November 30, 2004 NTHU/NCTS Seminar Flavor Diagram Approach to Hadronic B Decays Cheng-Wei Chiang National Central University Outline Beauty in B physics CPV in SM unitarity triangle Charm in B physics charmed decays for some B meson properties charmed decays for indirect CPV charmless decays for direct CPV global c2 fits and weak phase g Strangeness in B physics accumulating hints of new physics in charmless B decays FCNC Z0 as an example Perspective and Summary C.W. Chiang Flavor Diagram Approach 2 Beauty in B Physics C.W. Chiang Flavor Diagram Approach 3 Motivations for Studying B Decays We have observed in K meson system: indirect CPV: 1964 in KL p+ p– direct CPV: 1999 in CERN-NA48 and FNAL-KTeV exp’ts B factories have produced a lot of interesting results, particularly in measuring indirect CPV in the B system sin2b=0.725 0.037 from y KS data (ICHEP) indicating that B physics is entering a precision era Finally, we have recently observed direct CPV in B system (ACP(Bd p¨K§) = 0.113 § 0.019). Most branching ratios of charmless B P P and P V are currently measured with errors about 10%~20% (mostly based upon ~100M B anti-B pairs) 5%~10% errors on amplitudes One hopes to have <5% errors on the amplitudes of most modes more precise information on a and g (<10±) C.W. Chiang Flavor Diagram Approach 4 Beauty in the B Meson The beauty of B mesons lies in its large mass or the mass hierarchy: mq << LQCD << mb In the heavy quark limit, mQ 1, we discover: Flavor symmetry: dynamics unchanged under heavy flavor exchange (b c), corrections incorporated in powers of 1/mb–1/mc; Spin symmetry: dynamics unchanged under heavy quark spin flips, corrections incorporated in powers of 1/mb. B mesons provide an ideal system for studying heavy-to-heavy transitions. Much progress has been made in understanding heavy-to-light transitions in recent years: Perturbative approach: naïve factorization, generalized factorization, QCD-improved factorization, pQCD, and SCET; Nonperturbative approach: flavor SU(3) symmetry. C.W. Chiang Flavor Diagram Approach 5 The Matrix Within SM, CPV in the quark sector is explained using the CKM matrix, which is unitary and complex: 3 mixing angles 1 weak phase (Kobayashi and Maskawa, 1973) small in magnitude and least known but contain largest CPV phases Both these elements can be explored using various B meson mixing and/or decays: Vub from tree-level decays; Vtd from loop-induced processes. C.W. Chiang Flavor Diagram Approach 6 The Matrix Reloaded The CKM matrix written in terms of Wolfenstein parameters (l , A, r, and h) becomes [to O(l 3)] [Wolfenstein, PRL 51, 1945 (1983)] l ' 0.2264 A ' 0.801 / e– i b / e– i g The ultimate goal of studying B physics is not only to achieve precision measurements of the above parameters, but also to discover evidences of new physics and possibly its type (e.g. GUT, SUSY, XD). One way to detect new physics is to perform consistency checks for the sizes and phases of the CKM elements. Even if no deviation is seen from SM in these studies, we can still obtain useful and stringent bounds on new physics scales. C.W. Chiang Flavor Diagram Approach 7 Unitarity Triangle Vub and Vtd can be related to each other through the unitarity relation VudVub* + VcdVcb* + VtdVtb* = 0 A triangle can be formed on a complex plane as a geometrical representation of the above relation, where a nonzero area signifies CPV. This triangle has three sizeable angles. decay side oscillation side ACP [pp,ph,rp…] a (f2) BR(BXc,uln) DMBd and DMBs g (f3) b (f1) (0,0) (1,0) ACP [DCP K§, Kp,…] ACP (t)[J/Y KS, h’ KS, f KS(?),…] C.W. Chiang Flavor Diagram Approach 8 Charm in B Physics C.W. Chiang Flavor Diagram Approach 9 Charmed Decays B mesons decay dominantly into charmed final states; used to determine many properties: [2004 PDG] Bd: DMd = 0.502 § 0.007 ps-1; Gd = 1.542 § 0.076 ps. Bs: DMs > 14.5 ps-1; Gs = 1.461 § 0.057 ps. |Vcb| determined mainly from semileptonic B