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

2010-10-18 2

2010-10-18

+

+

3

2010-10-18 4

B Kπ Puzzle Branching Ratios - HFAG March 2009

Fleischer Hep-ph/0701217

At March 2007Rc = 1.11 ± 0.07Rn = 0.97 ± 0.07

5 2010-10-18

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

6 2010-10-18

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

®

®

7 2010-10-18

2010-10-188

2010-10-189

2010-10-1810

2010-10-1811

2010-10-1812

2010-10-1813

2010-10-1814

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| |

15 2010-10-18

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, , ,

16 2010-10-18

2010-10-1817

2010-10-1818

2010-10-1819

2010-10-1820

2010-10-1821

2010-10-1822

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

23 2010-10-18

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

24 2010-10-18

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)

25 2010-10-18

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

26 2010-10-18

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.

27 2010-10-18

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

28 2010-10-18

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

29 2010-10-18

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

30 2010-10-18

Additional Inputs a) Additional inputs from Flavor SU(3) Sym.

From B ππ decays

HFAG March 2007

Assuming no NP in B ππ

31 2010-10-18

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

32 2010-10-18

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

33 2010-10-18

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

34 2010-10-18

Dependance on Dependance on SKS 0

Discussions

35 2010-10-18

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

36 2010-10-18

in mixing and B→(π, K)π decays

Collaboration with Chuan-Hung Chen and Yeo-Woong Yoon

PLB671(2009)250

37

BB

2010-10-18

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

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,

39 2010-10-18

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

40 2010-10-18

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)

41 2010-10-18

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

42 2010-10-18

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

43 2010-10-18

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

44 2010-10-18

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

45 2010-10-18

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

46 2010-10-18

Unparticle contribution in B→(π, K)π decays

The SM decay amplitudes

The recent PQCD result for the SM parameters

47 2010-10-18

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

48 2010-10-18

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

49 2010-10-18

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 )

50 2010-10-18

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®

51 2010-10-18

in mixing and B→(π, K)π decays

Collaboration with S. W. Baek and J. H. Jeon

PLB664(2008)84

52

BB

2010-10-18

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)

53 2010-10-18

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

× ×

54 2010-10-18

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)

55 2010-10-18

(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))

56 2010-10-18

Neutral Current Interaction−

57 2010-10-18

Experimental result

Lattice QCD result

1%less than

27%about

58 2010-10-18

Experimental results

PQCD results

~ 4.3%~ 4.7%~ 3.1%

~ 6.1%

1 σ

59 2010-10-18

Experimental results

PQCD results

2 σ

60 2010-10-18

Experimental results

PQCD results

2 σ

61 2010-10-18

0 0 S S MixingB B−

, , '12 12/s SM s ZR M M=

RG

62 2010-10-18

B K decaysπ→

Leptophobic Z’ contributions

63 2010-10-18

64 2010-10-18

65 2010-10-18

66 2010-10-18

67 2010-10-18

68 2010-10-18

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 )

69 2010-10-18

70 2010-10-18

,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

71 2010-10-18