1 / 34

Weak CP Violation in Kaon and B Systems

Weak CP Violation in Kaon and B Systems. Hai-Yang Cheng Academia Sinica CPV in kaon system DCPV & Mixing-induced CPV in B decays. Lattice JC, May 25, 2007. CP Violation in Kaon System. Consider neutral K’s decays to pions

orpah
Download Presentation

Weak CP Violation in Kaon and B Systems

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. Weak CP Violation in Kaon and B Systems • Hai-Yang Cheng • Academia Sinica • CPV in kaon system • DCPV & Mixing-induced CPV in B decays Lattice JC, May 25, 2007

  2. CP Violation in Kaon System • Consider neutral K’s decays to pions • Since mK=497 MeV, m=137 MeV, K0,K0 ,  • CP| = |, CP| = -| • K0 and K0 can have mixing through weak interaction • K0  K0 (Pais, Gell-Mann) • Let CP|K0=|K0,  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 _ _ _ _ _ _ If CP is good  KL cannot decay into 

  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   direct CPV (CPV in decay amplitude) indirect (mixing) CPV (CPV in mass matrix) KL K2+ K1, KS K1+ K2 with   || with : mixing-induced CPV, ’: direct CPV A fit to K  data yields ||=(2.2320.007)10-3, Re(’/)=(1.660.26)10-3

  5. Fermilab CERN (E731) (NA31) KTeV: Bob Hsiung

  6. Direct CP Violation: Re(’/) (1993) CERN & Femilab expt’l didn’t agree until 1999 (1988)

  7. Direct CPV in neutral kaon decays: In kaon system, ’<< due mainly to I=1/2 rule; ’ vanishes in absence of I=3/2 interaction 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 Lattice: David Lin,…

  8. Taipei: Chinese J. Phys. 38, 1044 (2000)

  9. Lattice calculation of ’/ Using domain wall fermion, RBC obtained Re(’/)= - (4.0±2.3)10-4 A similar negative central value by CP-PACS (Computational Physics by Parallel Array Computer System) Recently, RBC concluded that no reliable estimate of <+-|O6|K0> (and hence QCD penguin contribution to ’/) can be made within quenched approximation

  10. Direct CP violation in charged kaon system Dalitz plot distribution for K→ is parametrized as (Weinberg ‘60) A difference between g+ & g- signals direct CP violation SM ⇒ Agc for K±→±+- & Agn for K± →±00 of order 10-5 At NLO, Agc= -(2.4±1.2)x10-5, Agn=(1.1±0.7)x10-5 (Gamiz, Prades,Scimemi) Preliminary NA48/2 results (03+04) Agc= -(1.3±2.3)x10-4 Agn=(2.1±1.9)x10-4

  11. 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

  12. M. Kobayashi & T. Maskawa, Prog. Theor. Phys. 49, 652-657 (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. Niu (丹生潔) et al. at Nagoya had found evidence for a charm production in cosmic ray data, Prog. Theor. Phys. 46, 652 (73).

  13. CKM 2006, Nagoya

  14. Some disadvantages for VCKM: • Determination of 2 and in particular 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 (喬玲麗)& Keung (姜偉宜) (84) 1>>s1>>s2>>s3 adapted by PDG as a standard parametrizarion CKM= Chau-Keung-Maiani

  15. mixing CPV () direct CPV (’) Can one observe similar mixing-induced & direct CPV in B systems ? Af 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%!

  16. 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=0.687  0.032, CK  0 Indirect CPV in KS, 0KS, f0KS, KS were also measured recently What about direct CPV in B decays ?

  17. B f ei(+) : strong phase : weak phase Need at least two different B  f paths with different strong & weak phases It is difficult to estimate direct CP reliably because strong phases are beyond our control.

  18. Direct CP asymmetries first confirmed DCPV (2004) » 3 large discrepancy

  19. Three 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, Li, 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. SCET (Bauer,Pirjol,Rothstein,Stewart) All the terms are factorized into two types of form factors FB(0)=+J Acc: charming penguin (nonfactorizable) Annihilation is real ⇒ strong phases come from charming penguin

  21. Comparison with theory: pQCD & QCDF input • pQCD (Keum, Li, Sanda): A sizable strong phase from penguin-induced annihilation by introducing parton’s transverse momentum • QCD factorization (Beneke, Buchalla, Neubert, Sachrajda): • Because of endpoint divergences, QCD/mb power corrections due to annihilation and twist-3 spectator interactions can only be modelled • QCDF (S4 scenario): large annihilation with phase chosen so that a correct sign of A(K-+) is produced (A=1, A= -55 for PP, A=-20 for PV and A=-70 for VP)

  22. Need sizable strong phases to explain the observed direct CPV • SD perturbative strong phases: penguin (BSS) vertex corrections (BBNS) annihilation (pQCD) • Nonperturbative LD strong phases induced from power correctionsespecially fromfinal-state rescattering If intermediate states are CKM more favored than final states, e.g. BDDsK  large strong phases  large corrections to rate strong weak

  23. FSI as rescattering of intermediate two-body states [HYC, Chua, Soni] • 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 • 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.] …

  24. Form factor is introduced to render perturbative calculation meaningful  LD amp. vanishes in HQ limit •  = 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

  25. B  K All rescattering diagrams contribute to penguin topology fit to rates  rD = rD*  0.69  predict direct CPV

  26. _ _ _ _ • For simplicity only LD uncertainties are shown here • FSI yields correct sign and magnitude for A(+K-) ! • K puzzle: A(0K-)  A(+ K-), while experimentally they differ by 5. Gronau argued that this is not a puzzle if |C| » |T|

  27. Time-dependent CP asymmetries Quantum Interference Oscillation, eiDm t (Vtb*Vtd)2 =|Vtb*Vtd|2 e-i 2b • Both B0 and B0 can decay to f: CP eigenstate. • If no CP (weak) phase in A: A=±A Cf=0, Sf=±sin2b Direct CPA Mixing-induced CPA

  28. Expressions of S & C for b→sqq 0.42 (=0.22) Hence, (Gronau 89) Sources of S: u-penguin, color-suppressed tree for two-body modes color-allowed tree for three-body modes (e.g. K+K-K0) or LD u-penguin and color-allowed tree induced from FSI

  29. b→s tCPV measurements • All Sf<0 • It is expected in SM that Sf is at most O(0.1) in B0KS, KS, 0KS, ’KS, 0KS, f0KS, K+K-KS, KSKSKS • [London,Soni; Grossman, Gronau, Ligeti, Nir, Rosner, Quinn,…] Naïve b→s penguin average: 0.53±0.05, 2.6 deviation from b→ccs average

  30. A current hot topic G. Kane (and others): The 2.7-3.7 anomaly seen in b→s penguin modes is the strongest hint of New Physics that has been searched in past many many years… It is extremely important to examine how much of the deviation is allowed in the SM and estimate the theoretical uncertainties as best as we can.

  31. Two-body modes QCDF: HYC, Chua, Soni; Beneke pQCD: Li, Mishima SCET: Willamson, Zupan

  32. Three-body modes (HYC, Chua, Soni): 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 sin2 < O(10%)

More Related