Flavor Diagram Approach to Hadronic B Decays Cheng-Wei Chiang National Central University Cheng-Wei...

Flavor Diagram Approach toHadronic B Decays

Flavor Diagram Approach toHadronic B Decays

Cheng-Wei ChiangCheng-Wei ChiangNational Central UniversityNational Central University

Cheng-Wei ChiangCheng-Wei ChiangNational Central UniversityNational Central University

November 30, 2004NTHU/NCTS Seminar

C.W. Chiang Flavor Diagram Approach 2

Outline Outline

Beauty in Beauty in BB physics physics CPV in SMCPV in SM unitarity triangleunitarity triangle

Charm in Charm in BB physics physics charmed decays for some charmed decays for some BB meson properties meson properties charmed decays for charmed decays for indirectindirect CPV CPV charmless decays for charmless decays for directdirect CPV CPV global global 22 fits and weak phase fits and weak phase

Strangeness in Strangeness in BB physics physics accumulating hints of new physics in charmless accumulating hints of new physics in charmless BB decays decays FCNC FCNC ZZ00 as an example as an example

Perspective and SummaryPerspective and Summary


Beauty in B PhysicsBeauty in B Physics


Motivations for Studying B DecaysMotivations for Studying B Decays

We have observed in We have observed in KK meson system: meson system:

indirect CPV: 1964 in indirect CPV: 1964 in KKLL ++ ––

direct CPV: 1999 in CERN-NA48 and FNAL-KTeV exp’tsdirect CPV: 1999 in CERN-NA48 and FNAL-KTeV exp’ts

B factories have produced a lot of interesting results, particularly in measuring B factories have produced a lot of interesting results, particularly in measuring indirect CPVindirect CPV in the B system in the B system

sin2sin2=0.725 =0.725 0.037 0.037 from from KKSS data (ICHEP) data (ICHEP)

indicating that indicating that BB physics is physics is entering a precision eraentering a precision era

Finally, we have recently observed Finally, we have recently observed direct CPVdirect CPV in B systemin B system ( (AACPCP((BBdd ¨̈KK§§) = ) =

0.113 0.113 §§ 0.019). 0.019).

Most branching ratios of charmless Most branching ratios of charmless BB P PP P and and P VP V are currently measured are currently measured with errors about 10%~20% (mostly based upon ~100M with errors about 10%~20% (mostly based upon ~100M BB anti- anti-BB pairs) pairs)

5%~10% errors on amplitudes5%~10% errors on amplitudes

One hopes to have <5% errors on the amplitudes of most modesOne hopes to have <5% errors on the amplitudes of most modes

more precise information on more precise information on and and (<10 (<10±±))


The beauty of The beauty of BB mesons lies in its large mass or the mass hierarchy: mesons lies in its large mass or the mass hierarchy:

mmqq << << QCDQCD << << mmbb

In the heavy quark limit, In the heavy quark limit, mmQQ 11, we discover:, we discover:

Flavor symmetryFlavor symmetry: dynamics unchanged under heavy flavor : dynamics unchanged under heavy flavor exchange (exchange (bb cc), corrections incorporated in powers of 1/), corrections incorporated in powers of 1/mmbb–1/–1/mmcc;;

Spin symmetrySpin symmetry: dynamics unchanged under heavy quark spin flips, : dynamics unchanged under heavy quark spin flips, corrections incorporated in powers of 1/corrections incorporated in powers of 1/mmbb..

BB mesons provide an ideal system for studying heavy-to-heavy mesons provide an ideal system for studying heavy-to-heavy transitions.transitions.

Much progress has been made in understanding heavy-to-light Much progress has been made in understanding heavy-to-light transitions in recent years:transitions in recent years:

Perturbative approachPerturbative approach: naïve factorization, generalized factorization, : naïve factorization, generalized factorization, QCD-improved factorization, pQCD, and SCET;QCD-improved factorization, pQCD, and SCET;

Nonperturbative approachNonperturbative approach: flavor SU(3) symmetry.: flavor SU(3) symmetry.

