Post on 09-Jan-2016
description
Fat penguinsand
PQCD
A.I. Sanda
Nagoya University
Collaborators:Y. Keum, E. Kou, T. Kurimoto, H-n. Li, C. D. Lu, N. Shinha, R. Shinha, K. Ukai, T. YoshikawaM. Yang
My friend and I
Bit of history
447)(
)(0
0
K
K
Bose statistics: S wave ππstate I=0, 2
π ＋ π― can be in I=0 or in I =2
But π ＋ π ０ can only be in I=2 2
1I rule
Gell-Man and Pais 50 years ago
Penguins came to save the day
s du c t
g
KsTsdTduTudTs aaaL
aL |)(|
Penguin can not cause ΔI=2 transitions
SVZ
KsTsdTduTudTs aaaL
aL |)(|
Kdsddduus LRLRLRRL |)(|
ffM
uTuKdTs
KuTudTs
K
La
LLa
L
La
LLa
L
2
0||||
||
Ffactor of 10 enhancement
0|| LRLRLR dsdddu Kus Ri
L ||
0|||| LRRRRRds
Li
Lds
dsdddumm
pKus
mm
q
fmm
Mf
mm
M
fpmm
pfpp
mm
pp
duds
K
dsK
ds
K
22
)()(
Chiral perturbation theory
Factorization approximation
π
π
σK
penguin
My understanding of theΔI=1/2 rule
Penguins play important rolein the ΔI=1/2 rule
For B physics it also play important role
Rare decays give us chance to hunt for physics beyond the standard model
But, they pollute CP asymmetries
What we have leaned
TVPeV
TVPeV
V
V
T
iP
T
iP
T
T
fBA
fBA
*
**
1
1
)(
)(
Ratio is independent of strong interaction if:
i
PT
i
PT
PeVTV
PeVTV
fBA
fBA**)(
)(
c
1. Penguin and Tree have same KM phase2. Penguin is absent
V V V V V Vcb cd ub ud tb td* * * 0
1
2
3 KS
ππ
V Vcb cd*
V Vtb td*V Vub ud
*
sin( ) Im[ ]* *
*2 1 V V V
V V Vtb td cb
tb td cb
cdV*
cdV
Nearly 100% ＣＰＶ Nearly 100% ＣＰＶ
Bj notationRosner&AIS
Fermilab proeedings
Large CP Violation has been discovered!
SKB
sin = 0.82±0.12(stat)±0.05(syst) Belle12
sin = 0.75±0.09(stat)±0.04(syst) Babar 12
Where do we go from here?
PT
PT
PVVTVV
PVVTVV
BA
KBA
tdtbudub
tstbusub33
24
**
**
)(
)(
If T dominated over P, 20
1
)(
)( 2
BBr
KBBr
Penguins seems to be large in B decays
We expected )(log12
22
O
M
T
P W
T
P
BBr
KBBr1
)(
)(Fat penguins
3)(
)(2
*
*
0
0
TVV
PVV
BBr
KBBr
udub
tstb
11.T
P
bu
T
0: IP
0B Pure T
s
u P
sb
u
d
d
0KB
Pure P
03.006.092.0 pq
With an assumption that |q/p|=1:
03.006.092.0)()(
S
S
KBAKBA
pq
Babar
1
)sin()(1
)(2
)(1
)(/Im2
1)(
)()(
)(1
)(1
sin)sin(1cos1)(
22
222
2
2
22
SC
pqS
BA
BAC
MtCMtCtG
16.13.
38.27.
25.31.
21.1
09.94.
S
C
11.03.0
14.25.053.56.
45.47..
S
C
Belle
Babar
)Im(2
)Im(2
||||
||1
)Re()|||(|
)Re()||1(
)Re()|||(|
)Re()||1(
sincos)(
*
1
22
21
*2221
12121
*2221
12121
2/2/
d
d
c
c
b
b
a
p
qa
MtdeMtcebeatG ttt
3 unknownsLots of observables
Model independent measurement is difficult
Dynamical calculation of P and TShould be used as guide lines
In digging for physics beyond the SM
We have learned that Penguins are large!
