Lightness of a Higgs Boson and Spontaneous CP-violation in the Lee Model: An Alternative Scenario

2.3 MB·

by  Ying-nan Mao

Lightness of Higgs Boson and Spontaneous CP-violation in the
Lee Model: An Alternative Scenario
Ying-nan Mao 1,4,∗ and Shou-hua Zhu 1,2,3,†
1 Institute of Theoretical Physics & State Key Laboratory of Nuclear Physics and Technology,
Peking University, Beijing 100871, China
2 Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
6
1 3 Center for High Energy Physics, Peking University, Beijing 100871, China
0
2 4 Center for Future High Energy Physics & Theoretical Physics Division,

p
e Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
S
(Dated: September 13, 2016)
0
1
Based on the weakly-coupled spontaneous CP-violation two-Higgs-doublet model
]
h
p (namedLeemodel)andthemechanismtogeneratethecorrelationbetweensmallness
-
p of CP-violation and lightness of scalar mass, as we proposed earlier, we predicted
e
h
a light CP-mixing scalar η in which pseudoscalar component is dominant. It is a
[

2 natural scenario in which m (10GeV) v. It means new physics might be
η
v ∼ O (cid:28)
9 hidden below the electro-weak scale v. Masses of all other scalars (h, H, H±) should
0
2
be around the electro-weak scale v. Among them, the 125 GeV Higgs boson (h)
0
0 couplings are standard-model like, and the charged Higgs boson (H±) mass should
.
2
0 be around the heaviest neutral scalar (H) mass. We discussed all experimental
6
1
constraints and showed that this scenario is still allowed by data. The strictest
:
v
i constraints come from the flavor violation experiments and the EDM of electron
X
r and neutron. We also discussed the future tests for this scenario. It is possible to
a
discover the extra scalars or exclude this scenario at future colliders, especially at
the LHC and e+e− colliders with (ab−1) luminosity. We also pointed out that
O
the Z-mediated Higgs pair production via e+e− h h (h ,h stand for two of the
i j i j
→
η,h,H) would be the key observable to confirm or exclude CP-violation in Higgs
sector. The sensitivity to test this scenario is worth further studying in detail.
∗ [email protected], [email protected]
† [email protected]
2
I. INTRODUCTION
The realization of electro-weak symmetry breaking and CP-violation are two important
topics both in the standard model (SM) and beyond the standard model (BSM). It is also
attractive to relate them with each other. In our previous work [1], we proposed the cor-
relation between lightness of Higgs boson and smallness of CP-violation. In this paper, we
will continue to explore an alternative natural scenario and its phenomenology.
In 1964, the Higgs mechanism [2] was proposed. In the Higgs mechanism, a scalar doublet
with nontrivial vacuum expectation value (VEV) was introduced to break the electro-weak
gauge symmetry spontaneously. After spontaneous gauge symmetry breaking in the SM,
there exists a scalar named the Higgs boson 1. In July 2012, both ATLAS [4] and CMS
[5] collaborations at LHC discovered a new boson with its mass around 125 GeV [6]. The
subsequent measurements by CMS and ATLAS [7–9] on its signal strengths showed that
the scalar behaves similarly with SM Higgs boson. However there is still spacious room
for the BSM. In some BSM models, there exist new light particles which may appear in
the final states during Higgs decay processes. For example, in the next-to-minimal super-
symmetric standard model (NMSSM) [10], the simplest little Higgs model (SLH) [11–13], or
the left-right-twin-Higgs model (LRTH) [14, 15], a light scalar η with its mass of (10)GeV
O
will naturally appear. For some cases in 2HDM [16–20], a light scalar η is allowed as well,
though there are strict constraints on them. If m < m /2 = 62.5GeV, there would be an
η h
exotic decay channel h ηη; while if m < m m = 34GeV, an exotic decay channel
η h Z
→ −
h Zη shouldalsobeopen. ThereisnoevidenceforexoticHiggsdecaychannelsatLHCtill
→
(cid:46)
now, theconstraintsontheexoticHiggsdecaybranchingratioissettobeBr (20 30)%
exo
−
[21] if the production rate of the Higgs boson is close to that in SM. The spin-parity property
for Higgs boson is expected to be 0+ in the SM. Experimentally, a pure pseudoscalar state
(0−) is excluded at over 3σ [22–24]. But a mixing state is still allowed, thus the spacious
room for BSM scenarios have not been closed yet.
Theoretically, CP-violation in SM is induced by the Kobayashi and Maskawa (K-M)
mechanism [25] proposed by Kobayashi and Maskawa in 1973. They proved that a nontrivial
1 There may exist more particles in the extension of SM. For example, in the two-Higgs-doublet model
(2HDM) [3] in which two scalar doublets were introduced, there exist five scalars. Two of them are
charged and three of them are neutral.
3
phase which leads to CP-violation in quark mixing matrix (called the CKM matrix [25, 26])
would appear if there exist three or more generations of quarks. The CKM matrix is usually
parameterized as the Wolfenstein formalism [27]
 
