Theory of Direct CP Violation in D hh

Chongqing, May 8, 2012

Hai-Yang Cheng (鄭海揚 )

Academia Sinica, Taipei

Diagrammatical approach

SU(3) breaking

CP violation at tree and loop levels

2012年兩岸粒子物理與宇宙學研討會

22

1. Null results in SM: ideal place to look for new physics in BSM Bs

s : CP-odd phase in Bs system CP violation in B-

Lepton number violation ( decay) CP violation in charmed meson: D0-D mixing, DCPV …

2. Take a cue form the current anomalies: B sin2s

B-CP puzzles, especially AK like-sign dimuon asymmetry forward-backward asymmetry in B0 K*0

polarization puzzle …

Stratage in search of NP

3

Experiment

))(())((

))(())(())((

tfDtfD

tfDtfDtfACP

Time-dependent CP asymmetry

Time-integrated asymmetry )()()( fat

fafA indCP

dirCPCP

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

ACP ACP(K+K-) - ACP() = - (0.820.210.11)%

3.5 effect: first evidence of CPV in charm sectorCDF: (11/21/2011) 5.9 fb-1

ACP(K+K-)= - (0.240.220.09)%, ACP() = (0.220.240.11)%

ACP- (0.460.310.11)%

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

ACP= Araw(K+K-) - Araw(-)= - (2.330.14)% - (-1.710.15)%

= - (0.620.210.10)%

will measure ACP(K+K-) & ACP(-) separately

44

New world averages of LHCb + CDF + BaBar + Belle

aCPdir = -(0.6560.154)%,

4.3 effect

aCPind = -(0.0250.235)%

Before claiming new physics effects,

it is important to have a reliable SM

estimate of ACP

Can we have reliable estimate of strong

phases and hadronic matrix elements ?

Can the LHCb result be accommodated

in SM ?

Given the expt’l results, can one

predict DCPV in other modes ?

5

Vcs

Vud

Vcd

Vud

Vcd

Vus

Vcs

Vus

Cabibbo favored

singly Cabibbo-suppressed

doubly Cabibbo-suppressed

D

6

Why singly Cabibbo-suppressed decays ?

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

sin102.1sinsin2sin||

)Im(2 3*

*

2*

**

T

A

T

A

VV

VV

T

A

VV

VVVVa

udcd

ubcb

udcd

uscsudcddirCP

DCPV is expected to be the order of 10-3 10-4

: strong phase

In SM, CPV is expected to be very small in charm sector

Consider DCPV in singly Cabibbo-suppressed decays

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

Common folklore: CPV is at most 10-3 in SM; 10-2 is a “smoking gun” signature of NP

77

Isidori, Kamenik, Ligeti, Perez [1111.4987] (11/21/2011)

Brod, Kagan, Zupan [1111.5000] (11/21/2011)

Wang, Zhu [1111.5196] (11/22/2011)

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]

Forthcoming papers:

Hiller, Jung, Schacht

Delaunay, Kamenik, Perez, Randall

…

8

Theoretical framework

Effective Hamiltonian approachpQCD: Li, Tseng (’97); Du, Y. Li, C.D. Lu (’05)

QCDF: Du, H. Gong, J.F. Sun (’01)

X.Y. Wu, X.G. Yin, D.B. Chen, Y.Q. Guo, Y. Zeng (’04)

J.H. Lai, K.C. Yang (’05); D.N. Gao (’06)

Grossman, Kagan, Nir (’07)

X.Y. Wu, B.Z. Zhang, H.B. Li, X.J. Liu, B. Liu, J.W. Li, Y.Q. Gao (’09)

However, it doesn’t make much sense to apply pQCD & QCDF to charm decays due to huge 1/mc power corrections

QCD sum rules: Blok, Shifman (’87); Khodjamirian, Ruckl; Halperin (’95)

Lattice QCD: ultimate tool but a formidable task now

Model-independent diagrammatical approach

99

All two-body hadronic decays of heavy mesons can be expressed interms of several distinct topological diagrams [Chau (’80); Chau, HYC(’86)]

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.

