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CP Violation and Final State Interactions

CP Violation and Final State Interactions in Hadronic Charmless B Decays. Hai-Yang Cheng 鄭海揚 Academia Sinica CPV in kaon system DCPV in B K, ,  FSIs. November 16, 2004, NTHU. CP Violation in Kaon System.

erich-francis
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CP Violation and Final State Interactions

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  1. CP Violation and Final State Interactions in Hadronic Charmless B Decays • Hai-Yang Cheng 鄭海揚 • Academia Sinica • CPV in kaon system • DCPV in BK, ,  • FSIs November 16, 2004, NTHU

  2. CP Violation in Kaon System Consider neutral K’s decays to pions. Since mK=497 MeV, m=137 MeV, K0,K0 ,  CP| = |, CP| = -|, Let CP|K1 = |K1, with K1 = (K0+K0)/2 CP|K2 = -|K2, K2 = (K0-K0)/2 Hence, K1   and K2  , but K2 is not allowed K1 & K2 have widely different lifetimes, K1=KS, K2=KL due to phase space effects : L/S 580 Christenson, Cronin, Fitch, Turlay (64) found KL   at BNL  First discovery of CP violation ! _ _ _

  3. Discoveryof CP Violation • Phys. Rev. Lett. 13, 138 (1964) “K20” →pp ~ 1/300 ! CP -+

  4. Two possible sources of CP violation:   KL K1 K2   indirect (mixing) CPV direct CPV (CPV in mass matrix) (CPV in decay amplitude) KL K2+ K1, KS K1+ K2 with   || with : mixing-induced CPV, ’: direct CPV A fit to K  data yields ||=(2.2840.014)10-3, Re(’/)=(1.670.26)10-3

  5. Direct CP Violation: Re(’/) CERN & Femilab expt’l didn’t agree until 1999 KTEV: Bob Hsiung(熊怡) PDG 2004 Average: Re(’/)=(1.670.23) 10-3

  6. Direct CPV in kaon decays: In kaon system, ’<< due to I=1/2 rule

  7. CP Violation in Standard Model VCKM is the only source of CPV in flavor-changing process in the SM. Only charged current interactions can change flavor Elements depend on 4 real parameters: 3 angles + 1 CPV phase 1>>1>>2>>3 First proposed by Kobayashi & Maskawa (73) CKM= Cabibbo-Kobayashi-Maskawa 小林‧益川

  8. M. Kobayashi & T. Maskawa, Prog. Theor. Phys. 49, 652 (73): before charm (J/) discovery by Ting & Richter in 1974 KM pointed out that one needs at least six quarks in order to accommodate CPV in SM with one Higgs doublet K. Nir(丹生潔) et al. at Nagoya had found evidence for a charm production in cosmic ray data, Prog. Theor. Phys. 46, 652 (73).

  9. Some disadvantages for VCKM: • Determination of 2 & 3 is ambiguous • Some elements have comparable real & imaginary parts A new parametrization similar to the one originally due to Maiani (76) was proposed by Chau & Keung (84) 喬玲麗，姜偉宜 1>>s1>>s2>>s3 adapted by PDG as a standard parametrizarion CKM= Chau-Keung-Maiani

  10. mixing CPV direct CPV Can one observe similar mixing-induced & direct CPV in B systems ? Cf meaures direct CPV, Sf is related to CPV in interference between mixing & decay amplitude According to SM, CPV in B decays can be of order 10%!

  11. Penguin Diagram Penguin diagram was first discussed by Shifman, Vainshtein, Zakharov (75) motivated by solving I=1/2 puzzle in kaon decay I=1/2 puzzle: why Why does it call penguin diagram ?

