New Effects on Rare B Decays

New Effects on New Effects on Rare B DecaysRare B Decays

2nd Semester in 2005

1. (leptophobic)Z’-mediated FCNCs1. (leptophobic)Z’-mediated FCNCs

2. Rare B decays in SM2. Rare B decays in SM

3. New effects on Rare B decays3. New effects on Rare B decays

*

,

,

B K B

B K B

(Leptophobic)Z’-mediated FCNCs(Leptophobic)Z’-mediated FCNCs

Jonghun Jeon

(2005.10.10)

FCNCsFCNCs Z-mediated FCNCsZ-mediated FCNCs Z’-mediated FCNCsZ’-mediated FCNCs Leptophobic Z’-mediated FCNCsLeptophobic Z’-mediated FCNCs

OutlineOutline

TT

u

l

l

b

,u d ,u d

W

0,B B 0 ,

PP l

l

Tree levelTree level

Not exist!!!Not exist!!!

(GIM)(GIM)

Z

1-loop level1-loop level

Possible!Possible!

Strongly suppressed !!!Strongly suppressed !!!

NP???NP???

FCNCs in SMFCNCs in SM

sb

,u d ,u d

0,B B 0,K K

FCNCs at the tree level ?FCNCs at the tree level ?

Z-mediated FCNCsZ-mediated FCNCs

Z’-mediated FCNCsZ’-mediated FCNCs

Yes !!!Yes !!!

Where ???Where ???

Low Energy Limit of ELow Energy Limit of E66 GUT !!! GUT !!!

Y.Nir, D.Silverman, PRD42,1477(1990)Y.Nir, D.Silverman, PRD42,1477(1990)

E.Nardi, PRD48,1240(1993)E.Nardi, PRD48,1240(1993)

E.Nardi et al, NPB409,69(1993)E.Nardi et al, NPB409,69(1993)

Z-mediated FCNCsZ-mediated FCNCs

Vector-like-(isosinglet)-Downquark : Vector-like-(isosinglet)-Downquark : hh

talked by Prof.Kim in the last semestertalked by Prof.Kim in the last semester

⇒⇒ Unitarity violation of the three-generation CKM matrixUnitarity violation of the three-generation CKM matrix

Z-mediated FCNCsZ-mediated FCNCs talked by Prof.Kim in the last semestertalked by Prof.Kim in the last semester

To understand how Z-mediated FCNCs ariseTo understand how Z-mediated FCNCs arise

3int

3ij

sin Z , 2cos

ZW EM

W

pq pL qL iL jL

gJ J

J U d d u u

L

VVij ij : 3x4 : 3x4 submatrix of 4x4 unitary matrix (K)submatrix of 4x4 unitary matrix (K)

( 6 angles & ( 6 angles & 3 phase3 phase !!! !!! → → CPV CPV !!!) !!!)

Non-vanishing non-diagonal elements of UNon-vanishing non-diagonal elements of Upqpq allow allow

Z-mediated FCNCs !!!Z-mediated FCNCs !!!

int , 2

( 1, 2,3 , 1,..., 4)

W

ij iL jL

gW J W J

J V u d i j

L

† 1 (non-unitarity !!!)pqU V V

Z’-mediated FCNCsZ’-mediated FCNCs Additional U(1)’ Additional U(1)’ arise from the breaking chainarise from the breaking chain

with with Q’=QQ’=Qψψcoscosθθ – Q – Qχχ sinsinθθ where where θθ is the usual E6 mixing angle is the usual E6 mixing angle

Note!!!Note!!! “ “ Q’ ≠ 0 “ : Q’ ≠ 0 “ :

⇒⇒ Z’-mediated FCNCs Z’-mediated FCNCs

( l & q have different U(1)’ quantum numbers)( l & q have different U(1)’ quantum numbers)

“ “ Q’ = 0 “ : Q’ = 0 “ :

⇒⇒ leptophobia ! leptophobia ! ( Not couple to the chared ptls)( Not couple to the chared ptls)

⇒⇒ No value of No value of θθ !!! !!!

Leptophobic Z´ ModelLeptophobic Z´ ModelK.S.Babu,C.Kolda,J.March-Russell (PRD54,4635)(1996)

The most general SU(2)The most general SU(2)LLXU(1)XU(1)YYXU(1)’ invariant Lagrangian includeXU(1)’ invariant Lagrangian include a kinetic mixing term between the U(1)a kinetic mixing term between the U(1)YY and U(1)’ : and U(1)’ : leptophobia!!!leptophobia!!!

' ' '1 1 1

4

sin

24 4a a

kin W W B ZZ BB Z

L

To remove the off-diagonal coupling of the and To remove the off-diagonal coupling of the and

⇒ ⇒ with the non-unitarity transformationwith the non-unitarity transformation

Z B

'

''

tan

cos

B B Z

ZZ

How ???How ???

Leptophobic Z´ ModelLeptophobic Z´ Model

The couplings of the physical gauge bosons to fermionThe couplings of the physical gauge bosons to fermion

can be written ascan be written as

'int ' 'a a

Y QgT W g YB g Q Z

L

''

3' '

5a a

SM Q SMgT W g Y B g Q Y Z

'

''

tan

cos

B B Z

ZZ

3 5 , 5 3 'SM YY Y g g

' ' ' , cos , tanY Y Q Q YQ Yg g g g g g

'' 'a a

Y QgT W g YB g Q Y Z

3em L SMQ T Y

' ' 'sinYQ Q Y Qg g g g

K.S.Babu,C.Kolda,J.March-Russell (PRD54,4635)(1996)

The Z’-fermion interaction term can be written asThe Z’-fermion interaction term can be written as

' 'int

5 3'

cos 3 5Z W

SMW

xgQ Y Z

L

2 2 2'sin , W W Q Yx e g g g

Note!!!Note!!!

