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Charmless Three-body Decays of B Mesons

Charmless Three-body Decays of B Mesons. Chun-Khiang Chua Chung Yuan Christian University HEP2007, 20 July 2007, Manchester. Introduction. Many three-body B decay modes are observed with rates~10 -5 . These modes usually have non-negligible (sizable) nonresonant (NR) contributions.

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Charmless Three-body Decays of B Mesons

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  1. Charmless Three-body Decays of B Mesons Chun-Khiang Chua Chung Yuan Christian University HEP2007, 20 July 2007, Manchester

  2. Introduction • Many three-body B decay modes are observed with rates~10-5. • These modes usually have non-negligible (sizable) nonresonant (NR) contributions. • Some modes, KSKSKS, K+K-KS, are useful for the extraction of sin2beff • Most theoretical works are based on flavor symmetry. (Gronau et al, …) • We (Cheng-CKC-Soni) use a factorization approach to study these modes (FA seems to work for DKK decay) A global analysis

  3. Different topological decay amplitudes Tree bu Penguin bs, d

  4. Factorized into creation and transition parts Creation Tree bu Transition Annihilation Penguin bs, d

  5. A brief look at a typical three-body amp. b→u b→s The creation part <0→K+K-> • is related to the kaon’s e.m. form factors, fitted from data • Non-resonant part is constrained by KSKSKS rate and K+K- mass spectrum The transiton part <B0→K-K0> • Use HMChPT amplitude with exponential form momentum dependence (aNR fixed from ppp rate)

  6. B0 to K+K-K0 rate: • NR rates: 88% from b→s (via <K+K-|ss|0>) and 3% from b→u transitions

  7. CP-odd K+K-KS decay spectrum b→s b→s b→u 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

  8. 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)

  9. K+K-KS(L) & KSKSKS(L) rates • KS KS KS rate is used as an input to fix the NR amplitude in 0→KK creation (denoted the  parameter) • SD rates agree with data within errors • c quark not considered yet • a small room for LD contribution 1st error: ms, B→K form factors,  2rd error: , NR

  10. B-→K+K-K- decay • The predicted NR rate agrees with Belle • The nature of broad X0(1550) (or fX(1500) by Belle) is not clear. 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

  11. B→Kpp decays • The predicted NR rate agrees with Belle

  12. B0→K-p+p0 decay • 1st theory error: NR 2nd theory error: ms, NR, form factors 3rd theory error:  • Calculations for K-KSKS, KS-0, KS00, KS+- modes are also available

  13. B→KKp and ppp (DS=0) decays B-→K+K-p- • KKp rate agrees with BaBar and Belle • ppp rate is sensitive to B →pp transition (can be used to fix the aNR parameter) • B0→p+p-p0 is predicted to have a rate (Br=26.310-6) larger than +-p- as it receives r+, r- and r0 resonant contributions B-→p+p-p-

  14. CP asymmetries in K+K-KS, KSKSKS • 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=0.6780.025 (all charmonium), 0.695+0.018-0.016 (CKM fit)

  15. Dsin2beff=sin2beff-sin2bcharmonium theory expt sin2(K+K-KS) =0.050+0.028-0.033 -0.098+0.18-0.16 sin2(KSKSKS) =0.041+0.027-0.032 -0.098±0.20 sin2(KS00) =0.051+0.027-0.032 -1.3980.71 sin2(KS+-) =0.040+0.031-0.032

  16. Conclusions • It is important to understand the NR amplitudes in 3-body decays. We have identified two NR sources. • We found large NR signal (35%~40%) in K modes, in favor of Belle measurements • Contribution of X0(1550) 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 • Final-state rescattering • known to be important for penguin-induced two-body modes • some FSI effects for 3-body modes are incorporated in the propagator of resonances • LD c-penguin, u-penguin • Full Dalitz plot analysis will be very helpful

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