含含含 W0 的的的电电电弱弱弱手手手征 ... - CAS · 10th China National Particle Physics Conference 含含含W0§;Z0的的的电电电弱弱弱手手手征征征拉拉拉氏氏氏量量量

10th China National Particle Physics Conference

含含含 W ′ 的的的电电电弱弱弱手手手征征征拉拉拉氏氏氏量量量

王王王顺顺顺治治治，，，张张张盈盈盈，，，蒋蒋蒋绍绍绍周周周，，，王王王青青青

清清清华华华大大大学学学

2008年年年4月月月27日日日, 南南南京京京大大大学学学

Qing Wang P. 1


工工工作作作的的的动动动机机机

含含含W ′±, Z ′的的的电电电弱弱弱手手手征征征拉拉拉氏氏氏量量量

W −W ′混混混合合合、、、费费费米米米子子子的的的混混混合合合

∆mK, |εK|, ∆mBd, ∆mBs

Qing Wang P. 2


工工工作作作的的的动动动机机机

• LHC开开开始始始运运运行行行！！！期期期待待待发发发现现现新新新的的的粒粒粒子子子, ⇒超超超出出出标标标准准准模模模型型型的的的新新新物物物理理理 !

• 我我我们们们关关关心心心新新新粒粒粒子子子是是是带带带电电电的的的矢矢矢量量量粒粒粒子子子的的的情情情形形形 !

• 理理理论论论的的的幺幺幺正正正性性性要要要求求求它它它是是是自自自发发发破破破缺缺缺的的的非非非阿阿阿贝贝贝尔尔尔规规规范范范理理理论论论中中中的的的规规规范范范粒粒粒子子子.

• 最最最小小小的的的非非非阿阿阿贝贝贝尔尔尔规规规范范范对对对称称称性性性是是是SU(2)，，，产产产生生生规规规范范范粒粒粒子子子W ′±, Z ′

• 构构构造造造含含含W ′±, Z ′的的的电电电弱弱弱手手手征征征拉拉拉氏氏氏量量量，，，进进进行行行模模模型型型无无无关关关和和和相相相关关关的的的研研研究究究

• 为为为改改改善善善理理理论论论的的的幺幺幺正正正性性性，，，还还还得得得加加加上上上一一一个个个中中中性性性Higgs粒粒粒子子子h

• 期期期待待待研研研究究究的的的物物物理理理情情情形形形：：：最最最轻轻轻的的的新新新粒粒粒子子子是是是 h 和和和 W ′±

Qing Wang P. 3


含含含W ′±, Z ′的的的电电电弱弱弱手手手征征征拉拉拉氏氏氏量量量

• 粒粒粒子子子内内内容容容：：：♠ 标标标准准准模模模型型型中中中所所所有有有已已已被被被发发发现现现的的的粒粒粒子子子♣ h, W ′±, Z ′及及及其其其对对对应应应的的的三三三个个个Goldstone玻玻玻色色色子子子

• 对对对称称称性性性的的的实实实现现现方方方式式式：：： SU(2)1 ⊗ SU(2)2 ⊗ U(1) → U(1)em

• W ′±, Z ′耦耦耦合合合夸夸夸克克克q − q、、、轻轻轻子子子l − l：：：

LR : Left− right symmetricLP : LeptophobicHP : HadrophobicFP : FermionphobicUN : UnunifiedNU : Non− universal

• 不不不讨讨讨论论论leptoquark: W ′将将将夸夸夸克克克耦耦耦合合合到到到轻轻轻子子子

Qing Wang P. 4


不不不同同同的的的费费费米米米子子子表表表示示示安安安排排排−

Fields/Models LR LP HP FP UN NU

qαL=

uαL

dαL

(2, 1, 1

6) (2, 1, 1

6) (2, 1, 1

6) (2, 1, 1

6) (1, 2, 1

6) (2, 1, 1

6)δαα1

+(1, 2, 1

6)δαα2

qαR=

uαR

dαR

(1, 2, 1

6) (1, 2, 1

6)

(1, 1, 2

3)

(1, 1,−1

3)

(1, 1, 2

3)

(1, 1,−1

3)

(1, 1, 2

3)

(1, 1,−1

3)

(1, 1, 2

3)

(1, 1,−1

3)

lαL=

ναL

e−αL

(2, 1,−1

2) (2, 1,−1

2) (2, 1,−1

2) (2, 1,−1

2) (2, 1,−1

2) (2, 1,−1

2)δαα1

+(1, 2,−1

2)δαα2

lαR=

ναR

e−αR

(1, 2,−1

2)

(1, 1, 0)

(1, 1,−1)(1, 2,−1

2)

(1, 1, 0)

