Lecture 2: Weakly-coupled Higgs bosons Problems with the ...
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pre-SUSY2008 Higgs 1
Lecture 2: Weakly-coupled Higgs bosons
• Problems with the SM Higgs boson.
• Two-Higgs-doublet models.
• Minimal supersymmetric standard model Higgs sector
• The next-to-minimal supersymmetric standard model Higgsbosons.
pre-SUSY2008 Higgs 2
Problems with the SM Higgs boson
• The electroweak symmetry breaking was put in by hand
VHiggs = µ2|φ|2 + λ|φ|4
By some unknown dynamics that the SM did not address theparameter µ2 < 0.
• Large Hierarchy between Mplanck and Mweak.
pre-SUSY2008 Higgs 3
Gauge Hierarchy Problem
Scalar boson mass has no symmetry protection.
f
H H
∆M2H =
|λf |216π2
[−2Λ
2UV + 6m
2f ln
(ΛUV
mf
)+ ...
]
The physical Higgs boson is then
(M2H)phys = (M2
H)bare + ∆M2H ' (100 GeV)2
We need a huge finely tuned cancellation in order to achieve a physical
(100 GeV)2 Higgs boson.
In literature, there are two classes of models to solve the hierarchy
problem.
pre-SUSY2008 Higgs 4
• Weakly-coupled models, e.g., supersymmetry. It predicts new scalars
such that they systematically cancel the quadratic divergences
H H
S
∆M2H =
λS
16π2
[Λ
2UV − 2m
2S ln
(ΛUV
mS
)+ ...
]
The leading term in ΛUV will cancel if
λS = |λf |2 and if there are 2 such scalars
• ΛUV is of order TeV. The SM would be replaced by a new theory at
the TeV scale. Just like the 4-fermi interaction was replaced by the
W -boson propagator. Examples include some new dynamics at TeV
scale, the technicolor type models, topcolor models, little Higgs
models.
pre-SUSY2008 Higgs 5
Extensions to the Standard Model Higgs sector
Weakly-coupled models usually contain more than one Higgs doublets,
may be two or more, triplets, or singlets. The MSSM contains two Higgs
doublets. The NMSSM contains two doublets and one singlet.
Basic Constraints for adding extra Higgs fields:
1. The first constraint is the experimental value of
ρ ≡ m2W
m2Z cos2 θw
' 1
very close to 1. The structure of the Higgs sector will affect the ρ
parameter. Doublets and singlets will satisfy ρ = 1 automatically.
But it is not true for an arbitrary Higgs representation. The general
formula for arbitrary representations is
ρ =
∑T,Y
[4T (T + 1)− Y 2]|VT,Y |2cT,Y∑T,Y
2Y 2|VT,Y |2
pre-SUSY2008 Higgs 6
where VT,Y = 〈φT,Y 〉, T is the total SU(2)L isospin and Y is thehypercharge. The constant cT,Y is
cT,Y =
{1, (T, Y ) ∈ complex representation12 , (T, Y ) ∈ real representation
It is easy to see that for arbitrary VT,Y the condition
4T (T + 1)− Y 2 = 2Y 2 ⇔ (2T + 1)2 − 3Y 2 = 1
can make sure ρ = 1.
Consider an example of Higgs triplet of T = 1, Y = 0 OR T = 1, Y = 2
φ+
φ0
φ−
,
φ++
φ+
φ0
Obviously, the triplets do not satisfy (2T + 1)2 − 3Y 2 = 1 condition. One can
satisfy the ρ = 1 within experimental uncertainty by restricting the VEV of
the triplet (use the current value from PDG):
1.0002+0.0007−0.0004 =
8|V1,0|2 + 2|V1/2,1|22|V1/2,1|2
pre-SUSY2008 Higgs 7
which gives|V1,0||V1/2,1|
≤ 0.03
2. The second constraint is the flavor-changing neutral current:
s ↔ d, c ↔ u
A theorem due to Glashow and Weinberg stated that tree-level
FCNC mediated by Higgs bosons will be absent if all fermions of a
given electric charge couple to no more than one Higgs doublet.
There are two natural choices:
• Model I: of 2HDM is that one of the Higgs doublets do not
couple to fermions at all;
• Model II: of 2HDM is that the Y = 1 doublet couples to the
up-type fermions while the Y = −1 doublet couples to the
down-type fermions and the charged leptons. This is also the
basis for the MSSM.
pre-SUSY2008 Higgs 8
Two Higgs Doublet Models
There are two complex Y = 1 doublets, φ1 and φ2 with the followingHiggs potential
V (φ1, φ2) = λ1(φ†1φ1 − v
21)
2+ λ2(φ
†2φ2 − v
22)
2+ λ3
[(φ†1φ1 − v
21) + (φ
†2φ2 − v
22)
]2
+ λ4
[(φ†1φ1)(φ
†2φ2)− (φ
†1φ2)(φ
†2φ1)
]2
+ λ5
[<e(φ
†1φ2)− v1v2 cos ξ
]2+ λ6
[=m(φ
†1φ2)− v1v2 sin ξ
]2
Some comments are in order here.
