Effects of Higgs in Electroweak Chiral Lagrangian
Qing Wang
Tsinghua University, Beijing
Oct 5, 2006,
Qing Wang
NCTS and NTHU
P. 1
Qing Wang
P. 2
Effects of Higgs in Electroweak Chiral Lagrangian
Standard Model and Beyond
Model Independent Description of New Physics
Equivalence between Linear and Nonlinear Realizations of EWCL with Higgs
Extended EWCL and Integrating out Higgs
Effects of Higgs in EWCL
Qing Wang
P. 3
Standard Model and Beyond
Qing Wang
P. 4
Standard Model and Beyond
Unknown Scalar field: linear representation of SU (2)L ⊗ U (1)Y = 3
6
+1
longitudinal W ± , Z
Higgs
600
Theory uncertainty
∆αhad =
(5)
5
500
0.02758±0.00035
0.02749±0.00012
∆χ
2
MH [GeV/c 2 ]
incl. low Q2 data
4
3
2
400
300
Triviality
EW
Precision
200
6 6
1
100
EW vacuum is absolute minimum
0
Excluded
30
Preliminary
100
mH [GeV]
Qing Wang
300
0
3
5
7
9
11
13
15
17
19
log 10 Λ [GeV]
P. 5
Standard Model and Beyond
Fig. 1: The flowering of the Higgs physics that is expected to bloom at the TeV scale.
Qing Wang
P. 6
Standard Model and Beyond
Questions
• Is it possible to find Higgs particle in future experiments ?
• If we do not find Higgs, what does it imply ?
• If we do find Higgs, can we judge whether it is SM or non-SM Higgs ?
Qing Wang
P. 7
Standard Model and Beyond
TeV Working Group in China
http://hep.tsinghua.edu.cn/tevworkinggroup
• organized and first meeting in Dec, 2005
• more than 40 professors
THU, PKU, USTC, ZJU, SDU, Nankai, ITP, IHEP...
• lead by Prof.Y.P.Kuang in THU and several subgroups
High Energy Physics in Tsinghua University
http://hep.tsinghua.edu.cn
• lead by Center for High Energy Physics, Tsinghua University TUHEP
•
New Physics and EWSSB; Collider phenomenology; Top; neutrino; Extra Dim; SUSY; QCD and Nonperturb; Quarkonium
• LHCb and CPV ; Rich Star and QGP; SuperK and Neutrino; BES and tau-charm
Qing Wang
P. 8
Model Independent Description of New Physics
High Energy Colliders
•
LEPII:
electroweak precision measurements; signals at 115GeV
shut down
•
Tevatron RunII:
try best to search for Higgs, SUSY, extra dim, . . . . . .
operating
•
LHC(2007): an expected discovery machine for new physics !
building up
• ILC: synergy with LHC, expect to fully investigate EWSB !
planning
An expected data rich era is coming !
Qing Wang
P. 9
Model Independent Description of New Physics
New Physics Models
•
SUSY: too many free parameters!
MSSM predicts MH ≤135GeV
•
Dynamical EWSB: technicolor, topcolor/topseesaw . . .heavy composite Higgs
no light Higgs
•
Extra Dimension: High dimension space induced Higgsless models!
new spin 1 gauge field
•
Little Higgs: Higgs as pseudo goldstone particle!
MH ∼ 100 − 200GeV
•
......
Too many models on the market !
Qing Wang
P. 10
Model Independent Description of New Physics
SUSY
Little Higgs
Twin
Higgs
Technicolo
r
Higgs
Qing Wang
less
P. 11
Model Independent Description of New Physics
CERN 2006-009
31 July 2006
ORGANISATION EUROPÉENNE POUR LA RECHERCHE NUCLÉAIRE
CERN
EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
Workshop on CP Studies and
Non-Standard Higgs Physics
May 2004 – December 2005
Edited by
1
Sabine Kraml , Georges Azuelos 2,3 , Daniele Dominici 4 , John Ellis 1 ,
Gerald Grenier 5 , Howard E. Haber 6 , Jae Sik Lee 7 , David J. Miller 8 ,
Apostolos Pilaftsis 9 and Werner Porod 10
GENEVA
2006
1
2
3
4
5
6
7
8
9
10
Qing Wang
CERN, Geneva, Switzerland.