The Z’-fermion coupling is no longer proportional to Q’The Z’-fermion coupling is no longer proportional to Q’

⇒⇒ Two unknown parameterTwo unknown parameter :: θθ andand δδ

⇒ ⇒ Leptophobia !!!Leptophobia !!!

3' 0

5 SMQ Y

Leptophobic Z´ ModelLeptophobic Z´ ModelK.S.Babu,C.Kolda,J.March-Russell (PRD54,4635)(1996)

Leptophobic Z´ ModelLeptophobic Z´ ModelK.Leroux, D.London (PLB526,97)

Leptophobia !!!Leptophobia !!!

3' 0

5 SMQ Y

Choice !!!Choice !!!

tan 3 5 and = 3 5

Note!!!Note!!!

However other embeddings are possible !!! However other embeddings are possible !!!


Other embeddings !!!Other embeddings !!!

First, switch the quantum numbers of L and H !!! First, switch the quantum numbers of L and H !!!

( L & H have the same SU(2)( L & H have the same SU(2)LLXU(1)XU(1)YY Q.Ns) Q.Ns)



Second, singlets under SU(3)Second, singlets under SU(3)CC and SU(2) and SU(2)LL !!! !!!

( e( eC C can be assigned to any one of these three) can be assigned to any one of these three)



Second, singlets under SU(3)Second, singlets under SU(3)CC and SU(2) and SU(2)LL !!! !!!

( e( eC C can be assigned to any one of these three) can be assigned to any one of these three)

Note!!!Note!!!

All three states have All three states have NotNot the same electric charge !!!the same electric charge !!!

⇒ ⇒ Need different definitions of the charge Need different definitions of the charge generator !!!generator !!!


There are thus a total of six choices for possible embeddings of the charged leptoThere are thus a total of six choices for possible embeddings of the charged leptons in the 27 representation of E6 !!! ns in the 27 representation of E6 !!!

⇒ ⇒ Leptophobic Z’ can be produced for any of these !!!Leptophobic Z’ can be produced for any of these !!!

Z’-mediated FCNCs can occur if the d,s and b mix with the h.Z’-mediated FCNCs can occur if the d,s and b mix with the h.

However , mixing of the dHowever , mixing of the dL L , s, sLL and b and bLL with h with hLL will lead to Z-mediated FCNCs among t will lead to Z-mediated FCNCs among the ordinary fermions.he ordinary fermions.

⇒ ⇒ Z-mediated FCNCs will always dominate over any ZZ-mediated FCNCs will always dominate over any Z´-´-mediated FCNCs !!!mediated FCNCs !!!

Note!!!Note!!! If we just consider mixing of the dIf we just consider mixing of the dR R , s, sR R and band bRR with h with hRR

⇒ ⇒ Z'-mediated FCNCs exist only !!!Z'-mediated FCNCs exist only !!!

(Leptophbic) Z´-mediated FCNCs(Leptophbic) Z´-mediated FCNCsK.Leroux, D.London (PLB526,97)

When ???When ???

Q‘(dQ‘(dcc) ≠ Q‘(h) ≠ Q‘(hcc))

Where ???Where ???

(Leptophobic) Z´-mediated FCNCs(Leptophobic) Z´-mediated FCNCs

K.Leroux, D.London (PLB526,97)

The contrbution of Z’-mediated FCNCs to The contrbution of Z’-mediated FCNCs to b s

Parameterize !!!Parameterize !!!

' ' 'FCNC

2cosZ Z

qp qR pRW

gU d d Z

L

' ' 'FCNC

2cos R

Z ZR R

W

gQ Z

L

quark quark

neutrino neutrino

R

2' 5 sin1

= 0.31 2 3

Z W

Q ' 'int

5 3'

cos 3 5Z W

SMW

xgQ Y Z

L

Two unknown parameters !!!Two unknown parameters !!!

'Z' , MZ

qpU

(Leptophobic) Z´-mediated FCNCs(Leptophobic) Z´-mediated FCNCs

K.Leroux, D.London (PLB526,97)

The contrbution of Z’-mediated FCNCs to The contrbution of Z’-mediated FCNCs to b s

s

b

W

2 2' 2 ' 2

2 2 2'

( )( )

( )

Z ZR sbs Z

Zub ps cb

Q UB X M

B X MV F V

BB where Fps ≈ 0.5 where Fps ≈ 0.5

2' 3

2'

7.1 10Z Zsb

Z

MU

M

' :ZsbU

' :ZMZ' 365 GeV M 61exclude 5 GeV (!!! )D0

4( ) 6.4 10 (ALEPH)b s B

SummarySummary In SM , FCNCs are forbbiden!!!In SM , FCNCs are forbbiden!!!

Z-mediated FCNCs can be occurred through the mixing of ordinary ptls witZ-mediated FCNCs can be occurred through the mixing of ordinary ptls with exotic ptlsh exotic ptls

Z‘-mediated FCNCs can be occurred through theZ‘-mediated FCNCs can be occurred through the mixing of the ordinary pamixing of the ordinary particles having additional U(1)’ gauge quantum numbersrticles having additional U(1)’ gauge quantum numbers

Leptophobic Z’ can couple to R-handed quarks and neutrinosLeptophobic Z’ can couple to R-handed quarks and neutrinos

The constraints on the flavor-changing coupling UThe constraints on the flavor-changing coupling UZ‘ Z‘ are relatively weak. are relatively weak.

(Because the Z‘ does not couple to charged leptons )(Because the Z‘ does not couple to charged leptons )

New Effects on Rare B Decays

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