1

A New Physics Study

in B K & B K* Decays

National Tsing Hua University, October 23, 2008

Sechul OH ( 吳世哲 ) ( 오세철 )

C.S. Kim, S.O., Y.W. Yoon, PLB665, 231 (2008)C.S. Kim, S.O., C. Sharma, R. Sinha, Y.W. Yoon, PRD76, 074019 (2007)

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The The B K puzzle puzzle

A model-independent analysis of B A model-independent analysis of B K K

-- reparametrization invariance reparametrization invariance

-- how to extract New Physics effects-- how to extract New Physics effects

A model-independent analysis of B A model-independent analysis of B K* K*

-- interesting observables sensitive to New Physics -- interesting observables sensitive to New Physics

effectseffects

SummarySummary

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4

5

6

Cabibbo-Kobayashi-Maskawa (CKM) matrix

Unitarity:

Unitarity triangle:

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Direct CP violation in decay occurs when

Direct CP violation

Time-dependent CP violation

= J/ Ks

8

9

q

q-

The dominant quark level subprocesses are loop (penguin) processes b s penguin is sensitive to NP

The 4 decay channels (& antiparticle decay channels)

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Large

Small

Conventional Hierarchy in B → KConventional Hierarchy in B → Kππ

strong penguin

EW penguin

color-suppressed tree

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Branching Ratios

Fleischer Hep-ph/0701217

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

= 0SM :

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CP Asymmetries

SM :

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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

p

p

p

p

+ +

+ -

+ +

¢ ¢® = +

¢ ¢ ¢® = - - -

¢ ¢ ¢ ¢ ¢ ¢® = - - - - - -

¢ ¢ ¢® = - -

P A

P P T

P P P T C A

P P C

* *tb ts tc ub us uc tc ucV V V V¢ ¢ ¢ ¢ ¢= + º +% %P P P P P

l 2 l 4

Hierarchy between the parameters

tc¢P

EW,¢ ¢T P

CEW,¢ ¢C P

uc,¢ ¢A P

1

l2l

3l

q

q-

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Final form

( )A B K A Pp0 0 + + + ¢® º = -

( ) ( )T C EWi i i i i iT C EWA B K A e P r e e r e e r ea g d g d dp

00 0 11

2

+ ¢ ¢ ¢+ + + ¢® º = - - +

( ) Ti i iTA B K A e P r e ea g dp0 (1 )

+- ¢+ - +- ¢® º = -

( ) ( )C EWi i i iC EWA B K A e P r e e r ea g d dp

000 0 0 00 11

2¢ ¢¢® º = - - +

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 analyses are real and positive, are phases of their amplitude

, ,Cuc EWP P A¢ ¢ ¢

¢ ¢ ¢ ¢, , , , , ,T C EW T C EWP r r r δ δ δ

ijA ija

EWtc T C EW

tc tc tc

P r r r, , ,¢ ¢ ¢

¢ ¢= = = =¢ ¢ ¢

T C PP

P P P

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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

f d

d

g

d

d d

g d d g ggff

g

0 00 1,

2

1 )2 sin sin

sin sin(

¢+

¢

¢É - + +

æ ö- ÷ç¢= - + + - ÷ç ÷ç ÷çè ø

CMC

NMN

i N iC C

ir ee r e rd d dfgsin

sin¢= -

EWMW

NEM i

E

NN

W EWiir ee r e rd d df g

gsin( )

sin¢ -

= -

( )CMEW

MM iC

ME

i iWP e e er rdg d1

2= +-¢

““Reparametrization invariance” of decay amplitudes Reparametrization invariance” of decay amplitudes Botella and Silva

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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

d

d d

d

( ) , ( )

,

¹ ¹

¹ ¹

( )A B K A Pp0 0 + + + ¢® º = -

( ) ( )MCT

MEWM i

EWi i i i

TM iCA B K A e P r e r e re eea g d g ddp

00 0 11

2

+ ¢+ + + ¢® º = - - +

( ) Ti i iTA B K A e P r e ea g dp0 (1 )