  12. The Duel of the B Factories KEK SLAC Belle BaBar

  13. It has been claimed by Bigi,Sanda (81) a large CPV in B0J/KS with SK  0.65- 0.80 In July 2000, BaBar & Belle announced first hints of CPV in B0 meson system, namely, the golden mode B0 J/KS SK=0.731  0.056, CK  0 Indirect CPV in KS, 0KS, f0KS, KS were also measured recently What about direct CPV in B decays ? B f ei(+) : strong phase : weak phase Need at least two different B  f paths with different strong & weak phases

  14. Direct CP Violation AK 2004 summer First confirmed DCPV observed in B decays ! Recall that in K system, ACPdir=5.510-6

  15. Direct CPV in B0 -+ Average: ACP(B0 -+) = -0.47+0.13-0.14

  16. B0 +-

  17. Average: ACP(B0+-) = 0.37  0.24

  18. Predictions of DCPV in B Decays Based on quark diagrammatic approach and effective Hamiltonian + factorization, we have studied charmless hadronic B decays Chau, HYC, Sze(施華強), Tseng(曾龍), Yao(姚珩): PR, D43, 2176 (91): decay rates PR, D45, 3143 (92): direct CP asymmetries

  19. Two popular models in recent years: • QCD factorization (QCDF): Beneke, Buchalla, Neubert, Sachrajda (99) TI: TII: • PQCD approach based on kT factorization theorem developed by Keum (琴龍淵), Li (李湘楠), Sanda (01) -- Introduce parton’s transverse mometum to regulate endpoint div. -- Form factors for B  light meson are perturbatively calculable -- Large strong phase stemming from annihilation diagrams

  20. Direct CP violation (%) in QCDF & PQCD  QCDF predictions for DCPV disagree with experiment ! though QCDF & pQCD describe BRs of hadronic B decays well

  21. “Simple” CP violation from perturbative strong phases: penguin (BSS) vertex corrections (BBNS) annihilation (pQCD) • “Compound” CP violation from LD rescattering:[Atwood,Soni] strong weak

  22. Other possible hints at large FSI effects in B physics: • Some decay modes do not receive factorizable contributions e.g. B  K0c with sizable BR, though 0c|c(1-5)c|0=0. • Color-suppressed B0  D0 h0 (h0=0,,0,,’) measured by Belle, CLEO, BaBar are larger than theoretical expectations. • Br(B0 00)  1.5 10-6 cannot be explained by QCDF or PQCD. • and likewise for B000 • BRs predicted by QCDF for penguin-dominated BK*,K,K,K* are too small by a factor of 2-3 compared to the data • Longitudinal fraction fL  50% for B K* by Belle & BaBar •  in sharp contrast to the scaling law: • for factorizable amplitudes in B decays to light vector mesons, •  rescattering effect or new physics ?

  23. quark annihilation possible FSIs quark exchange meson annihilation B0D00  W exchange  Color suppressed C At hadron level, FSIs manifest as resonant s-channel & OPE t-channel graphs.

  24. FSI as rescattering of intermediate two-body states [HYC, Chua(蔡俊謙), Soni; hep-ph/0409317] • FSIs via resonances are assumed to be suppressed in B decays due to the lack of resonances at energies close to B mass. • FSI is assumed to be dominated by rescattering of two-body intermediate states with one particle exchange in t-channel. Its absorptive part is computed via optical theorem: • Strong coupling is fixed on shell. For intermediate heavy mesons, • apply HQET+ChPT (for soft Goldstone boson) • Cutoff must be introduced as exchanged particle is off-shell • and final states are hard • Alternative: Regge trajectory [Nardulli,Pham][Falk et al.] [Du et al.] …

  25. Form factor is introduced to render perturbative calculation meaningful •  = mexc + rQCD (r: of order unity) •  or r is determined form a 2 fit to the measured rates •  r is process dependent • n=1 (monopole behavior), consistent with QCD sum rules Once cutoff is fixed  CPV can be predicted Dispersive part is obtained from the absorptive amplitude via dispersion relation subject to large uncertainties and will be ignored in the present work

  26. B   K Direct CPV in B0K+- was reported by BaBar & Belle SD PQCD for F0B(0)=0.25 from covariant LF model [HYC,Chua,Hwang(04)]

  27. All rescattering diagrams contribute to penguin topology fit to rates  rD = rD*  0.69  predict direct CPV

  28. Sign of +K- CP asymmetry is flipped after rescattering and is in agreement with experiment. • K rates are enhanced by (30-40)% via FSI • Isospin sum rule relation [Atwood,Soni] can be used to test the presence of EWP