(1, 1,−1)

(1, 1, 0)

(1, 1,−1)

(1, 1, 0)

(1, 1,−1)

Qing Wang P. 5


Y.Zhang, S-Z.Wang, F-J.Ge, Q.Wang, Phys. Lett. B653,259(2007)

W i,µν ≡ U†i giWi,µνUi Xµ

i ≡ U†i (DµUi) DµUi = ∂µUi + igi

τa

2W a

i,µUi − igUiτ3

2Bµ

LbosonEWCL =− V (h) +

12(∂µh)2 − 1

4f21 tr(X1,µXµ

1 )− 14f22 tr(X2,µXµ

2 ) +12κf1f2tr(X

µ1 Xµ

2 )

+14β1,1f

21 [tr(τ3X1,µ)]2 +

14β2,1f

22 [tr(τ3X2,µ)]2 +

12β1f1f2[tr(τ3X1,µ)][tr(τ3Xµ

2 )]

+LK + L1 + LH1 + L2 + LH2 + LC + O(p6)

LK =− 14W a

1,µνWµν,a1 − 1

4W a

2,µνWµν,a2 − 1

4BµνB

µν

Li =12αi,1gBµνtr(τ3W

µν

i )+iαi,2gBµνtr(τ3Xµi Xν

i )+2iαi,3tr(W i,µνXµi Xν

i )+αi,4[tr(Xi,µXi,ν)]2

+αi,5[tr(X2i,µ)]2 + αi,6tr(Xi,µXi,ν)tr(τ3Xµ

i )tr(τ3Xνi ) + αi,7tr(X2

i,µ)[tr(τ3Xi,ν)]2

+14αi,8[tr(τ3W i,µν)]2 + iαi,9tr(τ3W i,µν)tr(τ3Xµ

i Xνi ) +

12αi,10[tr(τ3Xi,µ)tr(τ3Xi,ν)]2

+αi,11εµνρλtr(τ3Xi,µ)tr(Xi,νW i,ρλ) + 2αi,12tr(τ3Xi,µ)tr(Xi,νW

µν

i )

+14αi,13gεµνρσBµνtr(τ3W i,ρσ) +

18αi,14ε

µνρσtr(τ3W i,µν)tr(τ3W i,ρσ)

Qing Wang P. 6


LHi =(∂µh){αHi,1tr(τ3Xµi )tr(X2

i,ν)+αHi,2tr(τ3Xνi )tr(Xµ

i Xi,ν)+αHi,3tr(τ3Xνi )tr(τ3Xµ

i Xi,ν)

+αHi,4tr(τ3Xµi )[tr(τ3Xi,ν)]2 + iαHi,5tr(τ3Xi,ν)tr(τ3W

µν

i ) + igαHi,6Bµνtr(τ3Xi,ν)

+iαHi,7tr(τ3Wµν

i Xi,ν) + iαHi,8tr(Wµν

i Xi,ν)}+ (∂µh)(∂νh)[αHi,9tr(τ3Xµi )tr(τ3Xν

i )

+αHi,10tr(Xµi Xν

i )] + (∂µh)2{αHi,11[tr(τ3Xi,ν)]2 + αHi,12tr(X2i,ν)}

+αHi,13(∂µh)2(∂νh)tr(τ3Xνi ) + αHi,14(∂µh)4

f(UR, UL, DµUR, DµUL)qα =

f(U2, U1, DµU2, DµU1)qα LR,LPf(1, U1, 0, DµU1)qα HP,FPf(1, U2, 0, DµU2)qα UNf(1, U1, 0, DµU1)qαδαα1 + f(1, U2, 0, DµU2)qαδαα2 NU

f(UR, UL, DµUR, DµUL)lα =

f(U2, U1, DµU2, DµU1)lα LRf(1, U1, 0, DµU1)lα LPf(U2, U1, DµU2, DµU1)lα HPf(1, U1, 0, DµU1)lα FP,UNf(1, U1, 0, DµU1)lαδαα1 + f(1, U2, 0, DµU2)lαδαα2 NU

Qing Wang P. 7


S-Z.Wang, F-J.Ge, Q.Wang, Phys. Lett. B662，，，375(2008)

LY,lepton = lI

αL[UL(yαβ+yαβ3 τ3)U†

R]lIβR +12[hαβ

L lIcαLU∗

L(1+τ3)U†LlIβL + (L → R)] + h.c.

LY,quark = qIαL[UL(τuyαβ

u + τdyαβd )U†

R]qIβR + h.c.

