b to k π - yonsei universitykimcs.yonsei.ac.kr/sub_pages/seminar/harbin2010/3_b2kpi... ·...
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C. S. Kim (Yonsei Univ.)Collaboration with Chuan-Hung Cheng, Sechul Oh, J.H. Jeon, Y.W. Yoon
®B K
1) Is there any puzzle of new physicsin decays?
2) Possible new physics from decays : Unparticle, Leptophobic Z’
®B K®B K
12010-10-18
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B Kπ Puzzle Branching Ratios - HFAG March 2009
Fleischer Hep-ph/0701217
At March 2007Rc = 1.11 ± 0.07Rn = 0.97 ± 0.07
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CP Asymmetries - HFAG March 2009
0
0 0( ) ( ) 0.14 0.03
(sin2 ) (sin2 ) 0.35 0.21S
CP CP
ccsK
B K B K
® ®
B Kπ Puzzle
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Quark Diagram Approach in B Kπ
Amplitude parameterization
0
0
0
0 0 0
( )
2 ( )
2
CEW
CEW EW
EW
A B K
A B K
A B K
A B K
®
®
®
®
with re-definition of 1 13 3
C CEW EW
CEW
®
®
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Quark Diagram Approach in B Kπ
* *tb ts tc ub us uc tc ucV V V V
2 4
Hierarchy between the parameters
tc
EW,
CEW,
uc,
1
23
bk m2 2/
cu tu| / |
uc tc| / |
Buras, Fleischer
PLB. 341. 379 (1995)
uc u c
tct c
W
G m k G m k
E x G m kM
2
2
( , , ) ( , , )2( ) ln ( , , )3
b
km
2
2
1 14 2
uc
tc
0.2 0.4
Mishima, Yoshikawa
PRD. 70. 094024 (2004)C
EW| |
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Final form A B K A P0 0 ®
, ,Cuc EWP P A
T C EWi i i i i iT C EWA B K A e P r e e r e e r e
00 0 1 12
®
Ti i iTA B K A e P r e e 0 (1 )
®
C EWi i i iC EWA B K A e P r e e r e
000 0 0 00 1 12
®
We Neglect We set the strong phase of P to be zero all phase is relative to it We hold 7 unknown parameters We use value given by other analysis are real and positive, are phases of their amplitude
, , , , , ,T C EW T C EWP r r rδδδγ
ijA ij
Quark Diagram Approach in B Kπ
EWtc T C EW
tc tc tc
P r r r, , ,
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Re-parameterization Invariance
We assume NP comes into PEW part (or C part)
sin( ) sin( )sin( ) sin( )
i i ie e e
For any phase
We can choose arbitrary at will, for any given
Botella, Silva 2005
N N N NN N N N N
i i i i ir r re e e e e
sin sin( )2 2 sin 2 sin
Absorbed into C Absorbed into EW
φ
,θη φ
0
Re-Parameterization Invariance
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NP term is absorbed into SM term
C EN N
N
W
C EWN
i i iC EW
i i i
N i i
N Nii
C EN N
Wi
A A P r e e r e
P r e e r e
r
re
e e
r e e
0 00 1,21 )2 sin sin
sin sin(
CMC
NMN
i N iC C
ir ee r e r sin
sin
EWMW
NEM i
E
NN
W EWiir ee r e r
sin( )
sin
CMEW
MM iC
ME
i iWP e e er r 1
2
Re-Parameterization Invariance
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Original Form does not change
If there is NP
M MC C
M MEW E
C SM C SM
EW EWSM SMWr
r
r
r
( ) , ( )
,
A B K A P0 0 ®
MCT
MEWM i
EWi i i i
TM i
CA B K A e P r e r e re ee 00 0 1 1
2 ®
Ti i iTA B K A e P r e e 0 (1 )
®
MEW
MCM i M i
C Ei
WiA B K A e erP ee r
000 0 0 00 1 12
®
Analytic re-Solution (CSK, S Oh, Y Yoon, PLB665(2008)231)
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P Br 0
CPT
CP
T CP T
RRA R
r R
2
2
sin2 1cot 1 1 1( ) cos 2 sin
(1 cot cot ) 1
Step 1 - , ,T TP rδ
Ti i iTA e P r e e (1 )
A P 0
Analytic Solution
T T T
CP T T
R r r
R r
21 2 cos cos
2 sin sin
B
B
R
0
0 0.90 0.05
T
T
P
r
(49.9 1.1)eV
0.14 0.07
20 11
reject
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Step 2 -
A A P xA P x
A A P xA P x
2 20 00 2 200
00
2 20 00 2 200
00
2 2ArcCos2 2
2 2ArcCos2 2
00 00,αα
T
T
i i i i iT
i i i i iT
A e A e P r e e xe
A e A e P r e e xe
0 00
0 00
0 00
0 00
2 (2 )
2 (2 )
Analytic Solution
x0A
00A
0A
00A
Two-fold ambiguity occurs.2 X 2 = 4 fold ambiguities in tatal.
