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New Effects on Rare B Decays. 2 nd Semester in 2005. 1. (leptophobic)Z’-mediated FCNCs 2. Rare B decays in SM 3. New effects on Rare B decays. (Leptophobic)Z’-mediated FCNCs. Jonghun Jeon (2005.10.10). Outline. FCNCs Z-mediated FCNCs Z’-mediated FCNCs - PowerPoint PPT Presentation
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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 !!!
Leptophobic Z´ ModelLeptophobic Z´ ModelK.Leroux, D.London (PLB526,97)
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)
Leptophobic Z´ ModelLeptophobic Z´ ModelK.Leroux, D.London (PLB526,97)
Other embeddings !!!Other embeddings !!!
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)
Leptophobic Z´ ModelLeptophobic Z´ ModelK.Leroux, D.London (PLB526,97)
Other embeddings !!!Other embeddings !!!
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 !!!
Leptophobic Z´ ModelLeptophobic Z´ ModelK.Leroux, D.London (PLB526,97)
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 )