theory of direct cp violation in d hh chongqing, may 8, 2012 hai-yang cheng ( 鄭海揚 ) academia...
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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
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)(
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.
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