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Step 3 - , , ,M MEW EW
M MC Crδ rδ
MEW
ME
MC
MC
W
y y yy
y y yy
y yy y
y yy y
r
r
2 2
2 2
1 cos( )sin 2
1 cos(2 )sin 2
cos cosArcTansin sin
cos( ) cos( )ArcTansin( ) sin( )
MEC
M
W
MEW
M
C
M iEW
M iE
M iC
M iC
i
W
i i
i i i
Ae e yePAe e y
rr e
r e
e
r e eP
00
00
00
00
2 1
2 1
Analytic Solution
y
yM
EWr
M iγCr e
γ γ
No discrete ambiguity
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Analytic Solution 4 different solutions for
We reject “Case 3” due to large prediction The SM estimate
0sKπS
0.12 0.039 , 61 , 22EW C C EWr rδδ
, , ,M MEW EW
M MC Crδ rδ
SKS 0 =0.33 0.21(data)
Case 2: Large C Case 4: Large EW
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Analytic Solution Step 4 - solutions for NP term
CMC
NMN
i N iC C
ir ee r e r sin
sin
EWMW
NEM i
E
NN
W EWiir ee r e r
sin( )
sin
4 Equations VS 7 unknowns - , , , , , ,N N NC EW C EWr rδδrφδ
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Additional Inputs a) Additional inputs from Flavor SU(3) Sym.
From B ππ decays
HFAG March 2007
Assuming no NP in B ππ
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Additional inputs from Flavor SU(3) Sym. B ππ parameterization
T C
T
C
i i i i
i i i
i i i
A B Te e Ce e
A B Te e Pe
A B Ce e Pe
®
®
®
0
0
0 0
2 ( )
( ) ( )
2 ( ) ( )
with 5 parameters
T C
P
Tδ
Cδ
Chisq-fitting with 5 measurements3 – Br, ( ),CP ππAππS
0 0 0.33CP 0.31( )=0.36 (data)
us
ud
VC CV
(3.8 0.4)eV
EW T Ci i iEW T C
b
c cr e r e r ec c R
9 10
21 2
3 1 ( )2
C C
EW EW
r
r
( , ) (0.076 0.008, 12 15 )
( , ) ( 0.14 0.04, 9 10 )
Gronau, Pirjol, Yan (1999)
Additional Inputs
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b) Additional inputs from PQCD result
Li, Mishima, Sanda, PRD72, 114005 (2005)
C C
EW EW
r
r
( , ) (0.039, 61 )
( , ) (0.12, 22 )
Additional Inputs
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Solution for NP term with additional inputs
MC C C
MEW EW EW
i M i iC C C
i M i iEW EW EW
r e r e r e
r e r e r e
NC C
NC
NEW
NCN
rr
r r
or
sinsin( )sin
sin
NC
NEW
Ni N i
C
Ni N i
EW
r e r e
r e r e
sinsin
sin( )sin
Defining
With inputs from SU(3) sym. With inputs from PQCD results
Cases 2&4 are suitable and consistent each other between two methods.
Determining NP parameters
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Dependance on Dependance on SKS 0
Discussions
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Due to the Re-parameterization Invariance(RI) the NP terms absorbed into the SM terms and in pair.
In order to extract NP parameters we need at least 3 additional inputs.