1 λ2/2 λ Aλ3(ρ iη)
 − − 
V =  λ 1 λ2/2 Aλ2 + (λ4). (1)
CKM  
 − −  O
Aλ3(1 ρ iη) Aλ2 1
− − −
The Jarlskog invariant J [28] defined as
(cid:16) (cid:104) (cid:105)(cid:17) (cid:89)(cid:16) (cid:17)(cid:89)(cid:16) (cid:17)
det i M M†,M M† = 2J m2 m2 m2 m2 (2)
U U D D Ui − Uj Di − Dj
i<j i<j
measures the effects of CP-violation where M is the mass matrix for up (down) type
U(D)
quarks. J λ6A2η 3 10−5 [29] means CP-violation in SM is small. Experimentally,
≈ ≈ ×
in K- and B-meson systems, several kinds of CP-violation have been discovered [29] which
represent the success of K-M mechanism. While it is still attractive to search for new
sources of CP-violation, not only to search for BSM physics, but also to understand the
matter-antimatter asymmetry in the universe [29, 30]. SM itself cannot provide enough
baryogenesis effects [29–32], but in some extensions of SM, for example, 2HDM with CP-
violation in Higgs sector, it is possible to generate large enough baryogenesis effect [31, 33].
Lee model [34] is a possible way to connect Higgs mechanism and CP-violation with each
other. It was proposed by Lee in 1973 as the first 2HDM. In Lee model, the lagrangian
is required to be CP-conserved, but the VEV of one Higgs doublet can be complex, thus
the CP symmetry is spontaneously broken due to the complex vacuum. In this case, the
neutral scalars are CP-mixing states so that CP-violation effects should occur in the Higgs
sector. All the three neutral scalars should couple to massive gauge bosons with the effective
interaction
(cid:88) (cid:18)2m2 m2 (cid:19)
= c h WW+µW− + ZZµZ (3)
LhiVV i,V i v µ v µ
i
where c g /g is the ratio between the h VV coupling strength and that in
i,V ≡ hiVV hVV,SM i
SM. c2 +c2 +c2 = 1 due to the mechanism of spontaneous gauge symmetry breaking.
1,V 2,V 3,V
The quantity
K c c c (4)
1,V 2,V 3,V
≡
measures the CP-violation effects in Higgs sector [3, 35] when the masses of the neutral
4
scalars are non-degenerate 2. In our recent paper [1], we proposed the correlation between
lightness of Higgs boson and smallness of CP-violation through small t s in Lee model 3.
β ξ
While in that paper, we treated the 125 GeV scalar as the lightest one thus it implied a
strong-interacted scenario beyond [36]. However, another natural scenario with a weakly-
interacted scalar in which the heavy scalars have the mass m (v) is also possible where
i
∼ O
v = 246GeV is the VEV of the scalar doublet in SM. In this scenario, Lee model would
predict a light scalar η with mass m v for the small t s case based on our paper [1]. In
η β ξ
(cid:28)
this paper, we will discuss this scenario and its phenomenology.
This paper is organized as follows. In section II we introduce the Lee model and its main
properties. In section III we discuss the constraints for this scenario by recent experiments,
including data from both high and low energy phenomena. In section IV we consider the
predictions and future tests for this scenario. And section V contains our conclusions and
discussions.
II. THE LEE MODEL AND A LIGHT SCALAR
In Lee model [34], the lagrangian is required to be CP-conserved in both scalar and
Yukawa sectors. For the scalar sector,
= (D φ )†(Dµφ )+(D φ )†(Dµφ ) V(φ ,φ ) (5)
µ 1 1 µ 2 2 1 2
L −
in which the scalar potential
V(φ ,φ ) = µ2R +µ2R +λ R2 +λ R R
1 2 1 11 2 22 1 11 2 11 12
+λ R R +λ R2 +λ R R +λ R2 +λ I2 . (6)
3 11 22 4 12 5 12 22 6 22 7 12
Here the scalar doublets
   