D(*) transitions; important for normalization in the UT. Bd J/y Ks involves a tree-level, dominant subprocess b c anti-c s with no CPV phase; Bd-anti-Bd mixing involves a factor e– 2 i b. Time-dependent CPA gives Sy Ks =sin2b = 0.725§0.037 (WA), consistent with constraints from other processes. The result is clean without much ambiguity or new physics pollution (unless contrived cancellation between mixing and decay). C.W. Chiang Flavor Diagram Approach 10 Overall UT Fit Results (2004 Winter) CKM Fitter Group http://ckmfitter.in2p3.fr/ C.W. Chiang Flavor Diagram Approach 11 Overall UT Fit Results (2004 Summer, ICHEP) CKM Fitter Group http://ckmfitter.in2p3.fr/ Everything simply fits together nicely! C.W. Chiang Flavor Diagram Approach 12 Charmless is Charmful ! Although rare in comparison with charmed decays (suppressed by CKM factors), charmless decays are actually very charmful and important processes. Include strangeness-conserving (DS=0) and strangeness-changing (|DS|=1) transitions; some processes in the latter category already give us hints about new physics. Offers opportunities to discover direct CPV because many of them involve more than one significant subprocesses with different weak and strong phases. B p p, p h(0), r p provide info on a, as a result of the interference between mixing and decay; B K p provides info on g. B Xu l n provides info on |Vub| (theoretically hard though because of the large charm background), thus one side of the UT. C.W. Chiang Flavor Diagram Approach 13 Importance of Strong Phases Strong interaction matters because what we observe are hadrons but not the fundamental degrees of freedom in the theory. Consider rate CP asymmetry of modes with the amplitudes Such an asymmetry requires at least two amplitudes characterized by distinct weak phases and strong phases. It is of great importance to understand the patterns of FSI phases in as wide as possible a set of decays, although what we really care about are weak phases (signals), not really strong phases (noises). C.W. Chiang Flavor Diagram Approach 14 Getting Strong Phases The Bander-Silverman-Soni (BSS) type strong phase calculation only accounts for the perturbative strong phases in penguin diagrams with intermediate q anti-q pair being on shell. [BSS, PRL 43, 242 (1979)] No first-principle method for computing FSI strong phases exists because they involve nonperturbative long-distance physics. [see a recent try by Cheng, Chua, Soni, hep-ph/0409317] One conventional and efficient method of obtaining strong phase information is to directly extract from data using isospin analysis. Flavor diagram approach offers a way to extract strong phases associated with individual topological amps and to relate them using flavor SU(3) symmetry. C.W. Chiang Flavor Diagram Approach 15 Flavor Diagram Approach This approach is intended to rely, to the greatest extent, on model independent flavor SU(3) symmetry arguments, rather than on specific model calculations of amplitudes. [Zeppenfeld, ZPC 8, 77 (1981); Chau + Cheng, PRL 56, 1655 (1986); PRD 36, 137 (1987); PRD 43, 2176 (1991); Savage+Wise, PRD 39, 2246 (1989); Grinstein + Lebed, PRD 53, 6344 (1996); Gronau et. al., PRD 50, 4529 (1994); 52, 6356 (1995); 52, 6374 (1995)] The flavor diagram approach: is diagrammatic (can be formulated in a formal way); only concerns the flavor flow (arbitrary gluon exchange among quarks); has a clearer weak phase structure (unlike isospin analysis where different weak phases usually mix). Very recent works in this direction include: Chua [PRD 68, 074001 (2003)] and Luo + Rosner [PRD 67, 094017 (2003)] for baryons; Charng + Li [PLB 594, 185 (2004) and hep-ph/0410005] for weak phase extraction; and He + McKellar [hep-ph/0410098] for analyzing recent data. C.W. Chiang Flavor Diagram Approach 16 Tree-Level Diagrams All these tree-level diagrams involve the same CKM factor. q = u,d,s q’= d,s tree (external W emission) color-suppressed (internal