We could pin down each hadronic parameter under four-fold discrete ambiguity using analytic method. And also NP parameter for given additional inputs
Results shows that there should be quitelarge NP contribution with maximal weak phase
Summary
EWC P
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in mixing and B→(π, K)π decays
Collaboration with Chuan-Hung Chen and Yeo-Woong Yoon
PLB671(2009)250
37
BB
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Unparticle Physics Georgi, PRL. 98. 221601 (2007)
field with IR fixed pointscale Invarant
at ( 1 TeV) scale physicsM
1smk
O OM
dimensional transmulation
at scale of
can not be described by ordinary particle
☞ Unparticle stuffBanks, Zaks, NPB.196.189(1982)
Interaction with the SM particle:
d d
smk
CO O
M
Matching onto Unparticle operator
: scaling dimension of Unparticle Op.d38 2010-10-18
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Unparticle Physics
p d d q q qp
44 4 2 0 0 2 2 2
311
(2 ) ( ) ( ) ( ) ( )( )(2 )
n nj n
j j j njj
d pP p p p A P P P
The vacuum matrix element
rp
4
†2 24
0| (0) |0 | 0| (0)| | ( )(2 )
i p xd pO O e O P P
should scale with dimension , by virtue of scale invariance. Therefore,2d
22 2 0 2 2| 0| (0)| | ( ) ( ) ( )( ) ,ddO P P A P P Pr q q
This characterizes the unparticle phase space.And, it resembles the phase space for n massless particles
pp
5/2
2
16 ( 1 / 2)(2 ) ( 1) (2 )n n
nA
n nWhere,
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Unparticle PhysicsGeorgi’s proporsal:
Identifying
5/2
2
( 1 / 2)16(2 ) ( 1) (2 )d d
dA
d dpp
,n dA A n d
“ Unparticle with scaling dimension ”d
“ Fractional number of invisible particles ”d
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Unparticle PhysicsBecause of scale invariance, The Unparticle propagator is
422 2
10| ( ( ) (0)|0
2sin( ) ( )d iip x
d
A p pd xe T O x O i g e
d p p
m nfm n mn
p
It carries CP conserving phase ( 2)df p
The Effective Lagrangian for the interaction with vector Unparticle is
5 51 1(1 ) (1 )q q q qL R
d d
C Cq qO q qOm m
m mg g g g
Georgi, PLB 650:275(2007), Cheung et al, PRL.99:051803(2007)
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Mixing Constraintsb
q
q
b
t
t
W
tbV
*tqV
W,d sB,d sB
q
b
b
q
bqC bqC,d sB ,d sB
,12q SM
,12q
Containing Weak Phase
From CKM Factor
Containing Strong Phase
From unparticle propagator
12
, ,12 12
q
q SM q
BB
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2 2
, ,2 * 212 0 122
( ) ( ) | |12
SMq
qq q
B iq SM q SMF WBB B tq tb t
G mm f B V V S x e fh
p
Lattice QCD results for the Non-perturbative parameters.
0 0.0030.023 0.002: 0.215 0.019 0.245 0.021
( ) : 0.244 0.026 0.295 0.036
d sd sB BB Bf B f B
JLQCD
HP JL QCD
The values for the SM mixing amplitudes
, ,12 12
0.20 1 10.26
1 1
2| | 2| |
: 0.75 ps 16.4 2.8 ps
( ) : 0.97 0.29 ps 23.8 5.9 ps
d SM s SM
JLQCD
HP JL QCD
22 45.2 5.7 , 2 2.3 0.2SM SMd sf b f l h
Mixing ConstraintsBB
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Current Experimental data (HFAG)1
1
(0.507 0.004) ps 43 2
(17.77 0.12) psd d
s
M
M
f
CDF, PRL. 97. 242003 (2006)
d dB BStrongly constraining on the mixing
122| |qqM
Especially on phases of ,
12d
: 130 180 , ( ) : 132 12d dJLQCD HP JL QCDf f
Mixing ConstraintsBB
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2 2
, 2 2 2 212 2 2
4 5 10 14( ) ( ) ( )
3 6 3 6q q
qq q
B Bq qb qb qb qbBB B L R L R
m mC p m f B C C C C
p p
determine the phase of
22 2 22
( ) ,2sin ( )
id
d d
A eC q
d p
f
p
( 2)df p
2( )C q ,
12q
Therefore (HP+JL)QCD can not give the right value of scaling dimension d
JLQCD allows all value of d
We choose JLQCD case and set 1.5d
Mixing ConstraintsBB
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Constraints on unparticle mixing amplitudes from experimental data
, 1 , 112 122| | 0.25 0.26 ps 2| | 7.6 6.6 psd s
Mixing ConstraintsBB
are strongly constrained as 4 4 3| | 3.1 10 , 3.5 10 | | 1.4 10 ,db db sb sb
L R L RC C C C
, ,db db sb sbL R L RC C C C
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Unparticle contribution in B→(π, K)π decays
The SM decay amplitudes
The recent PQCD result for the SM parameters
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Unparticle contribution in B→(π, K)π decays
Effective Hamiltonian for
2( ) ( ) ( ) ( ) ( )qb qb q q q qL V A R V A L V A R V AC q C qb C qb C q q C q q
b qq q ®
Unparticle contribution in decays
2 2 2 ,1 0
2 2 2 ,1 0
( ) ( ) ( )
( ) ( ) ( )
i j
i j
i j BB dec
i j B KK B K dec
A B C q f m F m a
A B K C q f m F m a
p p pp p
p p
p p
p
®
®
2 2 21 2( ),B B bq m m m q mp
2 2
1 2
2 2
1 2
,( ) ( )
,( ) ( )
b u d b d d
K KK K
b u s b d s
m mr r
m m m m m m
m mr r
m m m m m m
p pp p
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Unparticle contribution in B→(π, K)π decays
Unparticle Parameters:
,
, , , (
)
, , ,
db db sb sbL R L R
uu uu dd ddL R L R
d
C C C C Strong constraints
from mixing
C C C C
4 4 4 51.5 10 , 2.3 10 , 5.8 10 , 9.3 10
3.9, 12.4, 3.7, 12.2
db db sb sbL R L R
uu uu uu uuL R L R
C C C C
C C C C
We set
2cPerform minimum analysis for 8 free parameters with
16 experimental data of decays.