φ+ φ+
1 2
φ1 =  , φ2 =   (7)
v1+R√1+iI1 v2eiξ+√R2+iI2
2 2
2 If at least two of the scalars have the same mass, we can always perform a field rotation between them to
keep at least one c =0, thus there would be no CP-violation in Higgs sector.
i,V
3 The parameters will be defined next section, or see [1].
5
(cid:112)
and R(I) denotes the real (imaginary) part of φ†φ 4. v2 +v2 = v = 246GeV. The
ij i j 1 2
general Yukawa couplings can be written as
¯ ¯ ˜ ˜
= Q ((Y ) φ +(Y ) φ )D Q ((Y ) φ +(Y ) φ )U , (8)
y Li 1d ij 1 2d ij 2 Rj Li 1u ij 1 2u ij 2 Rj
L − −
where all coupling constants should be real and φ˜ iσ φ∗. We choose the Type III [3, 37]
i ≡ 2 i
Yukawa couplings because there is no additional discrete symmetry to forbid any term in
(8). It is possible to generate correct fermion mass spectrum and CKM matrix from (8), for
example, see [38, 39].
We should minimize the potential (6). For some parameter choices, there is a nonzero ξ
which means the spontaneous CP- violation 5. If v ,v ,ξ = 0, we have
1 2
(cid:54)
λ +λ λ
µ2 = λ v2 3 7v2 2v v cosξ; (9)
1 − 1 1 − 2 2 − 2 1 2
λ +λ λ
µ2 = 3 7v2 λ v2 5v v cosξ; (10)
2 − 2 1 − 6 2 − 2 1 2
λ λ
0 = 2v2 + 5v2 +(λ λ )v v cosξ. (11)
2 1 2 2 4 − 7 1 2
λ v2 +λ v2 < 2 λ λ v v is required to keep ξ = 0. Define s sinα,c cosα,t
| 2 1 5 2| | 4 − 7| 1 2 (cid:54) α ≡ α ≡ α ≡
tanα in the following parts of this paper, and t v /v is the ratio of the VEVs for scalar
β 2 1
≡
doublets. The vacuum stability conditions can be found in [3] or Appendix. A in [1]. The
Goldstone fields can be written as
G± = c φ± +e∓iξs φ±; (12)
β 1 β 2
G0 = c I +s c I s s R . (13)
β 1 β ξ 2 β ξ 2
−
The charged Higgs field is orthogonal to the corresponding charged Goldstone field as
H± = e±iξs φ± +c φ± (14)
− β 1 β 2
with the mass square
λ
m2 = 7v2. (15)
± − 2
4 We can always perform a rotation between φ and φ to keep the term proportional to R vanish.
1 2 12
5 We can always perform a global phase redefinition for φ and φ to keep one of the VEVs real, just like
1 2
the case in (7).
6
The symmetric mass matrix m˜ for neutral scalars is written as [1]
 
(λ λ )s2 ((λ λ )s c +λ c )s ((λ λ )c c +λ s )s
4 − 7 ξ − 4 − 7 β ξ 2 β ξ − 4 − 7 β ξ 5 β ξ
 
 
 
 
 ((λ +λ )+(λ λ )c2/2)s 
 4λ c2 +λ s c +(λ λ )s2c2 3 7 4 − 7 ξ 2β 
 1 β 2 2β ξ 4 − 7 β ξ +λ c2c +λ s2c  (16)
 2 β ξ 5 β ξ 
 
 
 
 
 (λ λ )c2c2 
 4 − 7 β ξ 
+λ s c +4λ s2
5 2β ξ 6 β
inthebasis( s I +c c I c s R ,R ,s I +c R )T inunitofv2/2. Tosolvetheeigenvalue
β 1 β ξ 2 β ξ 2 1 ξ 2 ξ 2
− −
equation with perturbation method 6, we should expand m˜ in powers of (t s ) in small t
β ξ β
limit as
m˜ = m˜ +(t s )m˜ +(t s )2m˜ +... (17)
0 β ξ 1 β ξ 2
For the two heavy scalars, we have [1]
v2 (cid:16) (cid:17)
m2 = (m˜ ) + (t s ) (18)
h,H 2 0 22(33) O β ξ
where
(cid:18) (cid:19)
4λ +λ λ 4λ (λ λ )
1 4 7 1 4 7
(m˜ ) = − − − c +λ s . (19)
0 22(33) 2θ 2 2θ
2 ∓ 2
Here θ = (1/2)arctan(2λ /(4λ λ +λ )) labels the mixing angle of the real parts of the
2 1 4 7
−
two scalar doublets. The scalar fields
    