Lf−4 = i∑α

{qI

αL /DqIαL + δL,1,αqI

αLUL( /DUL)†qIαL + δL,2,αqI

αRURU†L( /DUL)U†

RqIαR

+δL,3,αqIαL[( /DUL)τ3U†

L − ULτ3( /DUL)†]qIαL + δL,4,αqI

αLULτ3U†L( /DUL)τ3U†

LqIαL

+δL,5,αqIαRUR[τ3U†

L( /DUL)−( /DUL)†ULτ3]U†RqI

αR+δL,6,αqIαRURτ3U†

L( /DUL)τ3U†RqI

αR

+δL,7,α[qIαLULτ3U†

L/DqI

αL − (qIαL /D

†)ULτ3U†LqI

αL]}

+ qI → lI, δ → δl + L ↔ R

Dµqα =

8>>>><>>>>:

(∂µ+ ig1τa

2 W a1,µPL+ig2

τa

2 W a2,µPR + i

6gBµ)qα LR, LP

(∂µ+ ig1τa

2 W a1,µPL+igτ3

2 BµPR + i6gBµ)qα HP, FP

(∂µ+ ig2τa

2 W a2,µPL+igτ3

2 BµPR + i6gBµ)qα UN

(∂µ+ iδαα1g1

τa

2 W a1,µPL+ iδαα2

g2τa

2 W a2,µPL+igτ3

2 BµPR + i6gBµ)qα NU

Dµlα =

8>><>>:

(∂µ+ ig1τa

2 W a1,µPL+ig2

τa

2 W a2,µPR − i

2gBµ)lα LR, HP

(∂µ+ ig1τa

2 W a1,µPL+igτ3

2 BµPR − i2gBµ)lα LP, FP, UN

(∂µ+ iδαα1g1

τa

2 W a1,µPL+ iδαα2

g2τa

2 W a2,µPL+igτ3

2 BµPR − i2gBµ)lα NU

Qing Wang P. 8


W −W ′混混混合合合

tan 2ζ =2κx

1− x2

(W±

1

W±2

)=

(cos ζ − sin ζsin ζ cos ζ

)(W±

W ′±

)x =

f1g1

f2g2

M2W

M2W ′

=1 + x2 −

√(1− x2)2 + 4κ2x2

1 + x2 +√

(1− x2)2 + 4κ2x2

κ ∼ 10−2, x ∼ 10−1 ⇒ ζ ∼ 10−3, MW ′ ∼ 10MW

LbosonEWCL =− V (h) +

12(∂µh)2 − 1

4f21 tr(X1,µXµ

1 )− 14f22 tr(X2,µXµ

2 ) +12κf1f2tr(X

µ1 Xµ

2 )

+14β1,1f

21 [tr(τ3X1,µ)]2 +

14β2,1f

22 [tr(τ3X2,µ)]2 +

12β1f1f2[tr(τ3X1,µ)][tr(τ3Xµ

2 )]

+O(p4)

W i,µν ≡ U†i giWi,µνUi Xµ

i ≡ U†i (DµUi) DµUi = ∂µUi + igi

τa

2W a

i,µUi − igUiτ3

2Bµ

Qing Wang P. 9


轻轻轻子子子混混混合合合

LY,lepton|Unitary gauge = LMe + LMν LMe = e−IαL(yαβ − yαβ

3 )e−IβR + e−I

αR(y†αβ − y†αβ3 )e−I

βL ,

e−L,R = V eL,Re−I

L,R LMe = e−LMe†e−R + e−RMee−L Me = V eL(y − y3)V

e†R

LMν = νIαL(yαβ + yαβ

3 )νIβR + hαβ

L νIcαLνI

βL + hαβR νIc

αRνIβR + h.c.

=12

(νI

L νIcR

) (2hL y + y3

(y + y3)T 2hR

)(νIc

L

νIR

)+ h.c.

(V RS U

)†( 2hL y + y3

(y + y3)T 2hR

)(V RS U

)∗=

(Mν 00 MN

)

(V RS U

)=

(1− 1

8(y + y3)h−2R (y + y3)T 1

2(y + y3)h−1R

−12h−1R (y + y3)T 1− 1

8h−1R (y + y3)T (y + y3)h−1

R

)

(V RS U

)†( 2hL y + y3

(y + y3)T 2hR

)(V RS U

)∗

=(

2hL − 12(y + y3)h−1

R (y + y3)T + O(h−2R ) O(h−1

R )O(h−1

R ) 2hR + O(h−1R )

)

Qing Wang P. 10


夸夸夸克克克混混混合合合

LY,quark|Unitary gauge = qIαL(τuyαβ

u + τdyαβd )qI

βR + h.c.

uL,R = V uL,RuI

L,R dL,R = V dL,RuI

L,R V uL y0

uV u†R = Mu

diag V dLy0

dVd†R = Md

diag

qαL,R =(

uαL,R

dαL,R

)= [(V u

L,R)αβτu + (V dL,R)αβτd]