Diagrammatic Approach

T (tree) C (color-suppressed)

E (W-exchange)

A (W-annihilation)

P, PcEW S, PEW

PE, PEEW PA, PAEW

HYC, Oh (’11)

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

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]

Rosner (’99)

Wu, Zhong, Zhou (’04)

Bhattacharya, Rosner (’08,’10)

HYC, Chiang (’10)

T

CA

E

10

Phase between C & T ~ 150o

W-exchange E is sizable with a large phase importance of power corrections 1/mc

W-annihilation A is smaller than E and almost perpendicular to E

CLEO (’10)

Cabibbo-allowed decays

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

=0.39/d.o.f

11

1/mc power corrections

11E

Short-distance (SD) weak annihilation is helicity suppressed. Sizable long-distance (LD) W-exchange can be induced via FSI’s

FSIs: elastic or inelastic : quark exchange, resonance

A

Sizable 1/mc power corrections are expected in D decays

)()()(2

20

222 K

DDK

F mFmmfKaG

C a2= (0.820.02)exp[-i(1521)o]

Naïve factorization a2 = c2 + c1/Nc -0.11

Color-suppressed amplitude

121212

SCS

DCS

SU(3) flavor symmetry breaking

)(2

1))((

2

1

)()()( 0

PETPET

PAPEPPAPEPETDA

bsd

ssssdddd

KKbKKss

KKssssKKdddd

PETPET

PAPEPETPAPEPKKDA

)(2

1))((

2

1

)()()( 0

)()( ),()( with sssdddsssddd PAPEPPAPEPPPAPEPPAPEPP

Three possible scenarios for seemingly large SU(3) violation:

p =V*cpVup

A long standing puzzle: R=(D0 K+K-)/(D0 ) 2.8

131313

Large P

(i) If SU(3) symmetry for T & E, a fit to data yields P=1.54 exp(-i202o)

(ii) If (T+E)=(T+E)(1+/2), (T+E)KK=(T+E)(1-/2)

with | (0, 0.3) |P/T| 0.5

Brod, Grossman, Kagan, Zupan

Need large P contributing constructively to K+K- & destructively to

14

269.1)(

)(2

0

20

mF

mF

f

f

T

TD

KDK

KKK R=1.6

96.0)(

)(2

0

20

22

22

K

DK

D

KD

D

mF

mF

mm

mm

T

T

Nominal SU(3) breaking in T plus a small P

P=0.49 exp(-i129o) |P/T| 0.15

Bhattacharya et al. obtained )036.0141.0()023.0044.0()()( iPAPPAP ssdd

Nominal SU(3) breaking in both T & E; P negligible

SU(3) symmetry must be broken in amplitudes E & PA

Accumulation of several small SU(3) breaking effects leads to apparently large SU(3) violation seen in K+K- and modes

TKK/T=1.32

Assuming EKK=E

A(D0 K0K0)=d(Ed + 2PAd) + s(Es+ 2PAs) almost vanishes in SU(3) limit

Neglecting P, Ed & Es fixed from D0 K+K-, , , K0K0 to be

EeEEeE

EeEEeEi

si

d

is

id

oo

oo

7.140.15

8.90.15

58.0 ,19.1 II)(

62.1 ,19.1 I)(

15

Singly Cabibbo-suppressed D PP decays

1616

Tree-level direct CP violation

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

Large DCPV at tree level occurs in decay modes with interference between T & C (e.g. Ds

+) or C & E (e.g. D0 )

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

17

Decay CC LLY Decay CC

D0 0 0 D0 0

D0 0 0 D0 0

D0 0.82 -0.29 D0 0

D0’ -0.39 0.43 D0 K+K*- 0

D0 -0.28 -0.42 0.29 D0 K-K*+ 0

D0’ 0.49 0.38 -0.30 D0 K0K*0 0.73

D0 K+K- 0 0 D0 K0K*0 -0.73

D0 -0.73 -1.73 0.90 D0 0

D+ 0 0 D0 0

D+ 0.36 -0.46 D0 0.19

D+ ’ -0.20 0.30 D0 ’ -1.07

D+ K+K0 -0.08 -0.08 D0 0

Ds++K0 0.08 -0.01 D0 -0.53

Ds+ K+ 0.01 0.17 D0 ’ 0.59

Ds+ K+ -0.70 0.75

Ds+ K+’ 0.35 -0.48

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

Largest tree-level DCPV PP: D0K0K0, VP: D0 ’

Tree-level DCPV aCP(tree) in units of per mille

CC: Chiang, HYC

LLY: Li, Lu, Yu

T

E (CC)

EsEq (LLY)

Signs of aCP(tree) obtained by

LLY are opposite to ours

Penguin-induced CP violation

;sin102.1)( 3)(

PET

PAPEPa sssloopdir

KKKK

dddloopdir PET

PAPEPKKa sin102.1)( 3)(

DCPV in D0 , K+K- arises from interference between tree and penguin

In SU(3) limit, aCPdir(+-) = -aCP

dir(K+K-)

