1. Flavor Diagram Approach to Hadronic B Decays
November 30, 2004
NTHU/NCTS Seminar
Flavor Diagram Approach to Hadronic B Decays
Cheng-Wei Chiang
National Central University

2. Flavor Diagram Approach
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

3. Flavor Diagram Approach-
Beauty in B Physics
C.W. Chiang
Flavor Diagram Approach

4. 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§) = § 0.019).
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

5. Flavor Diagram Approach
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

6. The Matrix -
Within SM, CPV in the quark sector is explained using the CKM matrix, which is unitary and complex:
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.
3 mixing angles
1 weak phase
(Kobayashi and Maskawa, 1973)
C.W. Chiang
Flavor Diagram Approach

7. Flavor Diagram Approach
The Matrix Reloaded -
The CKM matrix written in terms of Wolfenstein parameters (l, A, r, and h) becomes [to O(l3)] [Wolfenstein, PRL 51, 1945 (1983)]
/ e– ib
/ e– ig
l '
A ' 0.801
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

8. 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(BXc,uln)
DMBd and DMBs
g (f3)
b (f1)
(1,0)
(0,0)
ACP[DCPK§, Kp,…]
ACP(t)[J/Y KS, h’ KS, f KS(?),…]
C.W. Chiang
Flavor Diagram Approach

9. Flavor Diagram Approach-
Charm in B Physics
C.W. Chiang
Flavor Diagram Approach

10. Flavor Diagram Approach
Charmed Decays -
B mesons decay dominantly into charmed final states; used to determine many properties: [2004 PDG]
Bd: DMd = § ps-1; Gd = § ps.
Bs: DMs > 14.5 ps-1; Gs = § 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

11. Overall UT Fit Results (2004 Winter)-
CKM Fitter Group
C.W. Chiang
Flavor Diagram Approach

12. Overall UT Fit Results (2004 Summer, ICHEP)-
CKM Fitter Group
Everything simply fits together nicely!
C.W. Chiang
Flavor Diagram Approach

13. Flavor Diagram Approach
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

14. 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

15. Flavor Diagram Approach
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/ ]
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

16. 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, (2003)] and Luo + Rosner [PRD 67, (2003)] for baryons; Charng + Li [PLB 594, 185 (2004) and hep-ph/ ] for weak phase extraction; and He + McKellar [hep-ph/ ] for analyzing recent data.
C.W. Chiang
Flavor Diagram Approach

17. Flavor Diagram Approach
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

18. Loop-Level (Penguin) Diagrams
QCD (strong) penguin (internal gluon emission)
penguin annihilation (neutral mesons)
q=u,d,s
q’=d,s
S, S'
flavor singlet (external gluon emission)
All these tree-level diagrams also have the same CKM factor.
C.W. Chiang
Flavor Diagram Approach

19. 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 and S in decay amps
appear together with T and P in decay amps
C.W. Chiang
Flavor Diagram Approach

20. 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

21. Flavor Diagram Approach
A Simple Example -
Quark contents:
When vector mesons are involved, one further labels the amplitude by which meson the spectator quark goes into.
Therefore,
A(p+p–) = – (T + P);
A(p+r–) = – (TV + PV).
Minus sign comes from the wave functions of p– and r–.
p+p-
p+r- Bd p- p+ T P PV Bd p+ r- TV
C.W. Chiang
Flavor Diagram Approach

22. 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 1st row to 2nd row:
- tree-type amps suppressed because VudVus
- loop-type amps favored because VtdVts
C.W. Chiang
Flavor Diagram Approach

23. 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

24. Flavor Diagram Approach
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

25. Flavor Diagram Approach-
B  V P Decays
CWC, M. Gronau, Z. Luo, J. Rosner, D. Suprun, PRD 69, (2004) [hep-ph/ ].
C.W. Chiang
Flavor Diagram Approach

26. 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

27. 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

28. Flavor Diagram Approach
List of Modes -
In our fit, there are totally 34 observables:
13 data points
C.W. Chiang
Flavor Diagram Approach

29. Flavor Diagram Approach
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

30. c2-g Plots (34 data points)
p’V/p’P = real; 11 parameters
p’V/p’P = complex; 12 parameters
All of them together
p’V/p’P = –1; 10 parameters
major changes in c2 at g'65± and 165± from step 1 to step 2
positions of minima almost unaffected
g=( )± 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

31. Flavor Diagram Approach
Fit Results -
physical solution prefers trivial strong phases while others give large strong phases,
consistent with perturbative calculations
C.W. Chiang
Flavor Diagram Approach

32. Predictions for VP Modes (DS=0, complex p’V/p’P)-
results showing significant differences
among the three fits
results showing significant
differences from exp’t data
C.W. Chiang
Flavor Diagram Approach

33. 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

34. Flavor Diagram Approach
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

35. Flavor Diagram Approach-
B  P P Decays
CWC, M. Gronau, J. Rosner, PRD 68, (2003) [hep-ph/ ];
CWC, M. Gronau, J. Rosner, D. Suprun, PRD 70, (2004) [hep-ph/ ].
C.W. Chiang
Flavor Diagram Approach

36. Flavor Diagram Approach
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

37. Flavor Diagram Approach
c2-g Plot -
From bottom to top, we use 8 and 6
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.
CKM fitter
C.W. Chiang
Flavor Diagram Approach

38. Flavor Diagram Approach
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

39. Predictions for PP Modes-
no problem in p p modes
still problematic in p K modes
C.W. Chiang
Flavor Diagram Approach

40. Flavor Diagram Approach
Some discussions -
[see also Chua, Hou and Yang, Mod. Phys. Lett. A18, 1763 (2003);
Buras et al, PRL 92, (2004); hep-ph/ ]
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

41. Strangeness in B Physics-
Strangeness in B Physics
V. Barger, CWC, P. Langacker, H.S. Lee, PLB 580, 186 (2004) [hep-ph/ ];
V. Barger, CWC, J. Jiang, P. Langacker, PLB 596, 229 (2004) [hep-ph/ ];
V. Barger, CWC, P. Langacker, H.S. Lee, PLB 598, 218 (2004) [hep-ph/ ].
C.W. Chiang
Flavor Diagram Approach

42. Flavor Diagram Approach
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/ ]
new physics. [Buras et al, PRL 92, (2004); NPB 697:133 (2004), hep-ph/ ]
One minimal explanation is that the color-allowed electroweak penguins cause the problem  isospin-violating new physics
C.W. Chiang
Flavor Diagram Approach

43. Flavor Diagram Approach
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

44. Flavor Diagram Approach
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

45. 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

46. 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

47. Flavor Diagram Approach-
Thank You
C.W. Chiang
Flavor Diagram Approach