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Enhanced KL to pi0 nu nubar from Enhanced KL to pi0 nu nubar from Direct CP Violation in B to K pi Direct CP Violation in B to K pi with with Four GenerationsFour Generations

Makiko Nagashima (NTU)Makiko Nagashima (NTU)

ICFP2005, Oct. 3-8 ICFP2005, Oct. 3-8

NCUNCU

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Contents

Paper hep-ph/0508237 (W.S.Hou, M.N, A. Soddu) 4th generation scenario and Implications for K and B physics

Paper hep-ph/0503072 (W.S.Hou, M.N, A. Soddu) to appear in Phys. Rev. Lett.

Impact of 4th generation on B to K pi Direct CPV

b → s s → d

b → d

motivated by extend our study to

3

3 generation

Standard Model and CKM mechanism

SU(2) doublet

SU(2) singlet

Quark sector

3 mixing angles

1 CP phase

CKM matrix

Unitarity Triangle Study of CPV / Test of SM / Search for NP

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Direct CP Violation (DCPV)

Difference of Yields

vs given by single term

no relative phases

DCPV goes away

CP

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TREE and PENGUIN diagramsTree diagram

su

u

d d

bW

b

u

u

u

u

s

W>1/Nc

b

d

W

g u

s

d

u

Penguin diagram

b

d

u

s

d

u

W

Z,γ

>

sub-dominant

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Result on DCPV in Kπ

PUZZLE

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The puzzle still persists

It calls for New Physics ?

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K pi DCPV riddle

QCDF (BBNS)

SM3

kT PQCD (KLS)

away

sub-dominant

If one neglects EWP and C, No phase differences

Theoretical expectations within different treatment of the hadronic matrix element

(2003) (2001)

contradiction

up to LO calculation

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We call for Large with an extra weak phase

We employ kTPQCD approach

must not be negligible

Assemble

4th generation scenario

consistent with ~12%

The deviation

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kTPQCD approach

Large strong phase comes from annihilation process

a hard gluon kicks spectator

At leading process

is introduced to cure the endpoint singularities

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A. Arhrib and W-S. Hou, EPJC27,555

T. Yanir, JHEP06, 044

Simple parameterization

4th generation scenarioA sequential 4th generation in addition to the SM particles

well-known

unknown

same quantum number

follows WS parameterization

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Remind

Our assumption

Neither Scalar OPE nor Tensor OPE.R.H. dynamics is suppressed by ms/mb

The low energy operators are the same as the SM

New physics enters though loop processes,and changes the short distance effects

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Effective Hamiltonian

Tree

QCD Penguin

EW/EM Penguin

t' effects well-satisfy b → sγrate and DCPV

Large enhancement

Wilson coefficient

Dividing ΔCi by QCD penguin

Natural ability of 4th generation to large enhancement of EWP

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Constraint

PDG04

PDG04

Belle(04)

B(b→sll) gets greatly enhanced

Δm is lower than EXP. bound

4th generation effects are not excluded!!

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Result

kTPQCD in the SM

4th generation+

sizable splitting between

Roughly,

described as

It naturally generates the phase diff. and sizable mag. of the extra term

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Our result is at leading order in kTPQCD.

A recent result finds a much larger color-suppressedtree (C) at next-to-leading order. is less negative (H-n. Li, S. Mishima and A.I. Sanda, hep-ph/0508041)

Remark

Comparably large C would allow more parameter space for the 4th generation

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Naively assumed

did not care about

One may have suspicion that b→s would spill over into s→d is not necessarily ~ 0

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should be all intertwined …

PLB 192 441 (1987) by W.S. Hou et al.

Precisely, should be written by 6 mixing angles and 3 CP phases

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Be moderate

From K pi study, we learned

Keep

We have some constraint on from

Imposebe close to the Cabibbo angle

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Allowed region from K processes

standard (1) is less stringent

(simulated dots)

(shaded region) (elliptic rings)depends on hadronic parameter R6 and R8

Bijnens (2)

We found(1)

(2)

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Outcome for

Current Upper Bound

It is very hard to measure but challenging…

We find enhancing to or even higher !!

It might be even larger than !!

we take

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Impact on Bd and D system

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SummaryStarting point → Direct CP Violation in B→Kπ

4th generation is possible to generate Large EWP

Extend our study to Bd and K system( to, phenomenologically, understand the possibilities of having still fourth generation )

( )

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BACKUP SLIDEBACKUP SLIDE

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2D plots in different way

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FROM PDG04Our anxiety

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We now know neutrinos have mass, will have CPV, andmore to be revealed. # of neutrino =3 is just one piece of info.

The rho parameter is less of a problem.The S parameter is the real problem (it ‘s so for most NP models.)

What the situation changes if the Higgs is not seen and actually heavy ?

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Extra generation vs. EW precision data V.A. Novikov et al., PLB529, 111

Ng

Δm

=sq

rt(m

U^2

-mD

^2)

[GeV

]

mH>113 GeV, mD=130 GeV

mN

[G

eV]

Ng

mD=200, mU=220, mE=100 [GeV]

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Some CuriositiesSome Curiosities

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MICPV is rather little sensitive to strong phases Specially, MICPV due to b→s transition behaves like

naïve factorization + 4th gene.

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No Rescattering

Another framework:extra strong phase from Final State Interaction

Naïve Factorization ⊗ Final State RescatteringOtherwise Double Counting

George W.S. Hou, BCP JC, Oct. 14 (2002)

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We followed Mod.Phys.Lett. A18,1763 by C-K. Chua, W-S. Hou and K-C. Yang

It accounts for

(strong phase)

ICHEP04

(strong phase)

problem

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This FSI picture doesn’t help for resolving the puzzle

There is no solution

We performed analysis by incorporating t’ effects

re-scattering happens between

EW penguin would be brought into amplitude from