W emission) 1/mb suppressed due to fB. exchange (neutral mesons only) annihilation (charged mesons only) C.W. Chiang Flavor Diagram Approach 17 Loop-Level (Penguin) Diagrams All these tree-level diagrams also have the same CKM factor. S, S' q=u,d,s q’=d,s QCD (strong) penguin penguin annihilation flavor singlet (internal gluon emission) (neutral mesons) (external gluon emission) C.W. Chiang Flavor Diagram Approach 18 NLO Flavor Diagrams in Weak Interactions Nothing forbids you from drawing one of the following diagrams whenever you see T, C, or P in your amplitude list. They involve two weak boson propagators. EW penguin color-suppressed EW penguin appear together with C appear together with T and S in decay amps and P in decay amps C.W. Chiang Flavor Diagram Approach 19 Physical Flavor Diagrams Treat T, C, P, E, A, S as “leading-order” amplitudes (note that only S is of loop nature) and PEW and PCEW as “higher-order” contributions (in the sense of weak interactions). Physical amplitudes contain flavor diagrams both “leading order” and “next-to-leading order” in weak interactions t ´ T + PCEW, c ´ C + PEW, p ´ P – PCEW / 3, s ´ S – PEW / 3, a ´ A. Moreover, P contains t-, c-, and u-quark mediated penguins, Pt,c,u. One may use the unitarity to rewrite Pt as the sum of two parts, one having the same weak phase as Pc and the other having the same weak phase as Pt. This amounts to separating P into Ptc + Ptu. Ptu involves the same CKM factor as the tree-level amplitudes. One may thus sweep this amplitude to the tree-level amplitude category. Note that this amplitude may be sizeable, particularly for DS = 0 decays. For example, what many people call T or C extracted from p p decays are actually T – Ptu and C + Ptu. Thus, “| C / T |” > 1 is possible. C.W. Chiang Flavor Diagram Approach 20 A Simple Example Quark contents: p+ p- p+ r- T TV p+ p+ When vector mesons are involved, one Bd p- Bd r- further labels the amplitude by which meson the spectator quark goes into. P PV Therefore, A(p+p–) = – (T + P); p+ p+ A(p+r–) = – (TV + PV). Bd Bd Minus sign comes p- r- from the wave functions of p– and r–. C.W. Chiang Flavor Diagram Approach 21 Hierarchy in Flavor Diagrams In our definition, the amplitudes contains CKM factors and may involve an arbitrary number of gluon exchanges. An educated guess tells us that the magnitudes of the amplitudes should roughly satisfy the following hierarchical structure. It should be emphasized that l appearing in the hierarchy is not an expansion parameter but merely an order parameter. It simply reflects our naïve expectation in the magnitudes of flavor amplitudes. when going from 1 st row to 2nd row: - tree-type amps suppressed because VudVus - loop-type amps favored because VtdVts C.W. Chiang Flavor Diagram Approach 22 Global Fits to Charmless Decays Goals for the global fits: Check if the SM offers a consistent picture for all available data; Check the working assumption of SU(3)F; Extract weak phase g (thus a by unitarity); Extract strong phases; check Lipkin conjecture in V P decays; Make predictions of unseen modes based upon current data. Parameters involved in the fits include: Amplitude sizes; Weak phases; Strong phases. Data points used in the c2 fits include: Branching ratios; CP asymmetries (time-dependent and -independent). C.W. Chiang Flavor Diagram Approach 23 Some Basic Formulas The invariant matrix element M for a decay process B M1 M2 and the corresponding decay width are where p is the 3-momentum of the final state particle in the rest frame of B. Note that M may contain polarization vector summation and average as is the case for final states containing vector mesons. We also assume the following SU(3)F relations (with l = 0.224): partial SU(3)F breaking taken into account assuming perfect SU(3)F symmetry for these amps C.W. Chiang Flavor Diagram Approach 24 B V P Decays CWC, M. Gronau, Z. Luo, J. Rosner, D. Suprun, PRD 69, 034001 (2004) [hep-ph/0307395]. C.W. Chiang