Beauty in the B MesonBeauty in the B Meson


The Matrix The Matrix

Within SM, CPV in the quark sector is explained using the CKM matrix, Within SM, CPV in the quark sector is explained using the CKM matrix, which is unitary and complex:which is unitary and complex:

3 mixing angles3 mixing angles1 weak phase1 weak phase

small in magnitude and least knownsmall in magnitude and least knownbut contain largest CPV phasesbut contain largest CPV phases

Both these elements can be explored using various Both these elements can be explored using various BB meson mixing meson mixing and/or decays:and/or decays:

VVubub from tree-level decays; from tree-level decays;

VVtdtd from loop-induced processes. from loop-induced processes.

(Kobayashi and Maskawa, 1973)


/ e– i / e– i

The CKM matrix written in terms of Wolfenstein parameters (The CKM matrix written in terms of Wolfenstein parameters (, , AA, , , and , and ) becomes [to O() becomes [to O(33)])] [Wolfenstein, PRL 51, 1945 (1983)][Wolfenstein, PRL 51, 1945 (1983)]

The ultimate goal of studying The ultimate goal of studying BB physics is not only to achieve precision physics is not only to achieve precision measurements of the above parameters, but also to discover evidences of measurements of the above parameters, but also to discover evidences of new physics and possibly its type (e.g. GUT, SUSY, XD).new physics and possibly its type (e.g. GUT, SUSY, XD). One way to detect new physics is to perform consistency checks for the One way to detect new physics is to perform consistency checks for the sizes and phases of the CKM elements.sizes and phases of the CKM elements. Even if no deviation is seen from SM in these studies, we can still Even if no deviation is seen from SM in these studies, we can still obtain useful and stringent bounds on new physics scales.obtain useful and stringent bounds on new physics scales.

' 0.2264A ' 0.801

The Matrix ReloadedThe Matrix Reloaded


VVubub and and VVtdtd can be related to each other through the unitarity relation 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 A triangle can be formed on a complex plane as a geometrical representation of the above relation, where a nonzero area signifies CPV.representation of the above relation, where a nonzero area signifies CPV.

This triangle has three sizeable angles.This triangle has three sizeable angles.

(2)

(3) (1)(0,0) (1,0)

ACP(t)[J/ KS, ’ KS, KS(?),…]ACP[DCPK§, K,…]

MBd and MBsBR(BXc,ul)

ACP[,,…]

decay sidedecay side oscillation sideoscillation side

Unitarity TriangleUnitarity Triangle


Charm in B PhysicsCharm in B Physics


BB mesons decay dominantly into charmed final states; used to determine mesons decay dominantly into charmed final states; used to determine many properties:many properties: [2004 PDG][2004 PDG]

BBdd: : MMdd = 0.502 = 0.502 §§ 0.007 ps 0.007 ps-1-1; ; dd = 1.542 = 1.542 §§ 0.076 ps. 0.076 ps.

BBss: : MMss > 14.5 ps > 14.5 ps-1-1; ; ss = 1.461 = 1.461 §§ 0.057 ps. 0.057 ps.

||VVcbcb| determined mainly from semileptonic | determined mainly from semileptonic BB DD(*)(*) transitions; transitions;

important for normalization in the UT.important for normalization in the UT.

BBdd J/J/ KKss involves a tree-level, dominant subprocess involves a tree-level, dominant subprocess bb cc anti- anti-cc ss

with no CPV phase; with no CPV phase; BBdd-anti--anti-BBdd mixing involves a factor mixing involves a factor ee– 2 – 2 i i ..

Time-dependent CPA gives Time-dependent CPA gives SS K Kss =sin2 =sin2 = 0.725 = 0.725§§0.037 (WA), 0.037 (WA),

consistent with constraints from other processes.consistent with constraints from other processes.