(uI

βL,R

dIβL,R

)

V CKML =

V udL V us

L V ubL

V cdL V cs

L V cbL

V tdL V ts

L V tbL

=

c12c13 s12c13 s13e−iδ

−s12c23−c12s23s13eiδ c12c23 − s12s23s13e

iδ s23c13

s12s23 − c12c23s13eiδ −c12s23−s12c23s13e

iδ c23c13

V CKMR =

V udR e2iα1 V us

R ei(α1+α2+β1) V ubR ei(α1+α3+β1+β2)

V cdR ei(α1+α2−β1) V cs

R e2iα2 V cbR ei(α2+α3+β2)

V tdR ei(α1+α3−β1−β2) V ts

R ei(α2+α3−β2) V tbR e2iα3

V udR V us

R V ubR

V cdR V cs

R V cbR

V tdR V ts

R V tbR

=

c12c13 s12c13 s13e−iδ

−s12c23 − c12s23s13eiδ c12c23 − s12s23s13e

iδ s23c13

s12s23 − c12c23s13eiδ −c12s23 − s12c23s13e

iδ c23c13

pseudo-manifest left-right symmetric: V αβR = (V αβ

L )∗

Qing Wang P. 11



∆mK = ∆mWWK + ∆mWW ′

K + ∆mhK

|εK| = |εK|WW + |εK|WW ′+ |εK|h

∆mBd= ∆mWW

Bd+ ∆mWW ′

Bd+ ∆mh

Bd

∆mBs = ∆mWWBs

+ ∆mWW ′Bs

+ ∆mhBs

Qing Wang P. 12


s u, c, t d

d su, c, t

W (φ1)W (φ1)

d

ds

s

u, c, t u, c, t

W (φ1)

W (φ1)

d

d s

W (φ1)

u, c, t

u, c, t

W ′(φ2)

s s

d s

d

h

d

s

h

d

s

Qing Wang P. 13



U1,2 = exp(ig1,2√2M1,2

φ1,2) φ1,2 =

0B@

φ01,2√2

φ+1,2

φ−1,2 −φ01,2√2

1CA M1,2 =

1

2f1,2g1,2

Lf−4

˛˛Unitary gauge

=X

α

qIα[i/∂ − ( ∆1,1,αg1

τa′

2/W

a′1 + ∆1,2,α

τa′

2g2 /W

a′2 + ∆

31,1,αg1 /W

3

1

+∆31,2,αg2 /W

3

2 + ∆1,αg /B )PL − ( ∆2,1,αg1

τa′

2/W

a′1 + ∆2,2,α

τa′

2g2 /W

a′2

+∆32,1,αg1 /W

3

1 + ∆32,2,αg2 /W

3

2 + ∆2,αg /B )PR]qIα + q

I → lI, δ → δ

l, ∆ → ∆

l,

uL,R = Vu

L,RuIL,R dL,R = V

dL,Ru

IL,R V

uL y

0uV

u†R = M

udiag V

dL y

0dV

d†R = M

ddiag

∆1,1,α = 1− δL,1,α − δL,4,α LR,LP,HP,FP ∆2,1,α =

1− δR,1,α − δR,4,α LR,LPδL,2,α − δL,6,α HP,FP

Qing Wang P. 14


0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

∆1,1

∆ mKWW/∆ m

Kexp (1,0.671)

|εK|WW/|ε

K|exp (1,1.131)

∆ mB

s

WW/∆mB

s

exp (1,1.231)

∆ mB

d

WW/∆mB

d

exp (1,1.139)

Qing Wang P. 15


∆mWW ′K =∆

22,1

g22

g21

∆mWW ′Ktt

»Re(λ

LRt λ

RLt ) + Re(λ

LRc λ

RLc )

∆mWW ′Kcc

∆mWW ′Ktt| {z }

10−3

+Re(λLRc λ

RLt + λ

LRt λ

RLc )