Flavor Diagram Approach 25 Fitting Parameters for VP Modes start with: related by symmetry: other quantities: ignored small amplitudes such as color-suppressed EW penguin, exchange, annihilation diagrams, and S(0)P,V. C.W. Chiang Flavor Diagram Approach 26 Fitting Parameters for VP Modes We thus have the following parameters: • amp sizes: | tP |, | tV |, | CP |, | CV |, | p0 P |, | p0 V |, |P0 EWP |, |P0 EWV |; • strong phases: dP, dV, f; • weak phase: g only (no b dependence). • symmetric under simultaneous changes: g p – g, dP,V p – d P,V and f – f. C.W. Chiang Flavor Diagram Approach 27 List of Modes In our fit, there are totally 34 observables: 13 data points C.W. Chiang Flavor Diagram Approach 28 List of Modes another 16 data points 13 data points finally, include time-dependent CP asymmetries: Sf Ks=-0.147§0.697 (S=2.11), Af Ks=0.046§0.256 (S=1.08) (contribute constant to c2) [Browder, talk at LP03] Srp=-0.13§0.18§0.04, DSrp=0.33§0.18§0.03 (provide b dependence) [BaBar, talk by Jawahery at LP03] C.W. Chiang Flavor Diagram Approach 29 c2-g Plots (34 data points) p’V/p’P = –1; 10 parameters p’V/p’P = real; 11 parameters p’V/p’P = complex; 12 parameters All of them together major changes in c2 at g'65± and 165± from step 1 to step 2 positions of minima almost unaffected g=(53+15-33)± if Srp is left out, c.f. g=(63§6)± here For the three major minima, we still have: g ' 25± and 165± disfavored by CKM Fitter and dynamics g ' 65± favored and consistent with CKMFitter C.W. Chiang Flavor Diagram Approach 30 Fit Results physical solution prefers trivial strong phases while others give large strong phases, consistent with perturbative calculations C.W. Chiang Flavor Diagram Approach 31 Predictions for VP Modes (DS=0, complex p’V/p’P) results showing significant differences from exp’t data results showing significant differences among the three fits C.W. Chiang Flavor Diagram Approach 32 Predictions for VP Modes (|DS|=1, complex p’V/p’P) results showing some significant differences among the three fits C.W. Chiang Flavor Diagram Approach 33 Some Discussions Overall, fits are satisfactory (at 38% and 55% CL for 10- and 12- parameter fits) and have solutions g = (65§6)± and (63§6)± consistent with constraints from other processes. Data of r p play the roles of breaking the g p – g symmetry and stabilizing the fit results. Note that the c2 fits allow us to extract preferred values of fitting parameters along with their 1 s errors. Moreover, we have an idea about how good our fits are from the CL. Global fits prefers the Lipkin conjecture p0= – p0 P . Only partial SU(3) breaking effect included for T amps; can verify SU(3) for penguin amps when B K* anti-K (pV) and anti-K* K (pP ) rates are measured. C.W. Chiang Flavor Diagram Approach 34 B P P Decays CWC, M. Gronau, J. Rosner, PRD 68, 074012 (2003) [hep-ph/0306021]; CWC, M. Gronau, J. Rosner, D. Suprun, PRD 70, 034020 (2004) [hep-ph/0404073]. C.W. Chiang Flavor Diagram Approach 35 List of Modes large CP asymmetries; BR too small compared To QCD fact. predictions BR too large compared to QCD fact. predictions purely p’ p K anomaly need s’=S’-P’EW / 3 C.W. Chiang Flavor Diagram Approach 36 c2-g Plot From bottom to top, we use 8 and 6 CKM fitter parameters to fit 14 data points (p p and K p) and 13 and 11 parameters to fit 24 data points (further including final states with h and h0). Find g ' 54± ~ 66±, results still consistent with but less stable than the V P case. C.W. Chiang Flavor Diagram Approach 37 Fit Results consistent with other constraints large |C/T| ratio and non-trivial relative strong phase; unable to account for in perturbation all strong phases relative to P’ required to account for the large h 0 K BR’s satisfactory overall fit results C.W. Chiang Flavor Diagram Approach 38 Predictions for PP Modes no problem in p p modes still problematic in p K modes C.W. Chiang Flavor Diagram Approach 39 Some discussions [see