1 / 30

QCD Factorization with Final-State Interactions

QCD Factorization with Final-State Interactions. Chun-Khiang Chua Academia Sinica, Taipei 3rd ICFP, Cung-Li, Taiwan. M 2. B. M 1. Factorization in B decays. We basically have three scales in a non-leptonic B decay: m W >> m B >> L QCD Integrating out d.o.f. above m B :

Download Presentation

QCD Factorization with Final-State Interactions

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. QCD Factorization with Final-State Interactions Chun-Khiang Chua Academia Sinica, Taipei 3rd ICFP, Cung-Li, Taiwan

  2. M2 B M1 Factorization in B decays • We basically have three scales in a non-leptonic B decay: mW >> mB >> LQCD • Integrating out d.o.f. above mB: H=ci(m) Qi(m) • Naïve factorization: A  BM1 0 M2 ai(cj)FFBM1 fM2 In mb limit, M2 produced in point-like interactions carries away energies O(mb) and will decouple from soft gluon effect Bjorken

  3. Naïve factorization in B Decays • For color allowed processes the naïve factorization approx. works well. • However, • Corrections (non factorization contributions) are incalculable. Neglected. • Dependence of scale m in amp. from ai(m) cannot be cancelled. BR(Theory)≈3 10-3 BR(Expt.)=(2.76±0.25)10-3

  4. Direct CP violations : strong phase : weak phase B f ei(+) One needs at least two different B  f paths with distinct weak & strong phases _ first confirmed DCPV (5.7) in B decays (2004) _ _ We do have 2 different paths strong phase ?

  5. Generalize factorization Ali, Greub (98) Chen,Cheng,Tseng,Yang (99) penguin corrections • For problem with scheme and scale dependence, consider vertex and penguin corrections to four-quark matrix elements • Strong phase from the BSS cut: k2~m2B/4  m2B/2 gives large uncertainty • Corrections (non-fac. Contributions) are still incalculable. Parameterized.

  6. QCD Factorization Beneke, Buchalla, Neubert, Sachrajda (99) TI: TII: hard spectator interactions • M(x): light-cone distribution amplitude (LCDA) and x the momentum fraction of quark in meson M • At O(s0) and mb, TI=1, TII=0, naïve factorization is recovered • At O(s), TI involves vertex and penguin corrections, • TII arises from hard spectator interactions(New)

  7. Comparison between QCDF & generalized fac. • QCDF is a natural extension of generalized factorization with the following improvements: • Corrections to naïve factorization are calculable [1+O(as)] • Hard spectator interaction, which is of the same 1/mb order as vertex & penguin corrections, is included (new)  crucial for a2 & a10 • Include distribution of meson momentum fraction  • 1. a new strong phase from vertex corrections • 2. fixed gluon virtual momentum in penguin diagram (imp.for dCP) • Except a6 and a8 all effective wilson coefficients are gauge and scheme independent. • a6 and a8 come with mc/mB=m2p/(mu+md) mB. Power correction. • QCDF is model independent in the large mB limit and reduces to naïve fac. in the O(as0) limit.

  8. Power corrections 1/mb power corrections: twist-3 DAs, annihilation, FSIs,… • We encounter penguin matrix elements from O5,6 such as • formally 1/mb suppressed from twist-3 DA, • numerically important (c enhancement) : (2GeV)m2/(mu+md)  2.6 GeV , 2 mc  mb For example, in the penguin-dominated mode B K A(BK)  a4+(2/mb) a6 where 2/mb 1 & a6/a4 1.7 • Phenomenologically, power corrections should be taken into account •  need to include twist-3 DAs p &  systematically OK for vertex & penguin corrections: (mc/mb) a6,8: scale independent.

  9. ai for B K at different scales black: vertex & penguin, blue: hard spectatorgreen: total

  10. Endpoint divergence in hard spectator and annihilation interactions • The twist-3 term is divergent as p(y) doesn’t vanish at y=1: Logarithmic divergence arises when the spectator quark in M1 becomes soft • Not a surprise ! Just as in HQET, power corrections are a priori nonperturbative in nature. Hence, their estimates are model dependent & can be studied only in a phenomenological way • BBNS model the endpoint divergenceby • with h being a typical hadron scale  500 MeV. • For annihilation contributions endpoint divergence starts at twist-2 term. • Both endpoint divergences occur as 1/mB power corrections (model dependent). • FSI could be important. Several hints…

  11. 1. Large strong phases in charmless modes are needed 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)

  12. 2. Rate enhancements in color-suppressed, fac.-forbidden or penguin-dominated modes • Some decay modes do not receive factorizable contributions e.g. B  Kc0 with sizable BR though c0|c(1-5)c|0=0. • Color-suppressed modes: B0  D0 h0 (0,,0,,’), 00, 00 have the measured rates larger than theoretical expectations. • Penguin-dominated modes such as BK*, K, K, K* predicted by QCDF are consistently lower than experiment by a factor of 2  3  importance of power corrections (inverse powers of mb) e.g. FSI, annihilation, EW penguin, New Physics, …