Université de Montréal, Montreal, Canada.
TRIUMF, Vancouver, Canada.
Università di Firenze and INFN, Firenze, Italy.
IPNL, Université Lyon-1, Villeurbanne, France.
University of California, Santa Cruz, USA.
Seoul National University, Seoul, Korea.
University of Glasgow, Glasgow, UK.
University of Manchester, Manchester, UK.
IFIC-CSIC, Valencia, Spain.
P. 12
Model Independent Description of New Physics
Effective Electroweak Chiral Lagrangian–EWCL
• To respect present status of SM:
Higgs not found! Its self coupling and Yukawa terms not tested !
• Need a theory describe present status of experiment:
need three goldstone bosons and their coupling with fermions!
• Subtract out Higgs in Standard Model:
EW symmetry and its breaking must be realized nonlinearly!
• Without Higgs makes theory model independent:
Underlying models are parameterized by choice of different coefficients.
Qing Wang
P. 13
Model Independent Description of New Physics
EW Chiral Lagrangian: boson part
LScalar → Lboson
EWCL
T = U τ 3U †
Vµ = (DµU )U †
DµU = ∂µU +ig2WµU −ig1Bµτ 3/2
2
µ
2
2
µν
Lboson
)
EWCL = − (f /4)tr(Vµ V ) + (f /4)β1 [tr(T Vµ )] + (1/2)α1 g2 g1 Bµν tr(T W
+(i/2)α2g1Bµν tr(T [V µ, V ν ])+ iα3g2tr(Wµν [V µ, V ν ])+ α4[tr(VµVν )]2 +α5[tr(VµV µ)]2
+α6tr(VµVν )tr(T V µ)(T V ν ) + α7tr(VµV µ)tr(T Vν )(T V ν ) + (1/4)α8g22[tr(T Wµν )]2
+(i/2)α9g2tr(T Wµν )tr(T [V µ, V ν ]) + (1/2)α10[tr(T Vµ)tr(T Vν )]2
+α11g2²µνρλtr(T Vµ)tr(Vν Wρλ) + α12tr(T Vµ)tr(Vν W µν )+ α13g2g1²µνρσ Bµν tr(T Wρσ )
+α14g22²µνρσ tr(T Wµν )tr(T Wρσ ) + 2iα15g2²µνρσ tr(Wµν VρVσ )
+α16g22²µνρσ tr(T Wµν )tr(T Wρσ ) + 2iα17g12g22²µνρσ tr(T Wµν tr(T VρVσ )
+α18g12²µνρσBµνBρσ +α19g22²µνρσtr(WµνWρσ )+(g12/4)Z1BµνB µν +(g22/2)Z2tr(WµνW µν )+O(p6)
Qing Wang
P. 14
Model Independent Description of New Physics
EW Chiral Lagrangian: fermion part
µ
Li =
µ
Qi =
Ei
µ
LYukawa → Lfermion
EWCL = Li
νi
¶
0 0
0 fie
Ui
Di
¶
µ
U PRLi + Qi
0
0
0
¶
µ
Φ=U
fiu
0
0
fid
0
¶
√v
2
¶
U PRQi + h.c.
0
ν αT
+fij
L CLβj Φα Φβ ²αα ²ββ + h.c.
Neutrino Majorana mass
+high order terms
high order terms: self interactions; interactions with gauge fields !