h c s R
θ θ 1
  =   + (tβsξ). (20)
O
H s c R
θ θ 2
−
(cid:112)
We treat the lighter one as m = (m˜ ) /2v = 125GeV. Different from the scenario in
h 0 22
[1], in this paper, the dominant component for the 125 GeV scalar should be CP-even thus
there exists SM limit for its couplings. While for the lightest scalar η, to the leading order
6 Forthecalculationsindetails,pleaseseetheAppendix.Binourrecentpaper[1],withthesameconventions
as those in this paper.
7
of (t s ), we have
β ξ
v2t2s2 (cid:18) (m˜ )2 (m˜ )2 (cid:19)
m2 = β ξ (m˜ ) 1 12 1 13
η 2 2 11 − (m˜ ) − (m˜ )
0 22 0 33
v2t2s2(cid:20) (cid:18) 1 1 (cid:19)
β ξ
= 4λ +2λ (λ +λ )s
6 5 3 7 2θ
2 (m˜ ) − (m˜ )
0 22 0 33
(cid:18) c2 s2 (cid:19) (cid:18) s2 c2 (cid:19)(cid:21)
4(λ +λ )2 θ + θ λ2 θ + θ ; (21)
− 3 7 (m˜ ) (m˜ ) − 5 (m˜ ) (m˜ )
0 22 0 33 0 22 0 33
(cid:18) (cid:19)
(m˜ ) (m˜ ) I
1 12 1 13 1
η = I t s (c R +s R )+ (c R s R )+
2 β ξ θ 1 θ 2 θ 2 θ 1
− (m˜ ) (m˜ ) − t
0 22 0 33 ξ
(cid:20)(cid:18) (cid:18) c2 s2 (cid:19) λ s (cid:18) 1 1 (cid:19)(cid:19)
= I t s 2(λ +λ ) θ + θ + 5 2θ R
2 β ξ 3 7 1
− (m˜ ) (m˜ ) 2 (m˜ ) − (m˜ )
0 22 0 33 0 22 0 33
(cid:18) (cid:18) 1 1 (cid:19) (cid:18) s2 c2 (cid:19)(cid:19) I (cid:21)
+ (λ +λ )s +λ θ + θ R + 1 . (22)
3 7 2θ 5 2
(m˜ ) − (m˜ ) (m˜ ) (m˜ ) t
0 22 0 33 0 22 0 33 ξ
Thus in the limit t s 0, we have m t s 0 and η I , which mean that η behaves
β ξ η β ξ 2
→ ∝ → →
like a light pseudoscalar but it has small CP-even component.
We can diagonalize the fermion mass matrixes as
   
