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Flavor , Charm , CP Related Physics. Hai-Yang Cheng Academia Sinica, Taipei. PASCOS, Taipei November 22, 2013. Outline: Quark and lepton mixing matrices Baryonic B decays Direct CP violation in D decays

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Flavor, Charm, CP Related Physics

Hai-Yang Cheng

Academia Sinica, Taipei

PASCOS, Taipei

November 22, 2013


  • Quark and lepton mixing matrices

  • Baryonic B decays

  • Direct CP violation in D decays

  • Direct CP violation in B decays

See the talk of Rodrigues (11/21)

CP Violation in Standard Model

VCKM is the only source of CPV in flavor-changing process in the SM. Only charged current interactions can change flavor

Kobayashi & Maskawa (’72) pointed out that one needs at least six quarks in order to accommodate CPV in SM with one Higgs doublet

1>>1>>2 >>3

Physics is independent of a particular parameterization of CKM matrix, but VKM has some disadvantages :

  • Determination of 2 & 3 is not very accurate

  • Some elements have comparable real & imaginary parts


Maiani (’77)

advocated by PDG (’86) as a standard parametrization.

However, the coefficient of the imaginary part of Vcb and Vts is O(10-2) rather than O(10-3) as s23  10-2

In 1984 Ling-Lie Chau and Wai-Yee Keung proposed a new parametrization

1>>12>>23 >>13

s13 ~ 10-3

The same as VMaiani except for the phases of t & b quarks. The imaginary part is O(10-3). This new CKM(Chau-Keung-Maiani) matrix is adapted by PDG as a standard parametrization since 1988.

Some simplified parametrizations

  • Wolfenstein (’83) used Vcb=0.04  A2,   0.22

Mixing matrix is expressed in terms of , A ~ 0.8,  and . Imaginary part = A3 10-3. However, this matrix is valid only up to 3

  • Motivated by the boomerang approach of Frampton & He (’10), Qin

    & Ma have proposed a different parametrization (’10)

Wolfenstein parameters A, ,  QM parameters f, h, 


The original Wolfenstein parametrization is not adequate for the study of CP violation in charm decays, for example. Hence it should be expanded to higher order of 

Wolfenstein parametrization up to 6

Wolfenstein parametrization can also be obtained from KM matrix by making rotations: s s ei, c c ei, b b ei(+), t t e-i(-) and replacing A, , ,  by A’, ’ , ’ and ’

Look quite differently from those of the study of CP violation in charm decays, for example. Hence it should be expanded to higher order of V(CK)Wolf



Buras et al. (’94): As in any perturbative expansion, high order terms in  are not unique in the Wolfenstein parametrization, though the nonuniquess of the high order terms does not change physics

Wolfenstein (’83) used |Vub| ~ 0.2 |Vcb| ~ A3

Now |Vub| ~ 0.00351, |Vcb| ~ 0.0412  |Vub| ~ 2 |Vcb|~ A4

  • ~ 0.129,  ~ 0.348 not order of unity !

    We define & of order unity


Most of the discrepancies are resolved via the definition of the parameters , of order unity

  • Remaining discrepancies can be alleviated through

  • Vus =  = ’

  • from Vcb

  • from Vub

Ahn, HYC, Oh



Lepton mixing matrix the parameters

Pontecorvo, Maki,

Nakagawa, Sakata

12 = solar  mixing angle, 23 = atmospheric  mixing angle,

13 = reactor  mixing angle

A different parametrization has been studied:

Huang et al.

1108.3906; 1111.3175

12 ~ 19o, 23 ~ 46o, 13 ~ 29o are quite different from

12 ~ 34o, 23 ~ 38o, 13 ~ 9o

the parameters 12 ~ 13o, 23 ~ 2.4o, 13 ~ 0.2o


1>>12>>23 >>13

12 ~ 34o, 23 ~ 38o, 13 ~ 9o


Baryonic B Decays the parameters

  • B  baryon + antibaryon

  • B  baryon + antibaryon + meson

  • B  baryon + antibaryon + 

A baryon pair is allowed in the final state of the parameters

hadronic B decays.

In charm decay, Ds+→pn is the only allowed baryonic D decay. Its BR ~ 10-3 (CLEO)

2-body charmless baryonic B decays the parameters

Very rare !













CY the parameters

CZ=Chernyak & Zhitnitsky (’90), CY= Cheng & Yang (’02)

What is the theory expectation of Br(B0 pp) ?