Qing Wang
P. 15
Model Independent Description of New Physics
Experimental Tests
S = −16πΠ03B(0) = −16πα1
e2[Π11(0)−Π33(0)]
0
0
αT =
(0)−Π
=
2β
U
=
16π[Π
1
33(0)] = −16πα8
11
c2s2m2Z
LW W V
V
−
= ig1V (Wµν
W −µV ν − Wµν
W +µV ν ) + iκV Wµ+Wν−V µν − g4V Wµ+Wν−(∂ µV ν + ∂ ν V µ)
gW W V
+g5V ²µνρσ [Wµ+(∂ρWν−) − (∂ρWµ+)Wν−]Vλ + iκ̃V Wµ+Wν−Ṽ µν
2
2
e
α
e
α3
β
1
1
Z
+
+
g1 − 1 = 2
c − s2 c2(c2 − s2) s2c2
e2(−α1 +α2 +α3 −α8 +α9)
κγ−1 =
s2
Qing Wang
g1γ
−1=0
2
e
α11
Z
g5 = 2 2
s c
g5γ = 0
β1
e2α1
e2(α1 −α2) e2(α3 −α8 +α9)
κZ−1 = 2 2 + 2 2 2 +
+
2
c −s c (c −s )
c
s2
P. 16
Model Independent Description of New Physics
Two Future Possibilities
•
Within SM:
Higgs is not found
•
Beyond SM: Many models, but no new particle is found now
In Future, next generation colliders will all work at TeV energy region
•
Possibility One: No new particle is found in TeV energy region
worst case
violate unitarity
•
Possibility Two: New particle is found in TeV energy region
probability: Z 0 >SUSY>Higgs;
Qing Wang
people will be excited and busy
P. 17
Model Independent Description of New Physics
•
New particle discovery needs time:
at least 3 years
•
Before discovery of new particle: EWCL works !
•
Once new particle is found: need go beyond EWCL
During the time before discovery of new particle:
not urgent now
urgent
•
Can we test effects of new particle below its threshold ?
•
New particles as virtual particle contribute to physics! ⇒ EWCL
•
It is most economical and effective theory to investigate new physics !
Qing Wang
P. 18
Model Independent Description of New Physics
Investigating New Physics in terms of EWCL
•
Experimentally: test and fix coefficients of the EWCL
need to analyze and choose the best process
•
Theoretically:
He,Kuang,Yuan,hep-ph/9704276
calculate coefficients of the EWCL
need to perform computation: integrate out new particles
QCD experience
PRD61,54011(00); PRD66,14019(02); PLB532,240(02); PLB560,188(03)
Each underlying model is corresponding to a group of coefficents!
Qing Wang
P. 19
Qing Wang
P. 20
Model Independent Description of New Physics
Calculate Coefficients of EWCL from Different Models
•
SM: need to integrate out Higgs
•
One doublet technicolor model: reproduce scale up result
•
One family technicolor model: find difference with scale up result
•
Top color assisted technicolor model
•
Little higgs models . . . . . .
Qing Wang
Hard and tedious work !
P. 21
Model Independent Description of New Physics
Investigating New Physics beyond EWCL
•
Model dependent research:
•
Model independent research:
......
The first discovered particles may be
Z0, h, ρ
–
Adding in EWCL a Z 0
–
Adding in EWCL a Higgs : either linearly or nonlinearly
–
Adding in EWCL a vector boson : Like QCD CL with ρ
Qing Wang
P. 22
Equivalence between Linear and Nonlinear Realizations of EWCL with Higgs
Adding in Higgs to EWCL: Two Types of Effective Theory
•
Linear Realization:
SM + high dimension operators !
µ + ¶
X fn
1
φ
On
Φ=√
Leff = LSM +
0
2
ΛH
2 φ
n
•
Nonlinear Realization:
c
2
Φ ≡ iτ Φ
∗
electroweak chiral Lagrangian
h+v
Σ ≡ (Φ , Φ) ≡ √ U
2
c
iπ iτ i
U =e
, i = 1, 2, 3
They are equivalent or not ?