m 0 0 m 0 0
u d
   
V M V† =  0 m 0 , V M V† =  0 m 0  (23)
U,L U U,R  c  D,L D D,R  s 
   
0 0 m 0 0 m
t b
in which according to (8), the mass matrixes are
v (cid:0) (cid:1) v (cid:0) (cid:1)
(M ) = (Y ) c +(Y ) s e−iξ , (M ) = (Y ) c +(Y ) s eiξ . (24)
U ij √2 1u ij β 2u ij β D ij √2 1d ij β 2d ij β
†
The CKM matrix V = V V as usual. We can rewrite the Yukawa couplings (8) in
CKM U,L D,L
quark sector as following adopting the Cheng-Sher ansatz [40]
(cid:18) (cid:19)
(cid:88) c R +s c R +s s I
(cid:48) = m f¯ f 1+ β 1 β ξ 2 β ξ 2
LYuk,Q − f L R v
f=Ui,Di
(cid:113)
ξU mUmU
(cid:88) ij i j
¯
U U ((c R s c R +s s I ) i(c I s c I s s R ))
i,L j,R β 2 β ξ 1 β ξ 1 β 2 β ξ 1 β ξ 1
− v − − − −
i,j
(cid:113)
ξD mDmD
(cid:88) ij i j
¯
D D ((c R s c R +s s I )+i(c I s c I s s R ))
i,L j,R β 2 β ξ 1 β ξ 1 β 2 β ξ 1 β ξ 1
− v − − −
i,j
(cid:113)
2mDmD
(cid:88) i j U¯ (cid:0)V ξD(cid:1) D H+
− v i,L CKM · ij j,R
i,j
(cid:113)
2mUmU
(cid:88) i j (cid:16) (cid:17)
D¯ V† ξU U H− +h.c. (25)
− v i,L CKM · ij j,R
i,j
8
Similarly in the lepton sector
(cid:18) (cid:19)
(cid:88) c R +s c R +s s I
(cid:48) = m (cid:96)¯ (cid:96) 1+ β 1 β ξ 2 β ξ 2
LYuk,(cid:96) − (cid:96) L R v
(cid:96)
(cid:113)
ξ(cid:96) m(cid:96)m(cid:96)
(cid:88) ij i j
¯
(cid:96) (cid:96) ((c R s c R +s s I )+i(c I s c I s s R ))
i,L j,R β 2 β ξ 1 β ξ 1 β 2 β ξ 1 β ξ 1
− v − − −
i,j
(cid:113)
2m(cid:96)m(cid:96)
(cid:88) i j (cid:0) (cid:1)
ν¯ V ξ(cid:96) (cid:96) H+ +h.c. (26)
− v i,L PMNS · ij j,R
i,j
Here V is the lepton mixing matrix [41] and
PMNS
ξU = (V ) (cid:0) s eiξ(Y ) +c (Y ) (cid:1)(V† ) ; (27)
ij U,L ik − β 1u kl β 2u kl U,R lj
ξD((cid:96)) = (V ) (cid:0) s e−iξ(Y ) +c (Y ) (cid:1)(V† ) . (28)
ij D((cid:96)),L ik − β 1d((cid:96)) kl β 2d((cid:96)) kl D((cid:96)),R lj
U,D,(cid:96)
The off-diagonal elements of ξ induce the flavor changing processes at tree level. It was
ij
proved in [1] that in the t s 0 limit, all the four quantities m ,c ,K,J t s which
β ξ η η,V β ξ
→ ∝
means the correlation between the lightest scalar and smallness of CP-violation.
In the scenario we discuss in this paper, there can be exotic Higgs decay channels h
→
ηη,Zη induced by
c g 1
= hη (h∂ η η∂ h)Zµ g vhη2. (29)
exo µ µ hηη
L 2c − − 2
W
It leads to the branching ratios
g2c2 m3 (cid:18)m2 m2(cid:19)
Br(h Zη) = hη h Z, η ; (30)
→ 64πm2 Γ F m2 m2
W h,tot h h
(cid:115)
g2 v2 4m2
hηη η
Br(h ηη) = 1 (31)
→ 32πm Γ − m2
h h,tot h
where (x,y) = (1 + x2 + y2 2x 2y 2xy)3/2, g is the weak coupling constant and
F − − −
c m /m . For the detail couplings, please see section A in appendices, in which all
W W Z
≡
¯
c are defined as the ratio between Higgs-ff couplings and those in SM.
h,f
III. CONSTRAINTS FOR THIS SCENARIO BY RECENT DATA
Besides the 125 GeV Higgs boson (h), there are two extra neutral scalars and one of
which is expected to be light in this scenario. For the lightest scalar η with its mass m
η
∼
(0.1 1)GeV, the BESIII [42], BaBar [43, 44] and CMS [45] experiments gave strict
O −
9
constraints thus we will focus on the cases m (10)GeV. Type II 2HDM including a
η
∼ O
¯
light scalar with mass (25 80)GeV is excluded [46] through the search for ηbb associated
−
production. While for a general case it is still allowed by collider data, as we will show
below. The two extra scalars would face the constraints from the direct searches at LEP
and LHC. In this scenario of Lee model, with a light particle η, the exotic decay channels
h ηη,Zη will modify the total width and signal strengths for the 125 GeV Higgs boson
→
that we should also consider the constraints from Higgs signal strengths.
In Lee model, there is no additional discrete symmetry to forbid flavor changing pro-