Talk presented at 7 the parameters th Particle Physics Phenomenology Workshop, 2007

LHCb (1308.0961) the parameters

Br(B0 pp)= (1.47+0.62+0.35-0.51-0.14)10-8

Br(Bs0 pp)= (2.84+2.03+0.85-1.08-0.18)10-8


first evidence

see the talk of Prisciandaro (22C1b)

LHCb (1307.6165) observed a resonance (1520) in B-ppK- decays

Br(B-(1520)p)= (3.9+1.0-0.90.10.3)10-7


The pQCD calculation of B0 pp is similar to the pQCD calculation of B→cp (46 Feynman diagrams) by X.G.He, T.Li, X.Q.Li, Y.M.Wang (’06)

Why is Br(B-(1520)p) >> Br(B0 pp) ?

Angular distribution the parameters

  • Measurement of angular distributions in dibaryon rest frame will provide further insight of the underlying dynamics

  • SD picture predict a stronger correlation of the meson with the antibaryon than to the baryon in B→B1B2M


pp rest frame

B rest frame






















- the parameters

Angular distribution in penguin-dominated B-ppK-









SD picture predicts a strong correlation between K- and p !












Belle: K- is preferred to move

collinearly with p in pp rest frame !

 a surprise in correlation








BaBar measured Dalitz plot


unsolved enigma !


Angular distribution in B the parameters -p-



SD picture: Both  & p picks up energetic s and u quarks, respectively ⇒ on the average, pion has no preference for its correlation with  or p⇒a symmetric parabola that opens downward









Tsai, thesis (’06)


Belle(’07): M.Z. Wang et al.

shows a slanted straight line

⇒another surprise !!




  • Correlation enigma occurs in penguin-dominated modes B→ppK, p

  • Cannot be explained by SD b→ sg* picture

  • Needs to be checked by LHCb & BaBar

  • Theorists need to work hard !


Radiative baryonic B decays the parameters

At mesonic level, bs electroweak penguin transition manifests in BK*. Can one see the same mechanism in baryonic B decays ?

  • Consider b pole diagram and apply HQS and static b quark limit to relate the tensor matrix element with b form factors

  • Br(B-p)  Br(B-0-) = 1.210-6

  • Br(B-0p)= 2.910-9

    Penguin-induced B-p and B-0- should be readily accessible to

    B factories

HYC,Yang (’02)

Belle [ Lee & Wang et al. PRL 95, 061802 (’05) ]

Br(B-p) = (2.45+0.44-0.380.22)10-6

Br(B-0p) < 4.610-6

first observation of bs in baryonic B decay


Extensive studies of baryonic B decays in Taiwan both experimentally and theoretically



Belle group at NTU (Min-Zu Wang,…)

Chen, Chua, Geng, He, Hou, Hsiao, Tsai, Yang, HYC,…

B-→ppK-: first observation of charmless baryonic B decay (’01)




B→pp, , p (stringent limits)

Publication after 2000: (hep-ph)

0008079, 0107110, 0108068, 0110263, 0112245, 0112294, 0201015, 0204185, 0204186, 0208185, 0210275, 0211240, 0302110,0303079, 0306092, 0307307, 0311035, 0405283, 0503264, 0509235, 0511305, 0512335, 0603003, 0603070, 0605127, 0606036, 0606141, 0607061, 0607178, 0608328, 0609133, 0702249, PRD(05,not on hep-ph), 0707.2751, 0801.0022, 0806.1108, 0902.4295, 0902.4831, 1107.0801, 1109.3032, 1204.4771, 1205.0117, 1302.3331

B→p: first observation of b→s penguin in baryonic B decays (’04)

Publication after 2002:

15 papers (first author) so far: 7PRL, 2PLB, 6PRD; 2 in preparation

Taiwan contributes to 86% of theory papers

Direct CP violation experimentally and theoretically

in charm decays

CP violation in charm decays experimentally and theoretically

  • DCPV requires nontrival strong and weak phase difference

  • In SM, DCPV occurs only in singly Cabibbo-suppressed decays.

    It is expected to be very small in charm sector within SM

Amp = V*cdVud (tree + penguin) + V*csVus (tree’ + penguin)

No CP violation in D decays if they proceed only through tree diagrams

Penguin is needed in order to produce DCPV at tree & loop level

: strong phase

DCPV is expected to be the order of 10-3  10-5 !