)(2

1))((

2

1)( 0 PETPETDA bsd

KKbKKss PETPETKKDA )(2

1))((

2

1)( 0

18

Apply QCD factorization to estimate QCD-penguin amplitude to NLO

ooo

ooo

35170152

35170152

009.0)/( ,24.0)/( ,24.0/

010.0)/( ,35.0)/( ,24.0/i

KKi

KKdi

KKd

iis

is

eTPeETPeTP

eTPeETPeTP

a(t+p)() - 410-5, a(t+p)(K+K-) 210-5,

DCPV from QCD penguin is small for D0 K+K- & due to almost trivial strong phase ~ 170o

)()()( 0 ssssdddd PAPEPPAPEPETDA

)()()( 0KKssssKKdddd PAPEPETPAPEPKKDA

19

How about power corrections to QCD penguin ? SD weak penguin annihilation is 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

Two other approaches for PE:

1.PE=(c3/c1)E+ GF/2(ifDfM1fM2)[c3A3i +(c5+Ncc6)A3

f]

A3f -2<P1P2|(uq)S+P|0><0|(qc)S-P|D>

2.Apply large-Nc argument to get

PE ~ (2Ncc6/c1) E

Li, Lu, Yu

Brod, Kagan, Zupan

valid only for SD contributions !

2020

Decay aCPdir

Decay aCP

dir

D0 +- 0.960.04 D0 -0.51

D0 00 0.830.04 D0 -0.27

D0 0 0.060.04 D0 -0.74

D0 0’ 0.010.02 D0 K+K*- 0.50

D0 -0.580.02-0.740.02

D0 K-K*+ 0.29

D0 ’ 0.530.03 0.330.02

D0 K0K*0 0.73

D0 K+K- -0.420.01-0.540.02

D0 K0K*0 -0.73

D0 K0K0 -0.670.01-1.900.01

D0 0.37

D+ + -0.780.06

D0 0

D+ +’ 0.340.07 D0 0.50

D+ K+K0 -0.400.04

D0’ -0.89

Ds+ +K0 0.460.03 D0 0

Ds+ 0K+ 0.980.10 D0 -0.23

Ds+ K+ -

0.610.05D0’ 0.20

Ds+ K+’ -

0.290.12

aCPdir (10-3)

aCPdir= -0.1390.004% (I)

-0.1510.004% (II)

about 3.3 away from -(0.6560.154)%

Even for PE T aCP

dir = -0.27%, an upper bound in SM, still 2 away from data

A similar result aCPdir=-0.128%

obtained by Li, Lu, Yu

21

Attempts for SM interpretation

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

However, D data do not show I=1/2 enhancement over I=3/2 one

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

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

Bigi, Paul, Recksiegel (’11)

New Physics interpretation

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

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

Hochberg, Nir

Altmannshofer et al; Chen, Geng, Wang

Rozanov, Vysotsky; Feldmann, Nandi, Soni

Tree level (applied to some of SCS modes)

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

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

Altmannshofer et al.

Altmannshofer et al.

After LHCb :

22

23

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(mc

2/v2). Need NP to enhance c8g by O(v/mc)

cGumg

O cs

g

)1(8 528

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

It can be realized in SUSY models

gluino-squark loops

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

trilinear scalar coupling

Giudice, Isidori, Paradisi

Grossman, Kagan, Nir

Giudice, Isidori, Paradisi

Loop level (applied to all SCS modes)

LRc

gNPg m

mxGc

~

8 )(

Hiller, Hochberg, Nir

2424

Consider two scenarios in which aCPdir is

accommodated:

(i) large penguin with ½P ~3T

(ii) large chromomagnetic dipole operator with c8g =0.012exp(i14o)

Large c.d.o. predicts large CP asymmetry

for , but small ones for D0 ’, D+

’, K+K0, Ds+ K0; other way around in

large penguin scenario.

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

Giudice, Isiori, Paradisi, Altamannshofer et al.

Decay Large penguin

Large c8g

D0 4.4 3.7

D0 1.0 6.2

D0 0.03 -4.2

D0’ 2.7 -0.4

D0 -1.6 -2.0

D0’ 1.5 -1.1

D0 K+K- -2.4 -2.9

D+ -3.6 -3.7

D+ ’ 3.3 0.6

D+ K+K0 -3.3 0.3

Ds++K0 3.7 -0.4

Ds+ K+ 5.1 3.1

Ds+ K+ -0.6 0.9

Ds+ K+’ -5.8 1.4

2525

Conclusions

The diagrammatical approach is very useful for analyzing hadronic D decays

DCPV in charm decays is studied in the diagrammatic approach. Our prediction is aCP

dir = -(0.1390.004)%

& -(0.1510.004)%

New physics models are highly constrained by D0-D0 mixing, ’/, … Chromomagnetic dipole operator is least constrained by experiment.