+- ¢+ - +- ¢® º = -

( ) ( )MEW

MCM i M i

C Ei

WiA B K A e erP ee r da g dp

000 0 0 00 11

2¢® º = - - +

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P Br +¢µ 0

CPT

CP

T CP T

RR

A R

r R

gd

g g

g d

+-

+-

+-

é ùæ öæ öê ú- ÷ç ÷ç ÷ç¢= ± + - - ÷ê úç ÷ç ÷÷ç ÷ççê ú- ÷è øçè øê úë û

¢= - -

2

2

sin2 1cot 1 1 1

( ) cos 2sin

(1 cot cot ) 1

A

A

Analytic Solution

MEW

ME

MC

MC

W

y yyy

y yyy

y yy y

y yy y

r

r

d

h hg

g h hg

h hh h

h gh g g

d

h gh

+= - -

+= - + -

æ ö- ÷ç= - ÷ç ÷ç ÷ç -è ø

æ ö- - + ÷ç ÷= -ç ÷ç ÷ç - - +è ø

2 2

2 2

1cos( )

sin 2

1cos(2 )

sin 2

cos cosArcTan

sin sin

cos( ) cos( )ArcTan

sin( ) sin( )

MEC

M

W

MEW

M

C

M iEW

M iE

M iC

M iC

i

W

i i

i i i

Ae e ye

PA

e e y

rr e

r e

e

r e eP

g a h

g a h

d d

dd-

- + = + º¢

- + = + º¢

00

00

00

00

2 1

2 1

A A P xA P x

A A P xA P x

a z

a z

+

+

æ ö¢- - ÷ç ÷= ± ç ÷ç ÷¢ ÷çè ø

æ ö¢- - ÷ç ÷= ± ç ÷ç ÷¢ ÷çè ø

2 20 00 2 200

00

2 20 00 2 200

00

2 2ArcCos

2 2

2 2ArcCos

2 2

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4 different solutions for

We reject “Cases 1 & 3” due to predictions different from data The SM estimate

0sKπ

S= > = » - =0.12 0.039, 61 , 22EW C C EWr r δ δo o

, , ,M MEW EW

M MC Cr δr δ

0=0.38 0.19(data)SK

Sp

±

Case 2: Large C Case 4: Large EW

( 4-fold discrete ambiguity )

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Find solutions for NP term

CMC

NMN

i N iC C

ir ee r e rd d dfgsin

sin¢= -

EWMW

NEM i

E

NN

W EWiir ee r e rd d df g

gsin( )

sin¢ -

= -

4 real equations vs 7 unknowns: , , , , , ,N N NC EW C EWr r δ δ r φ δ¢ ¢

Need at least 3 additional inputs to fix NP terms

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Additional inputs from flavor SU(3) symmetry

From B decays

Assuming no NP in B

Additional inputs

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B parametrization

( ) 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

g d g d

g d b

g d b

p p

p p

p p

+ +

+ - -

+ -

® =- +

® = - +

® = - -

0

0

0 0

2 ( )

( ) ( )

2 ( ) ( )

with 5 parameters T C

P

Tδ

Cδ

-fitting with 5 measurements3 Br’s, ( ),CP π π

A π π S + -+ -

p p +-

0 0 0.33CP 0.31( )=0.36 (data)A

us

ud

VC C

V¢= = ±(3.8 0.4)eV

EW T Ci i iEW T C

b

c cr e r e r e

c c Rd d d

l¢ ¢ ¢+

= - ++

9 102

1 2

3 1( )

2

C C

EW EW

r

r

d

d

¢ = ± - °± °

¢ = ± °± °

( , ) (0.076 0.008, 12 15 )

( , ) ( 0.14 0.04, 9 10 )

Gronau, Pirjol, Yan (1999)

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Li, Mishima, Sanda, PRD72, 114005 (2005)

C C

EW EW

r

r

d

d

¢ = - °

¢ = °

( , ) (0.039, 61 )

( , ) (0.12, 22 )

Additional inputs from PQCD result

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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

d d d

d d d

¢D

¢D

D º -

D º -

or

sinsin( )

sinsin

NC C

NC

NEW

NCN

rr

r r

d d d p

ff g

gf

= D D -

D=

- D

= D

NC

NEW

Ni N i

C

Ni N i

EW

r e r e

r e r e

d d

d d

fg

f gg

sinsin

sin( )sin

D

D

D = -

-D = -

Defining

With inputs from SU(3) symmetryWith 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 g

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Due to the Reparametrization Invariance(RI), the NP terms can be absorbed into the SM terms C & PEW in pair.

In order to extract NP parameters, we need at least

3 additional inputs. We could pin down each hadronic parameter und

er four-fold discrete ambiguity using analytic method. And also NP parameter for given additional inputs.

The result shows that there should be quite large NP contribution with a maximal weak phase ~ /2.