Experiment experimentally and theoretically

Time-dependent CP asymmetry

Time-integrated asymmetry

LHCb: (11/14/2011) 0.92 fb-1based on 60% of 2011 data

  • ACPACP(D0 K+K-) – ACP(D0+-) = - (0.820.210.11)%

  • 3.5 effect: first evidence of CPV in charm sector

CDF: (2/29/2012) 9.7 fb-1

ACP= Araw(K+K-) - Araw(+-)= - (2.330.14)% - (-1.710.15)%

= - (0.620.210.10)% 2.7 effect

Belle: (ICHEP2012) 540 fb-1

ACP = - (0.870.410.06)%

see Mohanty’s talk (11/25)


World averages of LHCb + CDF + BaBar + Belle in 2012

aCPdir = -(0.6780.147)%, 4.6 effect

aCPind = -(0.0270.163)%

Theory estimate is much smaller than the expt’l measurement of |aCPdir |  0.7%  New physics ?



Chen, Geng, Wang [1206.5158] 2012

Delaunay, Kamenik, Perez, Randall [1207.0474]

Da Rold, Delaunay, Grojean, Perez [1208.1499]

Lyon, Zwicky [1210.6546]

Atwood, Soni [1211.1026]

Hiller, Jung, Schacht [1211.3734]

Delepine, Faisel, Ramirez [1212.6281]

Li, Lu, Qin, Yu [1305.7021]

Buccella, Lusignoli, Pugliese, Santorelli [1305.7343]

Isidori, Kamenik, Ligeti, Perez [1111.4987]

Brod, Kagan, Zupan [1111.5000]

Wang, Zhu [1111.5196]

Rozanov, Vysotsky [1111.6949]

Hochberg, Nir [1112.5268]

Pirtskhalava, Uttayarat [1112.5451]

Cheng, Chiang [1201.0785]

Bhattacharya, Gronau, Rosner [1201.2351]

Chang, Du, Liu, Lu, Yang [1201.2565]

Giudice, Isidori, Paradisi [1201.6204]

Altmannshofer, Primulando, C. Yu, F. Yu [1202.2866]

Chen, Geng, Wang [1202.3300]

Feldmann, Nandi, Soni [1202.3795]

Li, Lu, Yu [1203.3120]

Franco, Mishima, Silvestrini [1203.3131]

Brod, Grossman, Kagan, Zupan [1203.6659]

Hiller, Hochberg, Nir [1204.1046]

Grossman, Kagan, Zupan [1204.3557]

Cheng, Chiang [1205.0580]

28 theory papers !



Diagrammatic Approach 2012

All two-body hadronic decays of heavy mesons can be expressed in

terms of several distinct topological diagrams [Chau (’80); Chau, HYC(’86)]

T (tree)

A (W-annihilation)

E (W-exchange)

C (color-suppressed)

HYC, Oh (’11)





All quark graphs are topological and meant to have all strong interactions encoded and hence they are not Feynman graphs. And SU(3) flavor symmetry is assumed.



Cabibbo-allowed decays 2012

For Cabibbo-allowed D→PP decays (in units of 10-6GeV)

T= 3.14 ± 0.06 (taken to be real)

C= (2.61 ± 0.08) exp[i(-152±1)o]

E= (1.53+0.07-0.08) exp[i(122±2)o]

A= (0.39+0.13-0.09) exp[i(31+20-33)o]

CLEO (’10)


Rosner (’99)

Wu, Zhong, Zhou (’04)

Bhattacharya, Rosner (’08,’10)

HYC, Chiang (’10)

  • Phase between C & T ~ 150o

  • W-exchange Eis sizable with a large phase  importance of 1/mcpower corrections

  • W-annihilaton A is smaller than Eand almost perpendicular to E





The great merit & strong point of this approach  magnitude and strong phase of each topological tree amplitude are determined


Tree-level direct CP violation 2012

DCPV can occur even at tree level

A(Ds+ K0+) =d(T + Pd+ PEd) + s(A + Ps+ PEs), p=V*cpVup

DCPV in Ds+ K0+ arises from interference between T & A

 10-4

DCPV at tree level can be reliably estimated in diagrammatic approach as magnitude & phase of tree amplitudes can be extracted from data

Larger DCPV at tree level occurs in decay modes with interference between T & C (e.g. Ds+K+) or C & E (e.g. D00)


Tree-level DCPV a 2012CP(tree) in units of per mille

10-3 > adir(tree) > 10-4

Largest tree-level DCPV

PP: D0K0K0, VP: D0’

aCP(tree) vanishes in

D0+-, K+K-


Short-distance penguin contributions are very small. How about power corrections to QCD penguin ? SD weak penguin annihilation is also very small; typically, PE / T  0.04 and PA / T  -0.02

Large LD contribution to PE can arise from D0 K+K- followed by a resonantlike final-state rescattering

It is reasonable to assume PE ~ E, PEP ~ EP, PEV ~ EV

Power corrections to P from PE via final-state rescattering cannot be larger than T

a about power corrections to QCD penguin ? SD weak penguin annihilation is also very small; typically, PE / T CPdir (10-3)

aCPdir= -0.1390.004% (I)

-0.1510.004% (II)

about 3.3 away from -(0.6780.147)%

A similar result aCPdir=-0.128% obtained by Li, Lu, Yu

see Hsiang-nan Li’s talk (11/25)

Even for PE  T aCPdir = -0.27%, an upper bound in SM

If aCPdir ~ -0.68%, it

is definitely a new physics effect !