∆mWW ′Kct

∆mWW ′Ktt| {z }

10−2

–

λLRx (K)λ

RLx (K) = |V xs

L Vxd∗

L Vxs

R Vxd∗

R |e−i(α1−α2−β1−φxs−φxs+φxd+φxd)x = c, t

λLRc (K)λ

RLt (K) = |V cs

L Vcd∗

R Vts

R Vtd∗

L |e−i(α1−α3−β1+β2−φcs+φcd−φts+φtd)arg(V

αβL )=φαβ

λLRt (K)λ

RLc (K) = |V ts

L Vtd∗

R Vcs

R Vcd∗

L |e−i(α1−2α2+α3−β1−β2−φts+φtd−φcs+φcd)arg(V

αβR )= φαβ

0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

1.2x 10

−3

∆ m

Kcc

WW

′ /∆ m

Ktt

WW

′

∆1,1

M

W ′=10M W

M W ′=15M

W

M W ′=20M

W

M W ′=25M

W

0 0.5 1 1.50.008

0.009

0.01

0.011

0.012

0.013

0.014

0.015

∆ m

Kct

WW

′ /∆ m

Ktt

WW

′

∆1,1

M

W ′=10M W

M W ′=15M

W

M W ′=20M

W

M W ′=25M

W

Qing Wang P. 16


∆mWW ′K =∆

22,1

g22

g21

∆mWW ′Ktt

»Re(λ

LRt λ

RLt ) + Re(λ

LRc λ

RLc )

∆mWW ′Kcc

∆mWW ′Ktt| {z }

10−3

+Re(λLRc λ

RLt + λ

LRt λ

RLc )

∆mWW ′Kct

∆mWW ′Ktt| {z }

10−2

–

0 0.5 1 1.5−3.5

−3

−2.5

−2

−1.5

−1

−0.5x 10

5∆

mK

tt

WW

′ /∆ m

Kexp

∆1,1

M W ′=10M

W

M W ′=15M

W

M W ′=20M

W

M W ′=25M

W

Qing Wang P. 17


|εK|WW ′= ∆

22,1

g22

g21

|εK|WW ′tt

˛˛Im(λ

LRt λ

RLt ) + Im(λ

LRc λ

RLc )

|εK|WW ′cc

|εK|WW ′tt| {z }

10−3

+Im(λLRc λ

RLt + λ

LRt λ

RLc )

|εK|WW ′ct

|εK|WW ′tt| {z }

10−2

˛˛

λLRx (K)λ

RLx (K) = |V xs

L Vxd∗

L Vxs

R Vxd∗

R |e−i(α1−α2−β1−φxs−φxs+φxd+φxd)x = c, t

λLRc (K)λ

RLt (K) = |V cs

L Vcd∗

R Vts

R Vtd∗

L |e−i(α1−α3−β1+β2−φcs+φcd−φts+φtd)arg(V

αβL )=φαβ

λLRt (K)λ

RLc (K) = |V ts

L Vtd∗

R Vcs

R Vcd∗

L |e−i(α1−2α2+α3−β1−β2−φts+φtd−φcs+φcd)arg(V

αβR )= φαβ

0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

1.2x 10

−3

|εK| ccW

W′ /|ε

K| ttW

W′

∆1,1

M

W ′=10M W

M W ′=15M

W

M W ′=20M

W

M W ′=25M

W

0 0.5 1 1.50.008

0.009

0.01

0.011

0.012

0.013

0.014

0.015

|εK| ctW

W′ /|ε

K| ttW

W′

∆1,1

M

W ′=10M W

M W ′=15M

W

M W ′=20M

W

M W ′=25M

W

Qing Wang P. 18


|εK|WW ′= ∆

22,1

g22

g21

|εK|WW ′tt

˛˛Im(λ

LRt λ

RLt ) + Im(λ

LRc λ

RLc )

|εK|WW ′cc

|εK|WW ′tt| {z }

10−3

+Im(λLRc λ

RLt + λ

LRt λ

RLc )

|εK|WW ′ct

|εK|WW ′tt| {z }

10−2

˛˛

0 0.5 1 1.5−5.5

−5

−4.5

−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5x 10

7

|εK| ttW

W′ /|ε

K|ex

p

∆1,1

M W ′=10M

W

M W ′=15M

W

M W ′=20M

W

M W ′=25M

W

Qing Wang P. 19


pseudo-manifest left-right symmetric case

Vαβ

R = (Vαβ

L )∗ ⇒ φαβ + φαβ = 0

λLRc (K)λ

RLc (K) = |V cs

L Vcd

L |2e−i(α1−α2−β1)λ

LRt (K)λ

RLt (K) = |V ts

L Vtd

L |2e−i(α1−α2−β1)

λLRc (K)λ

RLt (K) + λ

LRt (K)λ

RLc (K) = 2|V cs

L Vcd

L Vts

L Vtd

L |[cos(α1 − α2 − β1) cos(α2 − α3 + β2)

−i sin(α1 − α2 − β1) cos(α2 − α3 + β2)]