The result is clean without much ambiguity or new physics pollution The result is clean without much ambiguity or new physics pollution (unless contrived cancellation between mixing and decay).(unless contrived cancellation between mixing and decay).

Charmed DecaysCharmed Decays


Overall UT Fit Results(2004 Winter)

Overall UT Fit Results(2004 Winter)

CKM Fitter Group http://ckmfitter.in2p3.fr/


Overall UT Fit Results(2004 Summer, ICHEP)Overall UT Fit Results

(2004 Summer, ICHEP)CKM Fitter Group http://ckmfitter.in2p3.fr/

Everything simply fits together nicely!


Although rare in comparison with charmed decays (suppressed by CKM Although rare in comparison with charmed decays (suppressed by CKM factors), charmless decays are actually very factors), charmless decays are actually very charmful and importantcharmful and important processes.processes.

Include strangeness-conserving (Include strangeness-conserving (S=0) and strangeness-changing (|S=0) and strangeness-changing (|S|S|=1) transitions; some processes in the latter category already give us =1) transitions; some processes in the latter category already give us hints about new physics.hints about new physics.

Offers opportunities to discover Offers opportunities to discover direct CPVdirect CPV because many of them because many of them involve more than one significant subprocesses with different weak and involve more than one significant subprocesses with different weak and strong phases.strong phases.

BB , , ((00)), , provide info on provide info on , as a result of the , as a result of the interference between mixing and decay;interference between mixing and decay;

BB K K provides info on provides info on ..

BB XXuu l l provides info on | provides info on |VVubub| (theoretically hard though because of | (theoretically hard though because of

the large charm background), thus one side of the UT.the large charm background), thus one side of the UT.

Charmless is Charmful !Charmless is Charmful !


Strong interaction matters because what we observe are hadrons but not Strong interaction matters because what we observe are hadrons but not the fundamental degrees of freedom in the theory.the fundamental degrees of freedom in the theory.

Consider rate CP asymmetry of modes with the amplitudesConsider rate CP asymmetry of modes with the amplitudes

Such an asymmetry requires at least two amplitudes characterized by Such an asymmetry requires at least two amplitudes characterized by distinct weak phases and strong phases.distinct weak phases and strong phases.

It is of great importance to understand the patterns of FSI phases in as 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 wide as possible a set of decays, although what we really care about are weak phases (signals), not really strong phases (noises).weak phases (signals), not really strong phases (noises).

Importance of Strong PhasesImportance of Strong Phases


The Bander-Silverman-Soni (BSS) type strong phase calculation only The Bander-Silverman-Soni (BSS) type strong phase calculation only accounts for the perturbative strong phases in penguin diagrams with accounts for the perturbative strong phases in penguin diagrams with intermediate q anti-q pair being on shell.intermediate q anti-q pair being on shell.

[BSS, PRL 43, 242 (1979)][BSS, PRL 43, 242 (1979)]

No first-principle method for computing FSI strong phases exists No first-principle method for computing FSI strong phases exists because they involve nonperturbative long-distance physics.because they involve nonperturbative long-distance physics.

[see a recent try by Cheng, Chua, Soni, hep-ph/0409317][see a recent try by Cheng, Chua, Soni, hep-ph/0409317]

One conventional and efficient method of obtaining strong phase One conventional and efficient method of obtaining strong phase information is to directly extract from data using isospin analysis.information is to directly extract from data using isospin analysis.

Flavor diagram approach offers a way to extract strong phases Flavor diagram approach offers a way to extract strong phases associated with individual topological amps and to relate them using associated with individual topological amps and to relate them using flavor SU(3) symmetry.flavor SU(3) symmetry.

Getting Strong PhasesGetting Strong Phases


This approach is intended to rely, to the greatest extent, on model This approach is intended to rely, to the greatest extent, on model independent flavor SU(3) symmetry arguments, rather than on specific independent flavor SU(3) symmetry arguments, rather than on specific model calculations of amplitudes.model calculations of amplitudes.