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B → V V decays

by angular momentum conservation

B ! V1 V2

Spin: 0 ! 1 + 1 ) L = 0, 1, 2 or S, P, D waves

Sz : 0 ! 1 + (-1)

(-1) + 1 0 + 0

helicity: h S p

decay amplitudes:

In the B rest frame, the momenta of V1 and V2 are equal and opposite.

the helicities of both vector mesons are same.

1 2

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* *1 1 2 2 1 2 2 1 1 2

1 2 1 2

( , ) ( , )b ic

A B V p V p ag p p p pm m m m

♦ The most general covariant amplitude for B V V

21 1a xA c

• Helicity basis

20 ( 1)ax bA x

• Transversity basis

1 1

1

2A AA 1 1

1

2A AA 00A A

1 2

1 2

wherep p

xm m

parallel transverse longitudinal

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Total decay rate (in the B rest frame)

1

22 2

1 2 02

1V

B

B VV p A A Am

1 2 1 2

1

1/ 22 2 2 2( ) ( )

2

B V V B V V

VB

m m m m m mp

m

B Br

Longitudinal & Transverse polarization fractions

2

022 2

0

L

Af

A A A

2

22 2

0

Af

A A A

Standard model estimation:2

11L

b

fm

O

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0 01 2 1 2Define ,B f f B f f A A A A

01 2

2 22 2

*( ( ) ) co2 2

s( ) Im( )sin( )tB t f f e mt mtq

p

A A A AA A

Time dependent measurement

Hamiltonian / 2 ( , : Hermitian)ij ij ijH M i M

11 22 by CPT invarianceH H

* *12 12

12 12

where q

p

M i

M i

For B V V decay modes,

01 2 0 0

01 2 0 0

B VV A g A g iA g

B VV A g A g iA g

A

A

22 2 22 2 2 * * *0 0 0 0 0 0Re Im ImA g A g A g A A g g A A g g A A g g A

2 2 2 22 2 2 * * *0 0 0 0 0 0Re Im ImA g A g A g A A g g A A g g A A g g A

( g depend purely on angles

describing the kinematics )

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35 independent observables (18 magnitudes + 17 relative phases)

Time dependent measurement:

ObservablesObservables

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Observables for B Observables for B K K [ Example of B [ Example of B P P case ] P P case ]

Only 9 observablesOnly 9 observables

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An example of An example of New PhysicsNew Physics studystudy

beyond the Standard Model beyond the Standard Model

by using B by using B V V decays V V decays

B B K* K*

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q

q-

B K* is a vector version (B V V) of B K (B P P)

The dominant quark level subprocesses are loop (penguin) processes b s penguin is sensitive to NP

We expect that NP contribution to B K* has the same nature as that of B K

B K* (B V V) provides enormously many observables

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Large

Small

Conventional Hierarchy in B Conventional Hierarchy in B K* K*

strong penguin

EW penguin

color-suppressed tree

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Parameterization of decay Parameterization of decay amplitudesamplitudes

Isospin relations:

Hierarchy relation in the SM:

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Investigate how much sensitive to possible NP effects each observable for decays could be.

Assume that NP contributing via the EW penguins.

For simplicity, further assume that the SM amplitudes and are known (by additional information from somewhere, e.g. from future theoretical estimates). Thus, the SM amplitude is the only one modified by NP.

(SM part) (NP part)

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Procedure:

(i) In order to determine the theoretical parameters, adopt the

minimization technique & use thecurrently available experimental data as constraints on the parameters.

(HFAG)

2

022 2

0

L

Af

A A A

: longitudinal polarization fraction

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(ii) [number of data] < [number of parameters]

Try to fit the dominant strong penguins and their phases with , first.

(iii) Assume that the SM amplitudes ( ) follows the conventional hierarchy as in within the SM:

in PQCD,

(iv) Using the parameters determined, calculate all the 35 observables in the SM.

(v) To investigate the possible NP effects, consider two different cases.

(SM part) (NP part)

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For illustration:

Very sensitive to NP:

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For illustration:

Very sensitive to NP:

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For illustration:

Very sensitive to NP:

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For illustration:

Very sensitive to NP:

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B K* decays: useful for New Physics study

certain observables are expected to be very sensitive to NP effects.

B V V measurements

B factories: Belle (KEK), BaBar (SLAC, closed),

LHC-b (CERN), Tevatron (Fermi Lab), Super-B (?)