Attempts for SM interpretation about power corrections to QCD penguin ? SD weak penguin annihilation is also very small; typically, PE / T

Golden, Grinstein (’89): hadronic matrix elements enhanced as in I=1/2 rule.

However, D data do not show large I=1/2 enhancement over I=3/2 one.

Moreover, |A0/A2|=2.5 in D decays is dominated by tree amplitudes.

Brod, Kagan, Zupan: PE and PA amplitudes considered

Pirtskhalava, Uttayarat : SU(3) breaking with hadronic m.e. enhanced

Bhattacharya, Gronau, Rosner : Pb enhanced by unforeseen QCD effects

Feldmann, Nandi, Soni : U-spin breaking with hadronic m.e. enhanced

Brod, Grossman, Kagan, Zupan: penguin enhanced

Franco, Mishima, Silvestrini: marginally accommodated

We have argued that power corrections to P from PE via final-state

rescattering cannot be larger than T

LHCb in 2013: about power corrections to QCD penguin ? SD weak penguin annihilation is also very small; typically, PE / T

ACP = - (0.340.150.10)% D* tagged

ACP = (0.490.300.14)% B D0X, muon tagged

- (0.150.16)% combination

See D. Tonelli’s talk (11/25)

World average: aCPdir = -(0.3330.120)%, 2.8

aCPind = (0.0150.052)%

Recall that aCPdir = -(0.6780.147)%, 4.6 in 2012 !

It appears that SM always wins !

Direct CP violation in about power corrections to QCD penguin ? SD weak penguin annihilation is also very small; typically, PE / T

charmless B decays

Direct CP asymmetries (2-body) about power corrections to QCD penguin ? SD weak penguin annihilation is also very small; typically, PE / T


AKACP(K-0) – ACP(K-+)

K puzzle: AK is naively expected to vanish



A about power corrections to QCD penguin ? SD weak penguin annihilation is also very small; typically, PE / T CP(B- K-)



LHCb observed CP violation in B-K-K+K- but not around  resonance


LHCb (1309.3742) obtained ACP = (2.22.10.9)%

In heavy quark limit, decay amplitude is factorizable, expressed in terms of form factors and decay constants.


See Beneke & Neubert (’03) for mb results



A( expressed in terms of form factors and decay constants. B0K-+) ua1+c(a4c+ra6c)

Im4c  0.013  wrong sign for ACP


charming penguin, FSI penguin annihilation

1/mb corrections

penguin annihilation


New CP puzzles in QCDF expressed in terms of form factors and decay constants.

Penguin annihilation solves CP puzzles for K-+,+-,…, but in the meantime introduces new CP puzzles for K-, K*0, …

Also true in SCET with penguin annihilation replaced by charming penguin




All “problematic” modes receive contributions from expressed in terms of form factors and decay constants. uC+cPEW

PEW  (-a7+a9), PcEW  (a10+ra8), u=VubV*us, c=VcbV*cs

AK puzzle can be resolved by having a large complex C

(C/T  0.5e–i55 ) or a large complex PEW or the combination

AK 0 if C, PEW, A are negligible

 AK puzzle


Large complex C Charng, Li, Mishima; Kim, Oh, Yu; Gronau, Rosner; …

Large complex PEW needs New Physics for new strong & weak phases

Yoshikawa; Buras et al.; Baek, London;

G. Hou et al.; Soni et al.; Khalil et al;…


The two distinct scenarios can be tested in tree-dominated modes where ’cPEW << ’uC. CP puzzles of -, 00 & large rates of 00, 00 cannot be explained by a large complex PEW

00 puzzle: ACP=(4324)%, Br = (1.910.22)10-6



Direct CP asymmetries (3-body) modes where ’

LHCb found evidence of inclusive CP asymmetry in

B-+--, K+K-K-, K+K--

Large asymmetries observed in localized regions of p.s.