Qing Wang
P. 23
Equivalence between Linear and Nonlinear Realizations of EWCL with Higgs
Dimension Six Operators in Linear Realization
ODW = T r([Dµ, Ŵνρ][Dµ, Ŵ νρ])
OBW = Φ+B̂µν Ŵ µν Φ
OW W W = T r(Ŵµν Ŵ νρŴρµ)
OBB = Φ+B̂µν B̂ µν Φ
OB = (DµΦ)+B̂ µν (Dν Φ)
1 + 3
OΦ,3 = (Φ Φ)
3
Dµ = ∂µ + igT aWµa + ig 0Y Bµ
Qing Wang
g 02
ODB = − ∂µBνρ∂ µB νρ
2
£
¤£ + µ ¤
+
OΦ,1 = (DµΦ) Φ Φ D Φ
OW W = Φ+Ŵµν Ŵ µν Φ
OW = (DµΦ)+Ŵ µν (Dν Φ)
1
OΦ,2 = ∂µ(Φ+Φ)∂ µ(Φ+Φ)
2
¤
£
+
+
µ
OΦ,4 = (Φ Φ) (DµΦ) (D Φ)
a
Ŵµν = igT aWµν
B̂µν = ig 0Bµν
P. 24
Equivalence between Linear and Nonlinear Realizations of EWCL with Higgs
O(p4) Operators in Nonlinear Realization
l41 ≡ Bµν T r(T W µν )
l42 ≡ Bµν T r(T [V µ, V ν ])
l43 ≡ T r(Wµν [V µ, V ν ])
l44 ≡ [T r(VµVν )]2
l45 ≡ [T r(VµV µ)]2
l46 ≡ T r(VµVν )T r(T V µ)T r(T V ν )
l47 ≡ T r(VµV µ)T r(T Vν )T r(T V ν )
l48 ≡ [T r(T Wµν )]2
l49 ≡ T r(T Wµν )T r(T [V µ, V ν ])
l410 ≡ [T r(T Vµ)T r(T Vν )]2
l411 ≡ ²µνρλT r(T V µ)T r(V ν Wρλ)
l412 ≡ T r(T V µ)T r(Vν W µν )
l413 ≡ ²µνρλB µν T r(T W ρλ)
Qing Wang
l414 ≡ ²µνρλT r(T W µν )T r(T W ρλ)
P. 25
Equivalence between Linear and Nonlinear Realizations of EWCL with Higgs
Linear Realization ⇒ Nonlinear Realization
2(DµΦ)+Φ = ∂µh2 + h2T r(T Vµ)
2Φ+Wµν Φ = h2T r(T Wµν )
2(DµΦ)+(Dν Φ) = h2[T r(T VµVν ) − T r(VµVν )] + 2(∂µh)(∂ν h)
2(DµΦ)+W µν (Dν Φ) = h2T r(W µν VµVν ) − (∂µh2)T r(W µν Vν )
2Φ+W νρ(DµΦ) = h2[T r(T V µW νρ) + T r(V µW νρ)]
2(DµΦ)+W νρΦ = h2[T r(T V µW νρ) − T r(V µW νρ)]
Qing Wang
P. 26
Equivalence between Linear and Nonlinear Realizations of EWCL with Higgs
Nonlinear Realization ⇒ Linear Realization
T r(T Vµ) = (Φ+Φ)−1[2(DµΦ)+Φ − ∂µ(Φ+Φ)]
T r(T Wµν ) = 2(Φ+Φ)−1[Φ+Wµν Φ]
1 + −2
T r(VµVν ) = (Φ Φ) ∂µ(Φ+Φ)∂ν (Φ+Φ) − (Φ†Φ)−1[(DµΦ)†(Dν Φ) + h.c.]
2
T r(T VµVν ) = (Φ+Φ)−1[(DµΦ)+(Dν Φ) − h.c.]
T r(V µW νρ) = (Φ+Φ)−1[−(DµΦ)+W νρΦ + h.c.]
T r(T V µW νρ) = (Φ+Φ)−1[(DµΦ)+W νρΦ + h.c.]