  29. B    Af=-Cf : direct CP asymmetry; Sf: mixing-induced CP violation A(+-)=0.58 0.17 by Belle, 0.090.16 by BaBar SD PQCD

  30. Long-distance contributions to B    Cutoff scale is fixed by B K via SU(3) symmetry  too large +- ( 910-6) and too small 00 (0.410-6) A dispersive part unique to  but not available to K is needed to suppress +- and enhance 00 + D+(+) same topology as vertical W-loop diagram V D-(-) -

  31. Charming penguin alone doesn’t suffice to explain 00 rate • Sign of direct CP asymmetry is flipped after rescattering ! • DCPV in -0 mode is very small even after inclusion of FSI. It provides a nice way to search for New Physics • SU(3) relation: (+-)=-(+K-) [Deshpande,He]  A(+-)  -4.0 A(+K-) can be used to predict DCPV in +-

  32. B • W-exchange can receive LD contributions from FSI • |P/T| is of order 0.30, smaller than some recent claims • Define Teff=T+E+V, Ceff=C-E-V  Ceff/Teff=0.71 exp[i72] • BK • C/T is similar to the  case

  33. B   ﹣ _ _ ﹣ • DCPV in +- mode is well accounted for • Br(00)  1.310-6, recalling BaBar upper limit, 2.910-6, and Belle result of (5.11.8)10-6. Discrepancy between them should be clarified. • We useF1B(0)=0.30 [HYC,Chua,Hwang]. If F1B(0)=0.37 is employed, the  will become too large

  34. Summary for DCPV Expt(%) QCDF PQCD

  35. Summary for DCPV Expt(%) QCDF+FSI PQCD pQCD and FSI approaches for DCPV can be discriminated in 00 and +- modes

  36. Polarization anomaly in B  K*,K* Short-distance induced transverse polarization in B V1V2 (V: light vector meson) is expected to be suppressed Scaling law obeyed by  modes is violated in K* and K* (except 0K*+) decays

  37. Anomaly can be accommodated in QCDF via large penguin-induced annihilation by adjusting endpoint divergence [Kagan] BR is enhanced by a factor of 2 via annihilation, too large ? • Transverse gluon in bsg chromodipole operator  transversely polarized  [Hou & Nagashima] Similar behavior for K*, butno polarization anomaly in K* modes ?

  38. Get large transverse polarization from B Ds*D* and then convey it to K* via FSI [Colangelo, De Fazio, Pham] fT(Ds*D*)  0.51 contributes to A only f|| 0.41, f 0.08 • Regge analysis of FSI [Ladisa,Laporta,Nardulli,Santorelli] elastic FSI: Pomeron exchange (see also Chua,Hou,Yang) inelastic FSI: use Regge trajectory method to evalute charming penguins

  39. We found large cancellation occurs in B{ Ds*D,DsD*}K* processes. This can be understood as CP & SU(3) symmetry  0 ! ＋  very small perpendicular polarization, f 2%, in sharp contrast to f 15% obtained by Colangelo et al. While fT 0.50 is achieved, why is f not so small ?

  40. Cancellation in B{VP,PV}K* can be circumvented in • B{SA,AS}K*. For S,A=D**,Ds**, it is found • fL: f||: f= 0.71: 0.06 : 0.22 • However, K* rate gets only a small enhancement so that effect of • sizable f will be washed out by intermediate states from V,P • Strong phases in K* • For B+K*0+, fL: f||: f= 0.64: 0.35 : 0.01, fLexpt=0.740.08 fL is indeed suppressed • For B+K*+0, fL: f||: f= 0.62: 0.37 : 0.01, fLexpt=0.96+0.04-0.16 • Why is scaling law working here ?

  41. Conclusion • Color–suppressed modes such as B0 D00,00,00,K00 can be substantially enhanced by LD rescattering. • DCPV in charmless B decays is significantly affected by FSI rescattering. Correct sign and right magnitude of DCPV in K-+ and +-are obtained after inclusion of FSI. • Large transverse polarization with fT 0.50 can be obtained from rescattering of The anomaly of not so small f remains mysterious

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