α1−α2−β1=0 ⇒ Im[λLRc (K)λ

RLc (K)]=Im[λ

LRt (K)λ

RLt (K)]=Im[λ

LRc (K)λ

RLt (K)+λ

LRt (K)λ

RLc (K)]= 0

cc、、、tt和和和ct圈圈圈分分分别别别无无无CP破破破坏坏坏！！！ |εK|WW′= 0

∆mWW ′K

∆mexpK

= ∆22,1

g22

g21

∆mWW ′Ktt

∆mexpK| {z }

105

»Re(λ

LRt λ

RLt| {z }

5.9×10−6

) + Re(λLRc λ

RLc| {z }

0.049

)∆mWW ′

Kcc

∆mWW ′Ktt| {z }

10−3

+Re(λLRc λ

RLt + λ

LRt λ

RLc| {z }

0.0011×cos(α2−α3+β2)

)∆mWW ′

Kct

∆mWW ′Ktt| {z }

10−2

–

Qing Wang P. 20


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2−12

−11

−10

−9

−8

−7

−6

−5

−4

−3

−2

−1

0∆

mKW

W′ /∆

mKex

p /(∆ 2,

12

g 22 /g12 )

∆1,1

cos(α2−α

3+β

2)=1

M W ′=10M

W

M W ′=15M

W

M W ′=20M

W

M W ′=25M

W

M W ′=50M

W

M W ′=100M

W

Qing Wang P. 21


−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1−13

−12

−11

−10

−9

−8

−7

−6

−5

−4

−3

−2

−1

0∆

mKW

W′ /∆

mKex

p /(∆ 2,

12

g 22 /g12 )

cos(α2−α

3+β

2)

∆1,1

=1

M W ′=10M

W

M W ′=15M

W

M W ′=20M

W

M W ′=25M

W

M W ′=50M

W

M W ′=100M

W

Qing Wang P. 22


∆mWW ′Bd

= ∆22,1

g22

g21

∆mWW ′Bdtt

˛˛λLR

t λRLt + λ

LRc λ

RLc

∆mWW ′Bdcc

∆mWW ′Bdtt| {z }

10−3

+(λLRc λ

RLt + λ

LRt λ

RLc )

∆mWW ′Bdct


10−2

˛˛

λLRx (Bd)λ

RLx (Bd) = |V xb

L Vxd∗

L Vxb

R Vxd∗

R |e−i(α1−α3−β1−β2−φxb−φxb+φxd+φxd)x = c, t

λLRc (Bd)λ

RLt (Bd) = |V cb

L Vcd∗

R Vtb

R Vtd∗

L |e−i(α1+α2−2α3−β1−φcb+φcd−φtb+φtd)arg(V

αβL )=φαβ

λLRt (Bd)λ

RLc (Bd) = |V tb

L Vtd∗

R Vcb

R Vcd∗

L |e−i(α1−α2−β1−2β2−φtb+φtd−φcb+φcd)arg(V

αβR )= φαβ

0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

1.2x 10

−3

∆ m

Bd,

cc

WW

′ /∆ m

Bd,

tt

WW

′

∆1,1

M

W ′=10M W

M W ′=15M

W

M W ′=20M

W

M W ′=25M

W

0 0.5 1 1.50.008

0.009

0.01

0.011

0.012

0.013

0.014

∆ m

Bd,

ct

WW

′ /∆ m

Bd,

tt

WW

′

∆1,1

M

W ′=10M W

M W ′=15M

W

M W ′=20M

W

M W ′=25M

W

Qing Wang P. 23


∆mWW ′Bd

= ∆22,1

g22

g21

∆mWW ′Bdtt

˛˛λLR

t λRLt + λ

LRc λ

RLc

∆mWW ′Bdcc


10−3

+(λLRc λ

RLt + λ

LRt λ

RLc )

∆mWW ′Bdct


10−2

˛˛

0 0.5 1 1.5−14

−13

−12

−11

−10

−9

−8

−7

−6

−5

−4x 10

5

∆ m

Bd,

tt

WW

′ /∆ m

Bd

exp

∆1,1

M W ′=10M

W

M W ′=15M

W

M W ′=20M

W

M W ′=25M

W

Qing Wang P. 24


∆mWW ′Bs

= ∆22,1

g22

g21

∆mWW ′Bstt

˛˛λLR

t λRLt + λ

LRc λ

RLc

∆mWW ′Bscc

∆mWW ′Bstt| {z }

10−3

+(λLRc λ

RLt + λ

LRt λ

RLc )