ACP(KK) = -0.6480.0700.0130.007 for mKK2 <1.5 GeV2

ACP(KKK) = -0.2260.0200.0040.007 for 1.2< mKK, low2 <2.0 GeV2, mKK, high2 <15 GeV2

ACP() = 0.584+0.082+0.027+0.007 for m, low2 <0.4 GeV2, m, high2 > 15 GeV2

ACP(K) = 0.6780.0780.0320.007 for 0.08< m, low2 <0.66 GeV2, mK2 <15 GeV2


Correlation: modes where ’

ACP(K-K+K-)  – ACP(K-+-), ACP(-K+K-)  – ACP(-+-)

  • Relative signs between CP asymmetries of K-K+K- & -+-, -K+K- & K-+- are consistent with U-spin prediction.

  • It has been conjectured that CPT theorem & final-state rescattering of +- K+K- may play important roles

Zhang, Guo, Yang [1303.3676]

Bhattacharya, Gronau, Rosner [1306.2625]

Xu, Li, He [1307.7186]

Bediaga, Frederico, Lourenco [1307.8164]

Cheng, Chua [1308.5139]

Zhang, Guo, Yang [1308.5242]

Lesniak, Zenczykowski [1309.1689]

Xu, Li, He [1311.3714]

Conclusion of this section modes where ’

  • CP asymmetries are the ideal places to discriminate between different models.

  • In QCDF one needs two 1/mb power corrections (one to penguin annihilation, one to color-suppressed tree amplitude) to explain decay rates and resolve CP puzzles

  • Can we understand the correlation ?

    ACP(K-K+K-)  – ACP(K-+-), ACP(-K+K-)  – ACP(-+-)

Conclusions modes where ’

  • To expand Wolfenstein parametrization to higher order of , it is important to use  &  parameters order of unity.

  • First evidence of charmless baryonic B decays: time for updated theory studies. Correlation puzzle in penguin-dominated decays needs to be resolved.

  • DCPV in charm decays is studied in the diagrammatic approach. It can be reliably estimated at tree level. Our prediction is aCP = -(0.1390.004)%

Backup Slides modes where ’

modes where ’: strong phase

To accommodate aCP one needs P/T~ 3 for maximal strong phase, while it is naively expected to be of order s/

Bhattacharya, Gronau, Rosner Brod, Grossman, Kagan, Zupan

Can penguin be enhanced by some nonperturbative effects or unforeseen QCD effects ?

We have argued that power corrections to P from PE via final-state

rescattering cannot be larger than T


In D modes where ’ decays

( 22.40.1 in K )

In absence of penguin contribution & SU(3) breaking, this ratio is predicted to be 3.8, larger than the expt’l result. This means P should contribute destructively to A0/A2 .

In kaon decays, the predicted ratio due to tree amplitudes is too small compared to experiment  large enhancement of penguin matrix element.

New Physics interpretation modes where ’

Before LHCb: Grossman, Kagan, Nir (’07)

Bigi, Paul, Recksiegel (’11)

After LHCb :

  • Model-independent analysis of NP effects Isidori, Kamenik, Ligeti, Perez

  • Tree level (applied to some of SCS modes)

  • FCNC Z

  • FCNC Z’ (a leptophobic massive gauge boson)

  • 2 Higgs-doublet model: charged Higgs

  • Color-singlet scalar

  • Color-sextet scalar (diquark scalar)

  • Color-octet scalar

  • 4th generation

Giudice, Isidori, Paradisi; Altmannshofer, Primulando, C. Yu, F. Yu

Wang, Zhu; Altmannshofer, Primulando, C. Yu, F. Yu

Altmannshofer et al.

Hochberg, Nir

Altmannshofer et al; Chen, Geng, Wang

Altmannshofer et al.

Rozanov, Vysotsky; Feldmann, Nandi, Soni

NP models are highly constrained from D- modes where ’D mixing, K-K mixing, ’/,… Tree-level models are either ruled out or in tension with other experiments.

Loop level (applied to all SCS modes)

Large C=1 chromomagnetic operator with large imaginary coefficient

is least constrained by low-energy data and can accommodate large ACP.<PP|O8g|D> is enhanced by O(v/mc). However, D0-D0 mixing induced by O8g is suppressed by O(mc2/v2). Need NP to enhance c8g by O(v/mc)

Giudice, Isidori, Paradisi

It can be realized in SUSY models

  • gluino-squark loops

  • new sources of flavor violation from disoriented A terms, split families

  • trilinear scalar coupling

  • RS flavor anarchy warped extra dimension models

Grossman, Kagan, Nir

Giudice, Isidori, Paradisi

Hiller, Hochberg, Nir

Delaunay, Kamenik, Perez, Randall