[Zeppenfeld, ZPC 8, 77 (1981); Chau + Cheng, PRL 56, 1655 (1986); PRD 36, 137 (1987); PRD 43, [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 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)]et. al., PRD 50, 4529 (1994); 52, 6356 (1995); 52, 6374 (1995)]

The flavor diagram approach:The flavor diagram approach:

is diagrammatic (can be formulated in a formal way);is diagrammatic (can be formulated in a formal way);

only concerns the flavor flow (arbitrary gluon exchange among only concerns the flavor flow (arbitrary gluon exchange among quarks);quarks);

has a clearer weak phase structure (unlike isospin analysis where has a clearer weak phase structure (unlike isospin analysis where different weak phases usually mix).different weak phases usually mix).

Very recent works in this direction include:Very recent works in this direction include:Chua [PRD Chua [PRD 6868, 074001 (2003)] and Luo + Rosner [PRD , 074001 (2003)] and Luo + Rosner [PRD 6767, 094017 (2003)] for baryons; , 094017 (2003)] for baryons; Charng + Li [PLB Charng + Li [PLB 594594, 185 (2004) and hep-ph/0410005] for weak phase extraction; and , 185 (2004) and hep-ph/0410005] for weak phase extraction; and He + McKellar [hep-ph/0410098] for analyzing recent data.He + McKellar [hep-ph/0410098] for analyzing recent data.

Flavor Diagram ApproachFlavor Diagram Approach


Tree-Level DiagramsTree-Level Diagrams

q = u,d,sq’= d,s

All these tree-level diagrams involve the same CKM factor.All these tree-level diagrams involve the same CKM factor.

annihilation (charged mesons only)annihilation (charged mesons only)exchange (neutral mesons only)exchange (neutral mesons only)

tree (external W emission)tree (external W emission) color-suppressed (internal W emission)color-suppressed (internal W emission)

1/mb suppresseddue to fB.


Loop-Level (Penguin) DiagramsLoop-Level (Penguin) Diagrams

QCD (strong) penguinQCD (strong) penguin(internal gluon emission)(internal gluon emission)

penguin annihilationpenguin annihilation(neutral mesons)(neutral mesons)

q=u,d,sq’=d,s

S, S'

flavor singletflavor singlet(external gluon emission)(external gluon emission)

All these tree-level diagrams also have the same CKM factor.All these tree-level diagrams also have the same CKM factor.


EW penguinEW penguincolor-suppressed EW penguincolor-suppressed EW penguin

appear together with C and S in decay amps

appear together with T and P in decay amps

NLO Flavor Diagrams in Weak InteractionsNLO Flavor Diagrams in Weak Interactions

Nothing forbids you from drawing one of the following Nothing forbids you from drawing one of the following diagrams whenever you see diagrams whenever you see TT, , CC, or , or PP in your amplitude in your amplitude list. They involve two weak boson propagators.list. They involve two weak boson propagators.


Treat Treat TT, , CC, , PP, , EE, , AA, , SS as “leading-order” amplitudes (note that only as “leading-order” amplitudes (note that only SS is is of loop nature) and of loop nature) and PPEWEW and and PPCC

EWEW as “higher-order” contributions (in the as “higher-order” contributions (in the

sense of weak interactions).sense of weak interactions).

Physical amplitudes contain flavor diagrams both “leading order” and Physical amplitudes contain flavor diagrams both “leading order” and “next-to-leading order” in weak interactions“next-to-leading order” in weak interactions

t t ´ ´ TT + + PPCCEWEW, , c c ´ ´ C C + + PPEWEW, , pp ´ ´ PP – – PPCC

EW EW / 3, / 3, s s ´ ´ SS – – PPEW EW / 3, / 3, a a ´ ´ AA..