∆mWW ′Bsct


10−2

˛˛

λLRx (Bs)λ

RLx (Bs) = |V xb

L Vxs∗

L Vxb

R Vxs∗

R |e−i(α2−α3−β2−φxb−φxb+φxs+φxs)x = c, t

λLRc (Bs)λ

RLt (Bs) = |V cb

L Vcs∗

R Vtb

R Vts∗

L |e−i(2α2−2α3−φcb+φcs−φtb+φts)arg(V

αβL )=φαβ

λLRt (Bs)λ

RLc (Bs) = |V tb

L Vts∗

R Vcb

R Vcs∗

L |e−i(−2β2−φtb+φts−φcb+φcs)arg(V

αβR )= φαβ

0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

1.2x 10

−3

∆ m

Bs,

cc

WW

′ /∆ m

Bs,

tt

WW

′

∆1,1

M

W ′=10M W

M W ′=15M

W

M W ′=20M

W

M W ′=25M

W

0 0.5 1 1.50.008

0.009

0.01

0.011

0.012

0.013

0.014

∆ m

Bs,

ct

WW

′ /∆ m

Bs,

tt

WW

′

∆1,1

M

W ′=10M W

M W ′=15M

W

M W ′=20M

W

M W ′=25M

W

Qing Wang P. 25


∆mWW ′Bs

= ∆22,1

g22

g21

∆mWW ′Bstt

˛˛λLR

t λRLt + λ

LRc λ

RLc

∆mWW ′Bscc


10−3

+(λLRc λ

RLt + λ

LRt λ

RLc )

∆mWW ′Bsct


10−2

˛˛

0 0.5 1 1.5−4

−3.5

−3

−2.5

−2

−1.5

−1x 10

4∆

mB

s,tt

WW

′ /∆ m

Bs

exp

∆1,1

M W ′=10M

W

M W ′=15M

W

M W ′=20M

W

M W ′=25M

W

Qing Wang P. 26



LY,quark|Unitary gauge = qIαL(τuyαβ

u +τdyαβd )qI

βR+ h.c. yi=y0i +y1

i h+ · · · yi=V iLy1

i Vi†R i=u, d

∆mhK ¿ ∆mexp

K ⇒ Re[(ydsd +y†ds

d )2−11.4(ydsd −y†ds

d )2] ¿ 6.45×10−7( mh

1TeV

)2

|εK|h ¿ |εK|exp ⇒ Im[(ydsd +y†ds

d )2−11.4(ydsd −y†ds

d )2]

¿ 0.0065×Re[(ydsd + y†ds

d )2 − 11.4(ydsd − y†ds

d )2]

∆mhBd¿ ∆mexp

Bd⇒ [(ydb

d +y†dbd )2−11.4(ydb

d −y†dbd )2] ¿ 1.74×10−6

( mh

1TeV

)2

∆mhBs¿ ∆mexp

Bs⇒ [(ysb

d +y†sbd )2−11.4(ysb

d −y†sbd )2] ¿ 6.10×10−5

( mh

1TeV

)2

Qing Wang P. 27


小小小结结结

• 构构构造造造了了了含含含W ′±, Z ′的的的电电电弱弱弱手手手征征征拉拉拉氏氏氏量量量 !

• W −W ′混混混合合合是是是普普普适适适的的的，，，小小小的的的混混混合合合并并并不不不限限限制制制W ′一一一定定定很很很重重重 !

• 轻轻轻子子子的的的混混混合合合与与与在在在标标标准准准模模模型型型中中中加加加入入入右右右手手手中中中微微微子子子的的的情情情形形形相相相同同同。。。

• 夸夸夸克克克的的的混混混合合合涉涉涉及及及右右右手手手的的的CKM矩矩矩阵阵阵。。。

• 为为为保保保证证证W ′对对对∆mK, |εK|, ∆mBd, ∆mBs贡贡贡献献献不不不与与与实实实验验验冲冲冲突突突

– MW ′ À MW ; g2 ¿ g1; ∆2,1 ¿ 1; 特特特别别别选选选择择择右右右手手手CKM矩矩矩阵阵阵元元元

– W ′的的的额额额外外外贡贡贡献献献与与与W和和和Higgs的的的贡贡贡献献献相相相互互互抵抵抵消消消

• 没没没单单单独独独讨讨讨论论论Z ′: Y.Zhang, S-Z.Wang, Q.Wang, JHEP03（（（2008）））047

Qing Wang P. 28


Thanks!

Qing Wang P. 29


Backup

Qing Wang P. 30


0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

∆1,1

|εK|WW/|ε

K|exp (1,1.306)

∆ mB

s

WW/∆mB

s

exp (1,1.231)

∆ mB

d

WW/∆mB

d

exp (1,1.139)

∆ mKWW/∆ m

Kexp (1,0.814)

