Flavor Diagram

					         November 30, 2004
        NTHU/NCTS Seminar

Flavor Diagram Approach to
     Hadronic B Decays

        Cheng-Wei Chiang
      National Central University

 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
 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
        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
   BR(BXc,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

C.W. Chiang        Flavor Diagram Approach                          11
               Overall UT Fit Results
              (2004 Summer, ICHEP)
                                           CKM Fitter Group

              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
 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
     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'


        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 VudVus
- loop-type amps favored because VtdVts

       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

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
 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’
  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
  Flavor SU(3) generally fits data well, with some exceptions. Predictions
  are made based upon current measurements and provide tests of the
  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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