Moreover, Moreover, PP contains contains tt-, -, cc-, and -, and uu-quark mediated penguins, -quark mediated penguins, PPt,c,ut,c,u. One . One

may use the unitarity to rewrite may use the unitarity to rewrite PPtt as the sum of two parts, one having as the sum of two parts, one having

the same weak phase as the same weak phase as PPcc and the other having the same weak phase as and the other having the same weak phase as

PPtt. This amounts to separating . This amounts to separating PP into into PPtctc + + PPtutu..

PPtutu involves the same CKM factor as the tree-level amplitudes. One involves the same CKM factor as the tree-level amplitudes. One

may thus sweep this amplitude to the tree-level amplitude category. may thus sweep this amplitude to the tree-level amplitude category. Note that this amplitude may be sizeable, particularly for Note that this amplitude may be sizeable, particularly for S = 0 decays.S = 0 decays.

For example, what many people call For example, what many people call TT or or CC extracted from extracted from decays decays are actually are actually TT – – PPtutu and and CC + + PPtutu. Thus, “| . Thus, “| CC / / TT |” > 1 is possible. |” > 1 is possible.

Physical Flavor DiagramsPhysical Flavor Diagrams


A Simple ExampleA Simple Example

Quark contents:Quark contents:

When vector mesons When vector mesons are involved, one are involved, one further labels the further labels the amplitude by which amplitude by which meson the spectator meson the spectator quark goes into.quark goes into.

Therefore,Therefore,A(A(++––) = – (T + P);) = – (T + P);

A(A(++––) = – (T) = – (TV V + P+ PVV).). Minus sign comes Minus sign comes

from the wave from the wave functions of functions of –– and and ––..

Bd

Bd

-

+

+

-

T

P PV

Bd

Bd

+

+

-

-

TV

+- +-


In our definition, the amplitudes contains CKM factors and may involve In our definition, the amplitudes contains CKM factors and may involve an arbitrary number of gluon exchanges.an arbitrary number of gluon exchanges.

An educated guess tells us that the magnitudes of the amplitudes should An educated guess tells us that the magnitudes of the amplitudes should roughly satisfy the following hierarchical structure.roughly satisfy the following hierarchical structure.

It should be emphasized that It should be emphasized that appearing in the hierarchy is not an appearing in the hierarchy is not an expansion parameter but merely an expansion parameter but merely an order parameterorder parameter. It simply reflects . It simply reflects our naïve expectation in the magnitudes of flavor amplitudes.our naïve expectation in the magnitudes of flavor amplitudes.

when going from 1st row to 2nd row:- tree-type amps suppressed because VudVus

- loop-type amps favored because VtdVts

Hierarchy in Flavor DiagramsHierarchy in Flavor Diagrams


Goals for the global fits:Goals for the global fits: Check if the SM offers a consistent picture for all available data;Check if the SM offers a consistent picture for all available data;

Check the working assumption of SU(3)Check the working assumption of SU(3)FF;;

Extract weak phase Extract weak phase (thus (thus by unitarity); by unitarity); Extract strong phases; check Lipkin conjecture in Extract strong phases; check Lipkin conjecture in V PV P decays; decays; Make predictions of unseen modes based upon current data.Make predictions of unseen modes based upon current data.

Parameters involved in the fits include:Parameters involved in the fits include: Amplitude sizes;Amplitude sizes; Weak phases;Weak phases; Strong phases.Strong phases.

Data points used in the Data points used in the 22 fits include: fits include: Branching ratios;Branching ratios; CP asymmetries (time-dependent and -independent).CP asymmetries (time-dependent and -independent).

Global Fits to Charmless DecaysGlobal Fits to Charmless Decays


The invariant matrix element The invariant matrix element MM for a decay process for a decay process BB MM11 MM22 and the and the corresponding decay width arecorresponding decay width are

where where pp is the 3-momentum of the final state particle in the rest frame is the 3-momentum of the final state particle in the rest frame of of BB. Note that . Note that MM may contain polarization vector summation and may contain polarization vector summation and average as is the case for final states containing vector mesons.average as is the case for final states containing vector mesons.