Qing Wang P. 31


0 0.2 0.4 0.6 0.8 1 1.2

10−8

10−6

10−4

10−2

100

∆1,1

∆ mKWW/∆ m

Kexp

∆ mK,ccWW/∆ m

Kexp

∆ mK,ttWW/∆ m

Kexp

∆ mK,ctWW/∆ m

Kexp

Qing Wang P. 32


0 0.2 0.4 0.6 0.8 1 1.20

0.5

1

1.5

2

2.5

∆1,1

|εK|WW′/|ε

K|WW′

|εK|ccWW′/|ε

K|WW′

|εK|ttWW′/|ε

K|WW′

|εK|ctWW′/|ε

K|WW′

Qing Wang P. 33


LCC|quark = − 1√2qα(τ

+ /W+

1 + τ− /W

−1 )[(gL + ∆CL)PL + ∆CRPR]qα

LNC|quark = −1

2qα /Z{T3L[

gL

cos θW

(1−γ5)+∆NV T +∆NATγ5]+Q(−2gL sin2 θW

cos θW

+∆NV Q+∆NAQγ5)}qα

LEM|quark=−1

2qα /A[Q(2e+∆EV Q+∆EAQγ5)+T3L(∆EV T +∆EATγ5)]qα

∆CL = g1[cos ζ(1−δL,1 − δL,4)− 1] + g2 sin ζ(δR,2 − δR,6) ,

∆CR = g1 cos ζ(δL,2 − δL,6) + g2 sin ζ(1−δR,1 − δR,4)

∆NV T = − g1

cos θW+ g1x1[1−δL,1 + δL,4 + δL,2 + δL,6 −

2

Y(δL,3 + δL,7 + δL,5)] + gRy1[1−δR,1

+δR,4 + δR,2 + δR,6 −2

Y(δR,3 + δR,7 + δR,5)] + gv1[−2+δL,1 + δR,1 − δR,2 − δL,2−δL,4

−δR,4 − δR,6 − δL,6 + 2Y δL,7 + 2Y δR,7 +2

Y(δL,3 + δR,5 + δR,3 + δL,5)] ,

∆NAT =g1

cos θW− g1x1[1−δL,1 + δL,4 − δL,2 − δL,6 −

2

Y(δL,3 + δL,7 − δL,5)]− g2y1[1−δR,1

+δR,4 − δR,2 − δR,6 +2

Y(δR,3 + δR,7 − δR,5)] + gv1[δL,1 − δR,1 − δR,2 + δL,2−δL,4 + δR,4

−δR,6 + δL,6 + 2Y δL,7 − 2Y δR,7) +2

Y(−δL,3 − δR,5 + δR,3 + δL,5)] ,

Qing Wang P. 34


∆NV Q =2g1 sin2 θW

cos θW+

2

Y[g1x1(δL,3 + δL,7 + δL,5) + g2y1(δR,3 + δR,7 + δR,5) + gv1(Y − δL,3

−δR,5 − δR,3 − δL,5)] ,

∆NAQ = − 2

Y[g1x1(δL,3 + δL,7 − δL,5)− g2y1(δR,3 + δR,7 − δR,5) + gv1(−δL,3 − δR,5 + δR,3 + δL,5)] ,

∆EV Q = −2e+2

Y[g1x3(δL,3+ δL,7+ δL,5)+ g2y3(δR,3+ δR,7+ δR,5)+ gv3(Y − δL,3− δR,5− δR,3− δL,5)] ,

∆EAQ = − 2

Y[g1x3(δL,3 + δL,7 − δL,5)− g2y3(δR,3 + δR,7 − δR,5) + gv3(−δL,3 − δR,5 + δR,3 + δL,5)]

∆EV T = g1x3[1−δL,1 + δL,4 + δL,2 + δL,6 −2

Y(δL,3 + δL,7 + δL,5)] + g2y3[1−δR,1 + δR,4 + δR,2

+δR,6 −2

Y((δR,3 + δR,7 + δR,5))] + gv3[−2+δL,1 + δR,1 − δR,2 − δL,2−δL,4 − δR,4 − δR,6

−δL,6 + 2Y δL,7 + 2Y δR,7 +2

Y(δL,3 + δR,5 + δR,3 + δL,5)]

∆EAT = −g1x3[1−δL,1 + δL,4 − δL,2 − δL,6 −2

Y(δL,3 + δL,7 − δL,5)]− g2y3[1−δR,1 + δR,4 − δR,2

−δR,6 +2

Y((δR,3 + δR,7 − δR,5))] + gv3[δL,1 − δR,1 − δR,2 + δL,2−δL,4 + δR,4 − δR,6

+δL,6 + 2Y δL,7 − 2Y δR,7) +2

Y(−δL,3 − δR,5 + δR,3 + δL,5)] .

Qing Wang P. 35

Documents

含含含 W0 的的的电电电弱弱弱手手手征 ... - CAS · 10th China National Particle Physics Conference 含含含W0§;Z0的的的电电电弱弱弱手手手征征征拉拉拉氏氏氏量量量