Free
parameters
( , )B Kp p®
The fitted values are
( ) ( ) ( )SMA B f A B f A B f® ® ®
c 2 4.6, . . 8d o f
1TeV, 1.5d
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Unparticle contribution in B→(π, K)π decays
The unparticle contribution with fitted values of the parameters
Chisq is
Much
Reduced
( w/o : without Unparticle contribution )
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Summary We searched Unparticle contribution in mixing and
decays
mixing could give strong constraints on unparticle
parameters. The scaling dimension also can be constrained
when more precise estimation of the SM mixing amplitude is
provided.
The Unparticle contribution could successfully resolve the
discrepancy between theory and data for the
decays, such as and
( , )B Kp p®
, ,d s d sB B
d
, ,d s d sB B
( , )B Kp p®0 0( ), ( )d CP dBr B A Bp p p p ® ® 0( )CP dA B K p®
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in mixing and B→(π, K)π decays
Collaboration with S. W. Baek and J. H. Jeon
PLB664(2008)84
52
BB
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Leptophobic Z’ - does not couple to SM leptons - introduced to explain the Rb-Rc puzzle at LEP and
anomalous high-ET jet cross section at CDF - by introducing the superstring inspired models,
i.e., E6 or Flipped SU(5)
Extra neutral U(1) gauge boson, Z’ - has been considered one of the extensions of the SM - motivated by
String-inspired GUTs (J.L.Hewett, T.G.Rizzo, M.Cvetic, P.Langacker, etc)
Dynamical symmetry breaking models (G.Buchalla, G.Burdman, etc)
Extra dimension models (M.Masip, A.Pomarol)
Little higgs models (N.Arkani-Hamed, A.G.Cohen, T.Han, etc)
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6 E GUTs comes from heterotic superstring ( ) was the natural anomaly free choice for a GUT group after
SO(10) could have several intermediate mass breaking scales
Maximal breakings of E6 :
If we consider the following breaking chain
U(1)’ can be a linear combination of 1. two U(1)s [ (1) ' (1) sin (1) cos , (5)
2. three U(1)s [ (5)
] ambiguity of embeddings, ]U U U Flipped SU
Flipped SU Maψ χθ θ= −
+
3
1. (10) (1)2. [ (3)]3. (2) (6)
SO USU
SU SU
× ×
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directly SU(5) → SM : SU(5) (Geogri-Glashow)
SU(5)XU(1)χ → SM : Flipped SU(5) (S.M.Barr,1982)
Flipped SU(5) is a different breaking pattern of SO(10)
(5) : (10, ) { , } (5, ) { , } (1, ) { }
(1) ' (1) sin (1) cos
1 3 5, 2 2 2
c c c c cGGSU F Q u L d l
U U U
e f
ψ χ
ν
θ θ
• = = − = = =
• = −
=
(5)
Flipped (5) : (10, ) { , } (5, ) { , } (1, ) { }
1 3 5, 2 2 2
/ 2 (1) (1) ( 1/ 5)
c c c c c
SU
SU F Q d L u l ef
Y U U χ
ν
α β α β
• = = − = = =
•
=
= + = = −
Leptophobic Z’ does not couple to multiplet(f) and singlet(lc)
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(5)Leptophobic Z in stringy flipped SU′
5
(1) '
: SU(5) U(1) SO(10) SU(4) U(1)Uobservable hidden
Gauge group• × × × ×
(J.L Lopez, D.V. Nanopoulos, and K.J.Yuan (NPB399,654(1993))
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Neutral Current Interaction−
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Experimental result
Lattice QCD result
1%less than
27%about
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Experimental results
PQCD results
~ 4.3%~ 4.7%~ 3.1%
~ 6.1%
1 σ
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Experimental results
PQCD results
2 σ
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Experimental results
PQCD results
2 σ
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0 0 S S MixingB B−
, , '12 12/s SM s ZR M M=
RG
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B K decaysπ→
Leptophobic Z’ contributions
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Stringy leptophobic Z’ can possibly explain the apparent deviations from the SM predictions in the B→πK decays
This is phenomenologically interesting because
- The new Z’ coupling is generation dependent and can generate FC- The FCNC couplings allow large CP violation- The couplings also violate the isospin symmetry and can give large
contributions to the EW penguins (PEW and PCEW )
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,1) of the fields ( , , ) can be interchanged with those of ( , , )c c c cQ L d H h Sϕ χ ν
2) The pairs ( , ) and ( , ) are interchanged : Flpped SU(5)c c c cu e d ν
3) We can consider the interchange of both (1) and (2) simutaneously
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