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G. Buchalla LMU München
15
G. Buchalla LMU München Decays nguins with
description
Rare B Decays and Penguins with Charm. G. Buchalla LMU München. Outline. ● Charm Penguins in ● A Toy Model ● Quark-Hadron Duality ● Discussion ● Conclusions. - PowerPoint PPT Presentation
Transcript of G. Buchalla LMU München
G. BuchallaLMU München
Rare B Decays and Penguins with Charm
Outline
● Charm Penguins in
● A Toy Model
● Quark-Hadron Duality
● Discussion
● Conclusions
Beneke, G.B., Neubert, Sachrajda, Eur. Phys. J. C (2009) 61, 439
llXB s
llXB s
22bmqs
90)(
)(
SDs
ss
llXBB
llXXBB
6103.5
3108.7 2106
)0()(9
16
9
4ln9
8
),(3
22
299
qm
h
smmhaCC
cKS
bcNDR
Krüger-Sehgal model
SD coefficient
Toy Model
AVAVAVAVeff ttllccllG
H )()()()(2
1212
21 ll
ee
eellqeeG
eellA c 152
2221 )1()(
2)(
)()(0)0()(0 224 qgqqqjxjTexdi xiq
ccj
Properties of )( 2q
dispersion relation iqt
t
t
dtqq
20
22 )(Im
)0()(
quark loop2
2
22 ln
12)0()(
cm
iqNq
in toy model 2
2
2ln
12)0()0()0(
c
ttc m
mN
Quark-Hadron Duality in a NutshellShifman
Im
2q
0RR
22 M
22
21
2
1
22
.)1(12
1.
1
12
1
)(12
1Im
qz
constzconstinz
nq
n
n
exact:
OPE: ...120
1
12
1
2
1ln
1
22
1ln)1(
4221
2
zzzz
zk
B
zzz
kk
k
...720)('''12)('2)(1)0(Im12 zzzz
2
2
6
6
8
8
2
2
26
6
4
4
02
2
2sin123
1
30
11
)(Im24231
2
M
MMM
qM
q
M
q
M
dqR
M
OPE duality violation
22251
2221 )()21()1(
27
)(qss
mG
ds
eelld
contribution from resonance
MiMq
fq
22
22 )(
)(Im)( 22
22 qM
fq
more singular than for small
2
Im
450)()9(40
243560
32
22
MM
f
M
f
s
HQL
21
2 mqs
Quark-Hadron Duality (QHD)
?↔
21
22
0
2 )(Im
21
mfqdqm
M
ffqdq
m 2222
0
2 )(
21
)1()(Im)(Im 22
2 OMM
fM quark
local QHDviolated, but…
consistent withglobal QHD for Im
2
arbitrarily large!
global duality violated for betweenhadronic and fixed-order partonic result
►
resonance enhancement in toy model:
)(
)()(
2121
1
0
eell
ds
eelldds res
210]21)[ln(
)21()1(8
)(
)(2
21
2
2
25
21
221
M
f
m
f
mm
rr
eell
eelll
ctSD
res
55 0.007 560
>>
21
2 mMr
QHD violated
↔ no OPE for
restricted set of cuts
„exclusive“ final state even for integrated rate
)( 21 eell
AssdsmG
Xll
ImIm)21()1(16
)(1
0
22
51
2
21
„tau-decay“
duality holds in theusual sense
Charm Resonances in llXB s
90][9
)21()1(512
)(
)(
2
2
2
2
10
2
9
222
25
M
f
m
f
CC
rra
llXBB
llXXBBR
b
SDs
ss
[23] 0.007 560
60)(
)v(
)9(5
54]23[
2
23
2
b
c
s
cs
m
m
M
mR
Coulomblimit
lightresonance
]036.0007.0[]5010[2
2
2
M
f
m
fR
b
Discussion
● high- region in :
OPE
2q lslb
G.B., Isidori; Grinstein, Pirjol)0()( jxHT eff
2*9
2
9
2
92Re2~
CCC
dq
d
duality ↑ small
● charm-penguin in 21MMB
Conclusions► integrated rate:
no OPE for charm contribution,
enters as
► , very small
► huge violation of global duality between hadronic and fixed-order partonic result
► high- : global duality o.k.2q
lslb
2~
Mf 2
Happy Birthday Daniel !
