz plot analysis

  22. SP modes • QCDF predictions are from Chua, Yang, HYC. Assumption of Br(f0(980)→+-)=0.50 has been made • f0(980)K rates are well accommodated, K*0(1430) rates are too small by a factor of 2~3 compared to the data due to destructive interference between a4 & a6 terms charming penguin ? Lesniak et al [arXiv:0710.2469] penguin annihilation ?

  23. b→sqq tCPV measurements Sf= ± sin2eff from b→ccs 2-body: HYC,Chua,Soni;Beneke 3-body: CCS Also pQCD, SCET Naïve b→s penguin average: 0.68±0.04, 0.56±0.05 (if f0K0 excluded), 0.0.1, 2.2, 2.6 deviation from b→ccs average

  24. CP asymmetries in K+K-KS & KSKSKS See C.K. Chua talk • sin2b=O(+0.1) is naively expected in K+K-KS due to color-allowed tree contribution, tied to NR amplitude • DS, ACP are small in KsKsKs: no b→u tree diagram sin2=0.6800.025 (all charmonium), 0.695+0.018-0.016 (CKM fit)

  25. sin2eff=sin2eff-sin2charmonium Chua,Soni,HYC, PR,D76,094006 (2007) theory expt sin2(K+K-KS) =0.041+0.028-0.033 0.05±0.11 sin2(KSKSKS) =0.039+0.027-0.032 -0.10±0.20 sin2(KS00) =0.049+0.027-0.032 -1.200.41 sin2(KS+-) =0.038+0.031-0.032 sin2theory is always positive and less than O(0.1)

  26. Conclusions • It is important to understand the NR amplitudes in 3-body decays. We have identified two NR sources: • We found large NR signal in K modes. • Total NR issue should be clarified • Contribution of fX(1500) to K+K+K- should be clarified. • Intermediate vector & scalar meson contributions to 3-body decays are identified. The total rates of 3-body B decays are calculated for the first time. • m.e. of scalar density <KK|ss|0>, <K|qs|0>, BR  2010-6 • tree transition, BR  210-6

  27. Back-up slides

  28. Different topological decay amplitudes HYC, Yang (02’) Tree bu Penguin bs, d K, KKK: b → s penguin , KK: b → u tree & b → d penguin

  29. Factorizable contributions Creation Tree bu Transition Annihilation Penguin bs, d

  30. Three-Body Branching Ratios (10-6)

  31. CP-odd K+K-KS decay spectrum b→s b→u b→s b→u • The b→s transition prefers a small m(K+K-) Low mKK peak due mainly to KS • The b→u transition prefers a small m(K+K0) and hence large m(K+K-) ⇒ tiny interference between b→s & b→u transitions

  32. CP-even K+K-KS decay spectrum CP-even+CP-odd b→s b→u • low mKK peak: f0(980)KS + NR • peak at mKK  1.5 GeV due to X0(1550)

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