We also assume the following SU(3)We also assume the following SU(3)FF relations (with relations (with = 0.224):= 0.224):

Some Basic FormulasSome Basic Formulas

partial SU(3)F breaking taken into account

assuming perfect SU(3)F symmetry for these amps


B V P DecaysB V P DecaysCWC, M. Gronau, Z. Luo, J. Rosner, D. Suprun, PRD 69, 034001 (2004) [hep-ph/0307395].


related by symmetry:start with: other quantities:

ignored small amplitudes such ignored small amplitudes such as color-suppressed EW as color-suppressed EW penguin, exchange, penguin, exchange, annihilation diagrams, and annihilation diagrams, and SS((00))

P,VP,V..

Fitting Parameters for VP ModesFitting 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: P, V, ;• weak phase: only (no dependence).• symmetric under simultaneous changes:

– , P,V – P,V and –

Fitting Parameters for VP ModesFitting Parameters for VP Modes


In our fit, there are totally 34 observables:In our fit, there are totally 34 observables:

13 data points13 data points

List of ModesList of Modes


13 data points13 data points

another 16 data pointsanother 16 data points


finally, include time-dependent CP asymmetries: S Ks=-0.147§0.697 (S=2.11), A Ks=0.046§0.256 (S=1.08)

(contribute constant to 2) [Browder, talk at LP03] S=-0.13§0.18§0.04, S=0.33§0.18§0.03

(provide dependence) [BaBar, talk by Jawahery at LP03]


2- Plots (34 data points)2- Plots (34 data points)

major changes in major changes in 22 at at ''6565±± and and 165165±± from step 1 to step 2 from step 1 to step 2 positions of minima almost positions of minima almost unaffectedunaffected ==(53(53+15+15

-33-33))±± if S if S is left out, is left out, c.f. c.f. =(63=(63§§66))±± here here

For the three major minima, we still have:For the three major minima, we still have:'' 25 25±± and 165 and 165±± disfavored by CKM Fitter and dynamics disfavored by CKM Fitter and dynamics'' 65 65±± favored and consistent with CKMFitter favored and consistent with CKMFitter

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


Fit ResultsFit Resultsphysical solution prefers trivial strong phases while others give large strong phases,physical solution prefers trivial strong phases while others give large strong phases,consistent with perturbative calculationsconsistent with perturbative calculations


Predictions for VP Modes(S=0, complex p’V/p’P)

Predictions for VP Modes(S=0, complex p’V/p’P)

results showing significant differences results showing significant differences among the three fitsamong the three fits

results showing significantresults showing significantdifferences from exp’t datadifferences from exp’t data


results showing some significantresults showing some significantdifferences among the three fitsdifferences among the three fits

Predictions for VP Modes(|S|=1, complex p’V/p’P)Predictions for VP Modes(|S|=1, complex p’V/p’P)


Some DiscussionsSome Discussions

Overall, fits are satisfactory (at 38% and 55% CL for 10- and 12-Overall, fits are satisfactory (at 38% and 55% CL for 10- and 12-parameter fits) and have solutions parameter fits) and have solutions = (65= (65§§6)6)±± and (63 and (63§§6)6)±± consistent consistent with constraints from other processes.with constraints from other processes.

Data of Data of play the roles of breaking the play the roles of breaking the – – symmetry and symmetry and stabilizing the fit results.stabilizing the fit results.

Note that the Note that the 22 fits allow us to extract preferred values of fitting fits allow us to extract preferred values of fitting parameters along with their 1 parameters along with their 1 errors. Moreover, we have an idea errors. Moreover, we have an idea about how good our fits are from the CL.about how good our fits are from the CL.