cesses at tree level, and there are also new origins for CP-violation. Thus it must face the
constraints in flavor physics, including rare decays, meson mixing, etc. The electric dipole
moments (EDM) for electron [47] and neutron [48] would also give strict constraints in many
models with additional CP-violation source [49] including Lee model, so we must consider
the EDM constraints here as well.
A. Direct Searches for Extra Scalars
The LEP experiments [50–52] set strict constraints on this scenario through the e+e−
→
Zη and e+e− hη associated production processes. For η with its mass (15 40)GeV,
→ −
[50, 51] gave σ /σ (cid:46) (1.5 4) 10−2 at 95% C.L. which meant
Zη SM
− ×
c (cid:46) (0.12 0.2) (32)
η,V
−
thus t s (cid:46) 0.1 in this scenario. At the same mass region for η, assuming both η and h decay
β ξ
to b¯b final states dominantly, [51, 52] gave c2 (cid:46) (0.2 0.3). According to (A.15), c = c
hη − H,V hη
thus c should also be small. The results implied that c 1 thus the couplings of h
H,V h,V
∼
should be SM-like.
The direct searches for a heavy Higgs boson at LHC [53, 54] excluded a SM Higgs boson
in the mass region (145 1000)GeV at 95% C.L. A SM Higgs boson with its mass around v
−
would decay to WW and ZZ final states dominantly with Br(H VV) 1 [55], while
SM
→ ≈
in 2HDM it can be modified because of a suppressed HVV coupling and the existence of
other decay channels like H Zη,ηη,hη, and Zh (if m > m + m = 216GeV), hh (if
H Z h
→
m > 2m = 250GeV), H+H− (if m > 2m ). For a heavy scalar H, analytically the
H h H ±
10
partial widths should be
Γ (VV) c2 Γ ; (33)
H ≈ H,V H,SM
(cid:115)
g2 v2 4m2
Hηη η
Γ (ηη) = 1 ; (34)
H 32πm − m2
H H
c2 m3 (cid:18)m2 m2 (cid:19)
Γ (Zη) = h,V H η , Z . (35)
H 8πv2 F m2 m2
H H
The suppression in Γ (VV) comes from small c while Γ (Zη) c2 is not suppressed
H H,V H ∝ h,V
because h is SM-like and c 1. According to CMS results [53] which gave the most strict
h,V
∼
constraint, for m (200 300)GeV, the 95% C.L. upper limit for the signal strength is 7
H
∼ −
σ Br(H VV)
µ H → (cid:46) (0.1 0.2). (36)
H
≡ σ · Br (H VV) −
H,SM SM
→
Numerically, we show the Br(H VV) m plots for different parameter choices fixing
H
→ −
c = 0.1 in Figure 1. From the figures, we can see that if the production cross section
η,V
FIG. 1: Br(H VV) m plots for different parameter choices fixing c = 0.1. The green,
H η,V
→ −
yellow, blue, and red lines stand for c = 0.2,0.3,0.4,0.5 respectively in each figure. The upper
H,V
figures are for m = 20GeV while the lower figures are for m = 40GeV. In each line, from left to
η η
right, we take g = 0,0.5,1.
Hηη
BrH(cid:45)(cid:62)VV BrH(cid:45)(cid:62)VV BrH(cid:45)(cid:62)VV
0.30 0.30 0.30
0.25 0.25 0.25
0.20 0.20 0.20
(cid:72) (cid:76) (cid:72) (cid:76) (cid:72) (cid:76)
0.15 0.15 0.15
0.10 0.10 0.10
0.05 0.05 0.05
m GeV m GeV m GeV
200 220 240 260 280 300 H 200 220 240 260 280 300 H 200 220 240 260 280 300 H
BrH(cid:45)(cid:62)VV BrH(cid:45)(cid:62)VV BrH(cid:45)(cid:62)VV
0.30 0.30 0.30
0.25 (cid:72) (cid:76) 0.25 (cid:72) (cid:76) 0.25 (cid:72) (cid:76)
0.20 0.20 0.20
(cid:72) (cid:76) (cid:72) (cid:76) (cid:72) (cid:76)
0.15 0.15 0.15
0.10 0.10 0.10
0.05 0.05 0.05
m GeV m GeV m GeV
200 220 240 260 280 300 H 200 220 240 260 280 300 H 200 220 240 260 280 300 H
σ σ , c (cid:46) 0.3(cid:72) wo(cid:76)uld be allowed; while if σ(cid:72) (cid:76) 0.5σ , c (cid:46) 0.4 w(cid:72)oul(cid:76)d
H H,SM H,V H H,SM H,V
∼ ∼
also be allowed. It is not sensitive to m . We did not consider the H hh channel
η
→
for m > 2m = 250GeV in the discussions above. Numerically, for g 1, we have
H h Hhh
∼
Br(H hh) (cid:46) 0.1 which leads to σ(pp H hh) (cid:46) 0.4pb [55]. For this case, the direct
→ → →
7 For a heavy Higgs boson, Br (H VV) 1 according to [55].
SM
→ ∼