1 / 33

CP Violation in Hadronic 3-body B Decays: Future Challenges in Non-Leptonic B Decays

This paper discusses the CP violation in hadronic 3-body B decays and the future challenges in understanding non-leptonic B decays. It presents experimental results from LHCb and proposes ways to improve the understanding of non-resonant contributions in these decays.

sbach
Download Presentation

CP Violation in Hadronic 3-body B Decays: Future Challenges in Non-Leptonic B Decays

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. CP Violation in Hadronic 3-body B Decays Hai-Yang Cheng Academia Sinica, Taipei in collaboration with Chun-Khiang Chua Future Challenges in Non-Leptonic B Decays Bad Honnef, February 11, 2016

  2. Direct CP asymmetries (3-body) LHCb (’13) found first evidence of inclusive integrated CP asymmetry in B-+--, K+K-K-, K+K-- +-: + K+K-: - Large asymmetries observed in localized small invariant mass regions of p.s. ACPlow(KK) = -0.6480.0700.0130.007 for mKK2 <1.5 GeV2 ACPlow(KKK) = -0.2260.0200.0040.007 for 1.2< mKK, low2 <2.0 GeV2, mKK, high2 <15GeV2 ACPlow() = 0.5840.0820.0270.007 for m, low2 <0.4 GeV2, m, high2 > 15 GeV2 ACPlow(K) = 0.6780.0780.0320.007 for 0.08< m, low2 <0.66 GeV2, mK2 <15 GeV2

  3. LHCb (’14) measured another local CP asymmetry in the rescattering regions 1.0 GeV < m,KK < 1.5 GeV Except the K+K-K- mode, local CP asymmetries in low invariant-mass region are much larger than that in rescattering region |ACPlow | >> |ACPresc | >> |ACPincl |

  4. B-+ -- 2014 LHCb 2013 LHCb ACPincl() = 0.0580.014 inclusive (2013 data: 0.1170.024) ACPres() = 0.1720.027 for 1.0 < m2 < 2.25 GeV2 ACPlow() = 0.5840.087 for m, low2 < 0.4 GeV2, m, high2 > 15 GeV2 4

  5. B- K-+- 2013 LHCb 2014 LHCb ACPincl(K) = 0.0250.009 inclusive (2013 data: 0.0320.012) ACPres(K) = 0.1210.022 for 1.0 < m2 < 2.25 GeV2 ACPlow(K) = 0.6780.085 for 0.08< m, low2 < 0.66 GeV2, mK2 < 15 GeV2

  6. B-K+ K-- 2013 LHCb 2014 LHCb ACPincl(KK) = -0.1230.022 inclusive (2013 data: -0.1410.044) ACPres(KK) = -0.3280.041 for 1.0 < mKK2 < 2.25 GeV2 ACPlow(KK) = -0.6480.072 for mKK2 < 1.5 GeV2

  7. B- K-K+K- 2013 LHCb 2014 LHCb ACPincl(KKK) = -0.0360.008 inclusive (2013 data: -0.0430.012) ACPres(KKK) = -0.2110.014 for 1.0 < mKK2 < 2.25 GeV2 ACPlow(KKK) = -0.2260.022 for 1.2< mKK, low2 < 2.0 GeV2, mKK,high2 < 15 GeV2 7

  8. He, Li, Xu [1410.0476] Krankl, Mannel, Virto [1505.04111] C. Wang, Zhang, Z. Wang, Guo [1506.00324] Nogueira, Bediaga, Cavalcante, Frederico, Lourenco [1506.08332] Bediaga, Magalhaes [1512.09284] Zhang, Guo, Yang [1303.3676] Bhattacharya, Gronau, Rosner [1306.2625] Xu, Li, He [1307.7186] Bediaga, Frederico, Lourenco [1307.8164] Gronau [1308.3448] Cheng, Chua [1308.5139] Zhang, Guo, Yang [1308.5242] Lesniak, Zenczykowski [1309.1689] Di Salvo [1309.7448] Xu, Li, He [1311.3714] Cheng, Chua [1401.5514] Ying Li [1401.5948] Bhattacharya, Gronau, Imbeault, London, Rosner [1402.2909] Wang, Hu, Li, Lu [1402.5280] Ying Li [1402.6052] 8