also Chua, Hou and Yang, Mod. Phys. Lett. A18, 1763 (2003); Buras et al, PRL 92, 101804 (2004); hep-ph/0402112] Fits to p p + p K data: requires large |C/T| ratio (> 0.5); requires a nontrivial strong phase between C and T (» 100±). Fits to all PP data one needs to introduce S (singlet penguin), Ptu (t,u-mediated penguin); one needs to introduce Stu (t,u-mediated singlet penguin) particularly for the p+h’ mode. Robust results in our fits magnitude of QCD penguin |P|; relative strong phase between T and P; sizes of electroweak penguins (color-allowed and -suppressed), consistent with Neubert-Rosner relation; obtain g ' 60± (48± < g < 73±, 68%CL), consistent with CKM fitter and earlier analysis for VP modes. We do not fully trust the stability of the shallow minima. C.W. Chiang Flavor Diagram Approach 40 Strangeness in B Physics V. Barger, CWC, P. Langacker, H.S. Lee, PLB 580, 186 (2004) [hep-ph/0310073]; V. Barger, CWC, J. Jiang, P. Langacker, PLB 596, 229 (2004) [hep-ph/0405108]; V. Barger, CWC, P. Langacker, H.S. Lee, PLB 598, 218 (2004) [hep-ph/0406126]. C.W. Chiang Flavor Diagram Approach 41 p K Anomaly Within the SM, the following ratios should be approximately equal but show a 2.4s 1.9s difference. Possible explanations: underestimate of p 0 detection efficiency; [Gronau and Rosner, hep-ph/0402112] new physics. [Buras et al, PRL 92, 101804 (2004); NPB 697:133 (2004), hep-ph/0410407] One minimal explanation is that the color-allowed electroweak penguins cause the problem isospin-violating new physics C.W. Chiang Flavor Diagram Approach 42 Z0 Model With FCNC The B p K decay can be a tree-level process mediated by a Z' boson if there are FCNC couplings (possible for family non-universal charges). We simply a general Z' model by assuming: (i) no right-handed flavor-changing couplings, (ii) no significant RG running effect between MZ' and MW scales, (iii) negligible Z' effect on the QCD penguins so that the new physics is manifestly isospin-violating. With these simplifications, we have 3 parameters left in the model. carrying a new CP-violating source C.W. Chiang Flavor Diagram Approach 43 Parameter Extraction Following the arguments in Buras et al, new physics is coded by the parameters: Found solutions from p p and p K data: Correspond to our parameters: C.W. Chiang Flavor Diagram Approach 44 Simultaneous Solution to p K and f KS Can the p K anomaly and f Ks asymmetries be accounted for by the same thing at the same time? According to Buras et al, their solution [our solution (AL)] to the p K anomaly leads to S(f Ks) greater than S(Y Ks)! However, due to different interference patterns between O7,8 and O9,10 operators in our model, it is possible [all our other solutions (BL, ALR and BLR)] to have S(f Ks) smaller than S(Y Ks). C.W. Chiang Flavor Diagram Approach 45 Perspective and Summary Flavor diagram approach provides a simple and reliable picture for describing B decays. It is phenomenological (data driven), contains LO and NLO amps in weak interactions but all orders in strong interactions, includes final state interacting effects, and suffers from SU(3)F breaking effects. Flavor SU(3) generally fits data well, with some exceptions. Predictions are made based upon current measurements and provide tests of the formalism. All fits provide information on g that is consistent with other extractions. Results from ICHEP are being analyzed by D. Suprun for his thesis. We need to know more information about strong phases. In particular, one should understand better about final-state rescattering effects. We hope to see a proof of factorization in processes of interest to us, in particular, those involving penguin diagrams. We hope to see more affirmative evidence of new physics in B physics, e.g., Sf KS the p K anomaly, large Bs anti-Bs mixing, etc. C.W. Chiang Flavor Diagram Approach 46 Thank You C.W. Chiang Flavor Diagram Approach 47

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