  13. FSI as rescattering of intermediate two-body states [Cheng, CKC, 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 • Form factor or cutoff must be introduced as exchanged particle is • off-shell and final states are necessarily hard • Alternative: Elastic Rescattering [CKC, Hou Yang] Regge trajectory [Nardulli,Pham][Falk et al.] [Du et al.] …

  14. 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 by a fit to the measured rates •  r is process dependent • n=1 (monopole behavior), consistent with QCD sum rules Once cutoff is fixed  direct 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

  15. _ _ _ _ • For simplicity only LD uncertainties are shown here • FSI yields correct sign and magnitude for A(+K-) ! • K anomaly: A(0K-)  A(+ K-), while experimentally they differ by 3.4 SD effects?[Fleischer et al, Nagashima Hou Soddu, H n Li et al.] • Final state interaction is important.

  16. B   B  ﹣ _ _ _ • Sign and magnitude for A(+-) are nicely predicted ! • DCPVs are sensitive to FSIs, but BRs are not (rD=1.6) • For 00, 1.40.7 BaBar Br(10-6)= 3.11.1 Belle 1.6+2.2-1.6 CLEO Discrepancy between BaBar and Belle should be clarified.

  17. Mixing induced CP violation Bigi, Sanda 81 Quantum Interference Oscillation, eiDm t (Vtb*Vtd)2 =|(Vtb*Vtd)2| e-i 2b

  18. D sin2beff • CKM phase is dominated. Look for small effects. • Measuring the deviation of sin2beff in charmonium and penguin modes (dw0) is important in the search of NP [new physics (phase)] • Deviation  NP • How robust is the argument? • Originally, FSI was totally ignored.

  19. Time-dependent CP asymmetries: In general, Sf sin2eff sin(2+W). For bsqq modes, Since au is larger than ac, it is possible that S will be subject to significant “tree pollution”. However, au here is color-suppressed. • Penguin contributions to KS and 0KS are suppressed due to cancellation between two penguin terms (a4 & a6) • relative importance of tree contribution • may have large deviation of S from sin2

  20. FSI effects on sin2beff(Cheng, CKC, Soni 05) • FSI can bring in additional weak phase -- B→K*p, Kr contain tree Vub Vus*=|Vub Vus|e-ig

  21. FSI effects in rates • FSI enhance rates though rescattering of charmful intermediate states [rates are used to fixed cutoffs (L=m + r LQCD, r~1)].

  22. FSI effects on direct CP violation • Large CP violation in the rK mode.

  23. FSI effect on DS sin2b=0.6850.032 Input CKM sin2b=0.724 • Theoretically and experimentally cleanest modes: h’KsfKs • Tree pollutions are diluted for non pure penguin modes. wKS, r0KS

  24. FSI effects in mixing induced CP violation of penguin modes are small • The reason for the smallness of the deviations: • The dominated FSI contributions are of charming penguin like. Do not bring in any additional weak phase. • The source amplitudes (K*p,Kr) are small (Br~10-6) compare with Ds*D (Br~10-2,-3) • The source with the additional weak phase are even smaller (tree small, penguin dominate) • If we somehow enhance K*p,Kr contributions ⇒ large direct CP violation (AfKs). Not supported by data

  25. Conclusion • QCDF improve naïve and generalized factorizations. It is model independent in the large mB limit. • FSI should play some (sub-leading) role in B decays. (finite mB) • Rates are enhanced: PP modes Kp, ’K…; PV modes r0p0K, K, 0K… • Large direct CP violation in K-p+, r+p-, r0K0... • The deviation of sin2beff from sin2 = 0.6850.032 are at most O(0.1) in penguin-dominated B0KS, KS, 0KS, ’KS, 0KS, f0KS (w/wo FSI) • sin2beff on penguin modes are still good places to look for new phase. • We should also try to look for them in other places.

  26. Back up slides

  27. twist-2 & twist-3 LCDAs: Twist-3 DAs p &  are suppressed by /mb with =m2/(mu+md) Cn: Gegenbauer poly. with 01 du (u)=1, 01 du p,(u)=1

  28. In mb limit, only leading-twist DAs contribute The parameters ai are given by ai are renor. scale & scheme indep except for a6 & a8 strong phase from vertex corrections

  29. Penguin contributions Pi have similar expressions as before except that G(m) is replaced by Gluon’s virtual momentum in penguin graph is thus fixed, k2 xmb2 • Hard spectator interactions (non-factorizable) : not 1/mb2 power suppressed: i). B() is of order mb/ at =/mb   d/ B()=mB/B ii). fM  , fB  3/2/mb1/2, FBM  (/mb)3/2  H  O(mb0) [ While in pQCD, H  O(/mb) ] responsible for enhancement of color-suppressed graphs (see a2 below)

  30. Annihilation topology Weak annihilation contributions are power suppressed • ann/tree  fBf/(mB2 F0B)/mB • Endpoint divergence exists even at twist-2 level. In general, ann. amplitude contains XA and XA2 with XA10 dy/y • Endpoint divergence always occurs in power corrections • While QCDF results in HQ limit (i.e. leading twist) are model independent, model dependence is unavoidable in power corrections

More Related