  9. Three-body B decays Large nonresonant (NR) fractions in penguin-dominated B decay modes, recalling that NR signal is less than 10% in D decays Nonresonant fraction (%) KKK:  70-90% K: 35-40% by Belle, 20% by BaBar K0: 15-20% :  35% NR contributions are essential in penguin-dominated B decays One of our goals is to identify the origin of NR signals HYC, Chua, Soni (’07)

  10. P2 All three mesons energetic b P1 P3 (a) P2 All three mesons energetic, but two of them nearly parallel P1 P3 (b) P3 All three energetic & two of them nearly parallel. The spectator quark is kicked by a hard gluon to become hard P2 P1 (c) (b) & (c) mimic quasi-2-body decays P3 Two energetic (P1, P2) & one soft (P3) P1 P2 (d) 10

  11. Receive both resonant & NR contributions • Central 3-body region can be explored by QCDF or pQCD • 3-body decays resemble quasi 2-body ones through the use of 2-meson distribution amplitude in the Dalitz-plot regions depicted by [Wang, Hu, Li, Lu (’14); Krankl, Mannel, Virto (’15)] • Regions with a soft meson emission [Suzuki (`00)]

  12. Most of theory studies focus only on either resonant or NR effects. We discuss both resonant & NR contributions based on factorization. Under the factorization approximation, there are 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→u b→s

  13. b→u NR contribution of • Early attempt: Apply heavy meson chiral perturbation theory (HMChPT) to evaluate form factors r and  Bajc, Fajfer, Oakes, Pham; Deandrea et al. (’99) Yan et al.; Donoghue et al.; Wise (’92) K- K0 K- B0 +,r r B- B0 K0 K0 K- K0 +,-,r B0 B*0s B- r B0 B*0s K- 13

  14. NR rates for tree-dominated B→KK,  will become too large For example, BF(B-→K+K--)NR = 3310-6 larger than total BF, 510-6 BF(B-→+- -)NR = 7510-6 larger than total BF, 5.310-6 ⇒HMChPT is applicable only to soft mesons ! • Ways of improving the use of HMChPT have been suggested before • We write tree-induced NR amplitude as Fajfer et al; Yang, HYC,… p2 p1 -- HMChPT is recovered in soft meson limit, p1, p2→0 -- The parameter NR» 1/(2mB) is constrained from B-→+--

  15. b→s V = , , …, S = f0(980), f0(1370), f0(1500), f(1710),… Decay constants of scalar mesons have been evaluated in various approaches Chua, Yang, HYC (’06); C.D. Lu et al.; Z.G. Wang What about the NR contributions ? 15

  16. <K+K-|qq|0> can be related to the kaon’s e.m. form factors ch, x1, x2 fitted from kaon e.m. data Chua,Hou,Shiau,Tsai (’03) motivated by asymptotic constraint from QCD counting rules Brodsky, Farrar (’75) Fitted ch agrees with the model (~ mass  decay constant  strong coupling) NR Resonant NR exp[i/4](3.39+0.18-0.21) GeV Cheng,Chua,Soni (’05) 16 from K+K- spectrum of K+K-KS from KSKSKS rate

  17. The decay amplitude of B0 K+K-K0 consists of two pieces: • Nonresonant: <B0K+K-><0K0> <B0K0><0K+K-> (<B0K0><0 K+K->)penguin • Resonant:B0f0K0K+K-K0 , f0 = f0(980), f0(1500), f0(1710),… B0VK0K+K-K0, V =, , ,… Weak phase: CKM matrix elements Strong phases: (i) effective Wilson coefficients (ii) propagator (s - m2 + im)-1 (iii) matrix element <M1M2|qq|0> for NR contribution in the penguin sector

  18. B-→K+K-K- BF(10-6) 2.90.0+0.5-0.50.0 calculable for the first time theory errors: (NR) , (ms, NR, form factors), () • Power corrections from QCDF added to K- • Large NR rate is penguin-dominated and governed by <K+K-|ss|0>NR NR rates: mostly from b→s (via <KK|ss|0>) and a few percentages from b→u tree transitions

  19. B-→K-+- 2.40.0+0.6-0.50.0 31.03.03.8 +1.7-1.6 0.650.0+0.69-0.190.0 • Power corrections from QCDF added to K*0- and 0K- • BaBar has measured K0*0(1430)- from B- KS0-0 (2014) with a • result consistent with Belle. An issue for QCDF and pQCD. • If U-spin relation with =0 is • used, it will lead to (i) too large BR’s for NR and total, (ii) CP • asymmetries with wrong signs. Fit to BR   