Global fits prefers the Lipkin conjecture Global fits prefers the Lipkin conjecture pp00= – = – pp00 PP..

Only partial SU(3) breaking effect included for T amps; can verify Only partial SU(3) breaking effect included for T amps; can verify SU(3) for penguin amps when SU(3) for penguin amps when BB KK** anti- anti-KK ( (ppVV) and anti-) and anti-KK** KK ( (ppPP) ) rates are measured.rates are measured.


B P P DecaysB P P DecaysCWC, 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].



purely p’

need s’=S’-P’EW / 3

K anomaly

BR too large compared toQCD fact. predictions

large CP asymmetries;BR too small comparedTo QCD fact. predictions


2- Plot2- Plot

From bottom to top, we use 8 and 6From bottom to top, we use 8 and 6

parameters to fit 14 data points (parameters to fit 14 data points (and and K K ) and 13 and 11 parameters to) and 13 and 11 parameters to

fit 24 data points (further includingfit 24 data points (further including

final states with final states with and and 00).).

Find Find '' 54 54±± ~ 66 ~ 66±±, results still consistent, results still consistent

with but less stable than the with but less stable than the V PV P case. case.

CKM fitter


Fit ResultsFit Results

consistent with other constraintsconsistent with other constraints

large |C/T| ratio and non-triviallarge |C/T| ratio and non-trivialrelative strong phase; unable torelative strong phase; unable toaccount for in perturbationaccount for in perturbation

required to account for the largerequired to account for the large00 KK BR’s BR’s

satisfactory overall fit resultssatisfactory overall fit results

all strong phases relative to all strong phases relative to P’P’


Predictions for PP ModesPredictions for PP Modes

still problematic in K modes

no problem in modes


Some discussionsSome discussions

[see also Chua, Hou and Yang, Mod. Phys. Lett. [see also Chua, Hou and Yang, Mod. Phys. Lett. A18A18, 1763 (2003);, 1763 (2003);

Buras et al, PRL 92, 101804 (2004); hep-ph/0402112]Buras et al, PRL 92, 101804 (2004); hep-ph/0402112]

Fits to Fits to + + K data: K data: requires large |C/T| ratio (> 0.5);requires large |C/T| ratio (> 0.5); requires a nontrivial strong phase between C and T (requires a nontrivial strong phase between C and T (»» 100 100±±).).

Fits to all PP dataFits to all PP data one needs to introduce S (singlet penguin), Pone needs to introduce S (singlet penguin), P tutu (t,u-mediated penguin); (t,u-mediated penguin);

one needs to introduce Sone needs to introduce Stutu (t,u-mediated singlet penguin) particularly for the (t,u-mediated singlet penguin) particularly for the ++’ ’ mode.mode.

Robust results in our fitsRobust results in our fits magnitude of QCD penguin |P|;magnitude of QCD penguin |P|; relative strong phase between T and P;relative strong phase between T and P; sizes of electroweak penguins (color-allowed and -suppressed), consistent with sizes of electroweak penguins (color-allowed and -suppressed), consistent with

Neubert-Rosner relation;Neubert-Rosner relation; obtain obtain '' 60 60± ± (48(48± ± < < < 73< 73±±, 68%CL), consistent with CKM fitter and earlier , 68%CL), consistent with CKM fitter and earlier

analysis for VP modes.analysis for VP modes. We do not fully trust the stability of the shallow minima.We do not fully trust the stability of the shallow minima.


Strangeness in B PhysicsStrangeness in B PhysicsV. 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].


K AnomalyK Anomaly

Within the SM, the following ratios should be approximately equalWithin the SM, the following ratios should be approximately equal

but show a but show a 2.42.4 difference. difference.