T r(W µν VµVν ) = 2(Φ+Φ)−1[(DµΦ)+W µν (Dν Φ)]
+(Φ+Φ)−2∂µ(Φ+Φ)[−(DµΦ)+W νρΦ + h.c.]
Qing Wang
P. 27
Equivalence between Linear and Nonlinear Realizations of EWCL with Higgs
• Mathematically linear and nonlinear representations are equivalent
• mh ∝ higgs self coupling in linear representation
• Perturbation expansion converge ⇒ light higgs
• Discussion of light higgs favors linear repersentation
• Heavy higgs can only be discussed in nonlinear representation
• Nonlinear representation can discuss light higgs in principle
Qing Wang
P. 28
Extended EWCL and Integrating out Higgs
EEWCL:
EWCL include in Higgs field
•
Writing done most general EEWCL
•
Integrating out Higgs field
•
investigate its effects on EWCL coefficients
previous works only focus on special terms
Problems
•
Higgs dependence in EEWCL is rather arbitrary
•
Higgs field cannot be exactly integrated out!
•
Can we make estimations on Higgs Effects?
Qing Wang
P. 29
Extended EWCL and Integrating out Higgs
• Take low energy expansion
• VEV part of Higgs field is order of p0
• Quantum fluctuation part of Higgs field h is at least order of p2
• Only accurate to 1-loop precision
• Use dimensional regularization
• Apply equation of motion
Qing Wang
P. 30
Extended EWCL and Integrating out Higgs
All terms contribute to p4 EWCL at 1-loop
L(2) = m2[(f1 − f3δc)A2µ + (f2 − f4δc)T r(Vµ2)]
δc =
2
a ( 1 − γ + 1 + ln 4πµ )
32π 2 2− D
m2
2
1
L(4) = − m2(1−aδc)h2 + mh[(f3−f5δc)A2µ + (f4−f6δc)T r(Vµ2)] + [g0i−(g0i )0δc]l4i
2
1
1
1
1
L(6) = (∂µh)2 − amh3 + f5h2A2µ + f6h2T r(Vµ2)
2
6
2
2
1
1 3
1
1 k
µν
L(8) = − bh4 +
h [f7A2µ + f8T r(Vµ2)] + (g0i )00h2l4i +
g
(∂
h)(∂
h)l
µ
ν
2
12
6m
2
2m2 2
1
L(10) = (g2k )0m−3(∂µh)(∂ν h)hl2kµν
2
Qing Wang
P. 31
Extended EWCL and Integrating out Higgs
Aµ = tr(T Vµ)
l21µν = T r(T V µ)T r(T V ν )
l22µν = T r(V µV ν )
l31µ = T r(T V µ)T r(V ν Vν )
l32µ = T r(T V ν )T r(V µVν )
l33µ = T r(T V ν )T r(T V µVν )
l34µ = T r(T Vν )T r(T W µν )
l35µ = B µν T r(T Vν )
l36µ = T r(T W µν Vν )
l37µ = T r(W µν Vν )
Qing Wang
P. 32
Extended EWCL and Integrating out Higgs
Integrating out Higgs: loop expansion
Z
i
1loop
4
Γ
= d xLEEW CL + ln DetD̂
2
δ 2S
D̂(x, y) ≡
= −[∂x2 + m2 − A(x) + Cµν (x)∂xµ∂xν ]δ(x − y)
δh(x)δh(y)