  20. Tree-dominated B-→+--, K+K-- • NR B-+-- rate is used to fix the parameter NR • The predicted NR fraction is about 55% for B- K+K--

  21. Direct CP violation in 3-body B decays • Correlation seen by LHCb: • ACP(K-K+K-)  – ACP(K-+-), ACP(-K+K-)  – ACP(-+-) • U-spin symmetry (s  d) predictions for the relative signs between K-K+K- & -+- and between K-+- & -K+K- agree with experiment: Xu, Li, He; Bhattacharya, Gronau, Rosner • However, relative signs between -K+K- & -+- and between K-+- & K-K+K- cannot be fixed from symmetry argument alone

  22. Direct CP asymmetries     pQCD (Wang et al.) : 51.9+16.7-23.9  

  23. Some issues on CP asymmetries • Final-state rescattering • CP violation in B-0- • CP asymmetries at large invariant mass regions • The origin of the strong phase  for B K, KK

  24. Final-state rescattering It has been conjectured that CPT theorem & final-state rescattering of +- K+K- may play important roles to explain the CP correlation observed by LHCb. Consider +- & K+K- rescattering and neglect possible interactions with 3rd meson Bediaga et al Suzuki, Wolfenstein : inelasticity, assuming KK = For numerical calculations, we follow the parameterization of Pelaez and Yndurain

  25. Final-state +- K+K- rescattering seems to be in wrong direction

  26. CP violation in B-0- • In naïve factorization, ACP(0-) ~ 0.05. BaBar obtained ACP =0.18+0.09-0.17. However, QCDF, pQCD, SCET & diagrammatic approach all predict a negative & sizable CP violation for B-0-, ACP  -0.20 • LHCb has measured CP asymmetries in regions dominated by vector resonances I: 0.47 < m(+-)low <0.77 GeV, cos>0, II: 0.77 < m(+-)low <0.92 GeV, cos>0, III: 0.47 < m(+-)low <0.77 GeV, cos<0, IV: 0.77 < m(+-)low <0.92 GeV, cos<0 ACP changes sign at m(+-)  m Summing over regions I-IV yields CP asymmetry consistent with zero with slightly positive central value

  27. If we follow QCDF to add power corrections to render ACP -0.20, then CP violation in +-- induced by , f0 resonances will become negative -16.3 -6.7 -16.8 6.0 -11.4 0.4 An important issue needs to be resolved! 27

  28. CP asymmetries at large invariant mass regions +-- K++- K+K-- K+K-K- • ACP is large & positive at m2(+-)low= 5-10 GeV2 and • m2(+-)high= 9-12 GeV2 • Negative at m2()= 9.5-10.5 GeV2, m2(K)=10-18 GeV2 • Large & negative at m2(KK) =16-25 GeV2, m2(K) = 5-10 GeV2, • positive at m2(KK)= 7-14 GeV2, m2(K) =5-13 GeV2 • Positive at (i) m2(KK)low = 3-5 GeV2, m2(KK)high =18-22 GeV2, • (ii) m2(KK)low = 8-9 GeV2, m2(KK)high =18-19 GeV2 0.47 -0.09 0.36 -0.41 ? 0.11 0.41 Predicted CP asymmetries at some large invariant mass regions agree with the data in sign except for K+K--

  29. The origin of the strong phase  for B K, KK An additional phase  is introduced in B-K-+- in order to accommodate (i) NR rate, (ii) sign of CP asymmetry. What is the origin of this phase? final-state interactions?

  30. BFs & CP violation in 3-body Bs decays LHCb made first observation of three charmless 3-body Bs decays Penguin-dominated (10-6) (10-6) Tree-dominated • Penguin-dominated modes K0K-+, K0K+- have largest rates, dominated by K*0(1430) resonances • Tree-dominated mode K+K-K0 is predicted to have BF ~ 1.410-6 ACP(K0K+K-)  - 2ACP(K0+-) 30

  31. Conclusions • Three-body B decays receive sizable NR contributions governed by the matrix elements of scalar densities. • Three sources of strong phases responsible for direct CP violation in 3-body B decays. • In general, NR contributions alone yield large CP-violating effects. • It is important to pin down the mechanism responsible for regional CP asymmetries.

More Related