Possible explanations:Possible explanations: underestimate of underestimate of 00 detection efficiency; detection efficiency; [Gronau and Rosner, hep-ph/0402112][Gronau and Rosner, hep-ph/0402112]

new physics.new physics. [Buras et al, PRL [Buras et al, PRL 9292, 101804 (2004); NPB , 101804 (2004); NPB 697697:133 (2004), hep-ph/0410407]:133 (2004), hep-ph/0410407]

One minimal explanation is that the One minimal explanation is that the color-allowed electroweak color-allowed electroweak penguinspenguins cause the problem cause the problem isospin-violating new physics isospin-violating new physics


Z0 Model With FCNCZ0 Model With FCNC

TheThe B B K K decay can be a tree-level process mediated by a decay can be a tree-level process mediated by a ZZ' boson if ' boson if there are FCNC couplings (possible for family non-universal charges).there are FCNC couplings (possible for family non-universal charges).

We simply a general We simply a general ZZ' model by assuming: ' model by assuming:

(i) no right-handed flavor-changing couplings,(i) no right-handed flavor-changing couplings,

(ii) no significant RG running effect between (ii) no significant RG running effect between MMZ'Z'

and and MMWW scales, scales,

(iii) negligible (iii) negligible ZZ' effect on the QCD penguins so that the new physics is ' effect on the QCD penguins so that the new physics is manifestly isospin-violating.manifestly isospin-violating.

With these simplifications, we have 3 parameters left in the model.With these simplifications, we have 3 parameters left in the model.

carrying a new CP-violating source


Parameter ExtractionParameter Extraction

Following the arguments in Buras et al, new physics is Following the arguments in Buras et al, new physics is coded by the parameters:coded by the parameters:

Found solutions from Found solutions from and and K K data: data:

Correspond to our parameters:Correspond to our parameters:


Simultaneous Solution to K and KSSimultaneous Solution to K and KS

Can the Can the K K anomaly and anomaly and K Kss asymmetries be accounted for by the asymmetries be accounted for by the

same thing at the same time?same thing at the same time? According to Buras et al, their solution [our solution (AAccording to Buras et al, their solution [our solution (ALL)] to the )] to the K K

anomaly leads to S(anomaly leads to S( K Kss) greater than S() greater than S( K Kss)!)!

However, due to different interference patterns between However, due to different interference patterns between OO7,87,8 and and OO9,109,10

operators in our model, it is possible [all our other solutions (Boperators in our model, it is possible [all our other solutions (BLL, A, ALRLR and and

BBLRLR)] to have S()] to have S( K Kss) smaller than S() smaller than S( K Kss).).


Perspective and SummaryPerspective and Summary

Flavor diagram approach provides a simple and reliable picture for Flavor diagram approach provides a simple and reliable picture for describing describing BB decays. It is phenomenological (data driven), contains LO decays. It is phenomenological (data driven), contains LO and NLO amps in weak interactions but all orders in strong interactions, and NLO amps in weak interactions but all orders in strong interactions, includes final state interacting effects, and suffers from SU(3)includes final state interacting effects, and suffers from SU(3)FF breaking breaking effects.effects.

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

All fits provide information on All fits provide information on that is consistent with other extractions. that is consistent with other extractions.

Results from ICHEP are being analyzed by D. Suprun for his thesis.Results from ICHEP are being analyzed by D. Suprun for his thesis.

We need to know more information about strong phases. In particular, one We need to know more information about strong phases. In particular, one should understand better about final-state rescattering effects.should understand better about final-state rescattering effects.

We hope to see a proof of factorization in processes of interest to us, in We hope to see a proof of factorization in processes of interest to us, in particular, those involving penguin diagrams.particular, those involving penguin diagrams.

We hope to see more affirmative evidence of new physics in We hope to see more affirmative evidence of new physics in BB physics, physics, e.g., e.g., SS K KSS

the the K K anomaly, large anomaly, large BBss anti- anti-BBss mixing, etc. mixing, etc.


Thank YouThank You

Date post:	17-Jan-2016
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Flavor Diagram Approach to Hadronic B Decays Cheng-Wei Chiang National Central University Cheng-Wei...

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