A(x) = −amh(x) + f5A2µ(x) + f6T r[Vµ2(x)] − bh2(x) + f7m−1h(x)A2µ(x)
+f8m−1h(x)T r[Vµ2(x)] + m−2(g0i )00l4i (x)
C µν (x) = g2k m−2l2kµν (x) + (g2k )0m−3hl2kµν (x)
Qing Wang
P. 33
Extended EWCL and Integrating out Higgs
Integrating out Higgs:
Z
Γ
1loop
=
loop expansion
i
d xLEEW CL + ln DetD̂ =
2
4
Z
d4x[L(2) + L(2) + · · ·]
L(2) = m2[f¯1A2µ + f¯2T r(Vµ2)]
(4)
L
Qing Wang
1 2 2
= − mhh + m[f¯3hA2µ + f¯4hT r(Vµ2)] + ḡ0i l4i
2
P. 34
Extended EWCL and Integrating out Higgs
1
4πµ2
L≡
− γ + ln
D
m2
2− 2
·
¸
(L + 3/2) 1
1
¯
−
g2 − (L + 1)(f5 + af3)
f1 = f1 +
2
32π
4
·
¸
1
(L + 3/2) 2
¯
f2 = f2 +
−
g2 − (L + 1)(f6 + af4)
2
32π
4
¸
·
2
a
1
2
2
2
mh = m 1 −
(L + 1)(a + b) −
2
16π
32π 2
·
¸
1
L + 3/2 1 0 L + 1 1
¯
f3 = f3 +
−(L + 1)f7 −
(g2 ) −
ag2 − (2L + 1)af5
2
32π
4
2
·
¸
L + 3/2 2 0 L + 1 2
1
¯
−(L + 1)f8 −
(g2 ) −
ag2 − (2L + 1)af6
f4 = f4 +
2
32π
4
2
Qing Wang
P. 35
Extended EWCL and Integrating out Higgs
¸
¤
£
1
L + 3/2 2 2
4 00
4 0
= g04 +
−
(L
+
1)
(g
)
+
a(g
)
+
(g2 )
0
0
2
32π
8
¸
·
¤
£
1
L + 3/2 1 2
6 0
6 00
= g06 +
+
)
)
+
a(g
g2 g2
−
(L
+
1)
(g
0
0
2
32π
4
·
¸
£
¤
1
L
L + 1 2 L + 3/2 2 2
5 00
5 0
2
= g05 +
−
(L
+
1)
(g
)
+
a(g
)
+
(f
)
+
f6g2 +
(g2 )
6
0
0
2
32π
2
2
16
·
¸
£
¤
1
L+1
L + 3/2 1 2
7
7 00
7 0
2
1
= g0 +
− (L + 1) (g0 ) + a(g0 ) + Lf5f6 +
(f5g2 + f6g2 ) +
g2 g2
32π 2
2
8
·
ḡ04
ḡ06
ḡ05
ḡ07
·
£ 10 00
¤ L
L + 1 1 3(L + 3/2) 1 2
1
10 0
2
10
10
− (L + 1) (g0 ) + a(g0 ) + (f5) +
f5g2 +
(g2 )
ḡ0 = g0 +
32π 2
2
2
16
·
¸
£
¤
1
i
i
i 00
i 0
ḡ0 = g0 +
−
(L
+
1)
(g
)
+
a(g
)
i = 1, 2, 3, 8, 9, 11, 12, 13, 14
0
0
32π 2
Qing Wang
¸
P. 36
Extended EWCL and Integrating out Higgs
m ¯
hc = 2 [f3T r(T Vµ)T r(T V µ) + f¯4T r(VµV µ)]
mh
£
¤
µ
2
LEW CL = m f¯1T r(T Vµ)T r(T V ) + f¯2T r(Vµ ) + (g0i + ∆g0i )l4i
2
2
m
¯4)2 + δg 5
∆g05 =
(
f
0
2m2h
2
m
∆g07 = 2 f¯3f¯4 + δg07
mh
∆g0j = δg0j
δfi = f¯i − fi
Qing Wang
2
m
¯3)2 + δg 10
(
f
∆g010 =
0
2m2h
j 6= 5, 7, 10
δg0i = ḡ0i − g0i
δm2 = m2h − m2
P. 37
Effects of Higgs in EWCL
¤
£
µ
2
¯
¯
LEW CL = m f1T r(T Vµ)T r(T V ) + f2T r(Vµ ) + (g0i + ∆g0i )l4i
2
2
m
¯4)2 + δg 5
∆g05 =
(
f
0
2m2h
2
m
∆g07 = 2 f¯3f¯4 + δg07
mh
2
m
¯3)2 + δg 10
∆g010 =
(
f
0
2m2h
Effects of Higgs
♣ From loop
♠ From equation of motion for Higgs
Assumption
higgs will be the next new particle we find in future experiment!