)(
)(
B
KB
Nonleptonic 2 body decays
Over 70 decay modes
• Brodsky Lepage PR D22,2157(80)
• Isgar Llewellynsmith NPB317,526(89)• Botts Sterman NP B325, 62(89)
• Li and his collaborators
• Kroll Eur.Phys.J.C12,99(00)
• Li, Keum, AIS hep-ph/0004173 PR hep-ph/0004004 PL
History of pQCD approach
Feynman’s Mistake? Pion form factor
)( 2QF Probability of finding a parton near 1x
)( 2QF
Depends on wee dynamicsCannot be computed by perturbative QCD
1p
2p
2Q),0,0,(2 PPp
2QP
Wee parton
1pP
1x
2Q
Wee’s don’t know which way they are moving
2p
P
Feynman’s reasoning – Naive QCD
Infrared singularity! Infrared singularity!Isgar Llewellynsmith NPB317,526(89) Isgar Llewellynsmith NPB317,526(89)
B
1k
b
2k
uB
d1k
b
2k
u
d a b
Sudakov Factor in QED
This is not so in QCD!
Feynman says small x and small dominates k
The quark and anti-quark are far apart in space
Sudakov factor suppress these regions
xb
1
PQCD approach to pion form factor
X ""
Gluon
S
π
π
Color Singlet state does not radiate
Sudakov factor
Pion form factor
Factorization Theorem
H + H=
H + H-H X 1+
This is free of infrared and linear divergences
This is a divergent operatorBut it is multiplicative and can beabsorbed into the wave function
Brodsky Lepage PR D22,2157(80)Botts Sterman NP B325, 62(89)
Li and his collaborators
Pion wave function
Pion formfactor
)( 2QF
d
XB
b
dB
b quark decay
PQCD approach
Gluon
d
d
B
buVG
ubF )1(2
5
X
d
Bb
u
)(
)()(
)()1()(
222
22
212
22
21
152
qFqq
mM
qFqq
mMpp
pBbup
B
B
transition form factor
)( 22 GeVQ
transition form factor
We now know Why FA works
Exp PQCD
K ０ π± 18.4± 2.2 16.4± 3.3
K±π± 18.5± 1.5 15.5± 3.3
K±π ０ 11.5± 1.5 9.1± 1.9
K ０ π ０ 8.8 ± 2.2 8.6± 2.2
π ＋ π― 4.6± 0.8 7.0± 2.0
π ＋ π ０ 5.9± 1.4 3.7± 1.3
π ０ π ０ 0.3±0.1
ππ branching ratio would agree better if penguins are larger
)cos()cos(2||||
)sin()sin(2
)()(
)()(22
ABBA
AB
fBfB
fBfB
)''()()( ii BeAefBA
)''()()( ii BeAefBA
CP asymmetry
The diagram which produces strong interaction phase -> CP violation
)()(
)()(
fBfB
fBfB
K ０ π± 0.186±0.105
K±π± -0.062±0.054
K±π ０ -0.087±0.115
CP asymmetries will become smallerif penguins are larger
We should not worry about the disagreement until K ０ π± asymmetry is settled
P
b
u
s
d
d 0KB
Pure P
)''()()( ii BeAefBA
)cos()cos(2||||
)sin()sin(2
)()(
)()(22
ABBA
AB
fBfB
fBfB
)''()()( ii BeAefBA
Conclusion
• PQCD is at its infant stage
• Seems very promising
• Predicts 2 body decay rates
• Input: wave function
• Predicts strong interaction phase
• Existence of CP violation at 10-20% level for some channels
Summary 2
• Are large CPV inconsistent with experiment?
• May be, but can’t say until K+π0 CP asymmetry is in order 0∼