⇒ Some of fl and g0i may be small
Qing Wang
P. 38
Effects of Higgs in EWCL
Higgs decay and four-gauge-boson coupling
Γh→ZZ
(2f¯3 + f¯4)2e4mh
4m2Z 1
(1 − 2 ) 2
=
4
4
32s c
mh
Γh→W W
(f¯4)2e4mh
4m2W 1
=
(1 −
)2
2
4
32s
mh
¯
¯
LEW CL¯¯
·
32s4
4m2W − 1
4m2Z − 1
4
(1 −
= 4
) 2 Γh→W W − 2c (1 − 2 ) 2 Γh→ZZ
2
e mh
mh
mh
5,7,10
¸
2
2
2
4mW 1
4mZ −1 (Γh→ZZ )
2
2 (1 −
+c8(1 −
)
)
[T
r(T
V
)T
r(T
V
)]
µ
ν
m2h
m2h
Γh→W W
·
¸
4
2
2
16s
4mZ − 1
4mW − 1
4
µ
2
2
2Γ
+ 4
)
c (1 − 2 ) Γh→ZZ − (1 −
T
r(V
V
)[T
r(T
V
)]
h→W
W
µ
ν
e mh
mh
m2h
4m2W − 1
4s4
µ 2
2Γ
)
[T
r(V
V
)]
+ 4 (1 −
h→W
W
µ
2
e mh
mh
Qing Wang
i and δg i
Dominate if we ignore g0
0
P. 39
Effects of Higgs in EWCL
higgs mass dependence
¸
¸
·
·
¯
¯
df2
df1
1 1 1 1
1 1 1 2
=
g2 + f5 + af3
=
g2 + f6 + af4
2
2
2
2
2
2
dm
32π m 4
dm
32π m 4
dβ1
1 1
2 dαT
¯
¯
−β1 = f1/f2 ⇒ m
= 2 2≈
[f5 + β1f6]
2
2
¯
dm
dm
16π f2
1
dḡ
1
0
2
1 00
1 0
m
=
[(g
)
+
a(g
0
0) ]
2
2
dm
32π
0
0
d(gg
S)
dgg
α1
1 1 00
1 0
1
2
1 0
gg α1 = ḡ0 ⇒ m
=
−16π
=
−
[(g
)
+
a(g
0
0) ]
2
2
2
dm
dm
π
Qing Wang
P. 40
Effects of Higgs in EWCL
higgs mass dependence
Qing Wang
C
f¯1
16π 2 d dC
ln m |p6
f¯2
f¯3
f6
f5
16π 2 d dC
ln m |p8
g21
4
g22
4
f7
f¯4
g̃04
g̃06
f8
(g04)00
(g06)00
g̃05
g̃07
g̃010
g̃0i
(g05)00
(g07)00
(g010)00
(g0i )00
16π 2 d dC
ln m |p10
16π 2 d dC
ln m |p12
af3
af4
(g21 )0
4
(g22 )0
4
2af5
2af6
a(g04)0
a(g04)0
(f6 )2
f4f8 +
− 2
f3f7 +f4f8 +a(g07)0 +f5f6
(f5 )2
10 0
f3f7 + a(g0 ) − 2
a(g0i )0
a(g05)0
P. 41
Summary
• R&E of Theory and exp all asked for M Ind investigation for Higgs
• Before higgs is discovered, EWCL is a good tool to do research
• We have calculated effects from comprehensive higgs 1-loop
• Wait for exp data and more detail phenomenology analysis
• Also need to estimate effects of other new physics particles
Qing Wang
P. 42
Thanks!
Qing Wang
P. 43