• All λs are real. This potential is the most general with respect to
gauge invariance.
• For a large range of parameters correct pattern of EWSB is
guaranteed. The minimum of the potential occurs at
〈φ1〉 =
(0
v1
), 〈φ2〉 =
(0
v2eiξ
),
which breaks the SU(2)L × U(1)Y → U(1)em.
pre-SUSY2008 Higgs 9
• If sin ξ 6=0 then CP is violated in the Higgs sector. But if λ5 = λ6
the last two terms can be combined into a single one
|φ†1φ2 − v1v2eiξ|2 and the phase can be removed by a redefinition of
one of the fields, e.g.,
φ2 −→ φ2eiξ
which does not change any other terms in the potential.
• We set ξ = 0, there will be no CP violation in the Higgs sector.
• Define the ratio of the VEVs
tan β =v2
v1
pre-SUSY2008 Higgs 10
Spectrum
There are 8 d.o.f. in two complex doublets. 3 of which will be eaten tobecome the longitudinal components of the gauge bosons. We substitute
φ1 =
(φ+
1
φ01
), φ2 =
(φ+
2
φ02
)
into the potential.
• Charged Higgs: The mass terms of the charged fields are
λ4(φ−1 φ
−2 )
(v22 −v1v2
−v1v2 v21
) (φ+
1
φ+2
)
It can be diagonalized by(G±
H±
)=
(cos β sin β
− sin β cos β
) (φ±1φ±2
)
After subsituting we obtain
λ4(G−
H−
)
(0 0
0 v21 + v2
2
) (G+
H+
)
pre-SUSY2008 Higgs 11
The charged Higgs mass is
m2H+ = λ4(v
21 + v
22)
• Pseudoscalar: Again look for the mass terms for =mφ01 and =mφ0
2:
λ6(φ0,i1 φ
0,i2 )
(v22 −v1v2
−v1v2 v21
) (φ0,i
1
φ0,i2
)
We rotate them by the same angle as the charged fields:
(G0
A0
)=√
2
(cos β sin β
− sin β cos β
) (φ0,i
1
φ0,i2
)
Then the mass term becomes
λ6
2(G
0A
0)
(0 0
0 v21 + v2
2
) (G0
A0
)
The G0 is the goldstone boson. The pseudoscalar mass is
m2A = λ6(v
21 + v
22)
pre-SUSY2008 Higgs 12
• Neutral Higgs bosons: We rotate the real part of φ01 and φ0
2 as(
H0
h0
)=√
2
(cos α sin α
− sin α cos α
) (φ0,r
1 − v1
φ0,r2 − v2
)
where it is assumed mH0 > mh0 . The mass matrix was
(φ0,r1 −v1 φ
0,r2 −v2)
(4v2
1(λ1 + λ3) + v22λ5 (4λ3 + λ5)v1v2
(4λ3 + λ5)v1v2 4v22(λ2 + λ3) + v2
1λ5
) (φ0,r
1 − v1
φ0,r2 − v2
)
The masses can be obtained as
m2H0,h0 =
1
2
[M11 + M22 ±
√(M11 −M22)2 + 4M2
12
]
and the mixing angle is
sin 2α =2M12√
(M11 −M22)2 + 4M212
, cos 2α =M11 −M22√
(M11 −M22)2 + 4M212
,
• So totally, we have 5 physical Higgs bosons: 2 charged, 2 CP even,
and 1 CP odd.
pre-SUSY2008 Higgs 13
MSSM Higgs Sector (Model II)
In model II, up-type fermions couple to φ1 while down-type fermions
couple to φ2:
L = −yuQLuRφ2 − ydQLdRφ1 + h.c.
We obtain the Yukawa interactions
L = − gmu
2mwsβ
uu(sin αH0
+ cos αh0) +
gmu cot β
2mw
uiγ5uA
0
− gmd
2mwcβ
dd(cos αH0 − sin αh
0) +
gmd tan β
2mw
diγ5dA
0
+g√
2mW
[d(mu cot βPR + md tan βPL)u H
−
+u(mu cot βPL + md tan βPR)d H+]
pre-SUSY2008 Higgs 14
MSSM Higgs potential
The Higgs fields of the model consist of the two Higgs doublets
Hu =
(H+
u
H0u
), Hd =
(H0
d
H−d
)
The Higgs potential receives contributions from F terms, D terms, andthe soft terms
W = εab
yu
QaH
buU
c − εab
ydQ
aH
bdD
c+ µε
abH
auH
bd
VF ≡∣∣∣∂W
∂φi
∣∣∣2
= |µ|2(|Hu|2 + |Hd|2)
VD ≡ 1
2(D
aD
a+ D
′D′) =
1
8(g
2+ g
′2)(|Hd|2 − |Hu|2)2 +
1
2g2|H†
uHd|2
Vsoft = m2Hu|Hu|2 + m
2Hd|Hd|2 + (Bε
abH
auH
bd + h.c.)
where Da = g φ†iτa
2φi, D′ = g′φ†i
Y2
φi. Putting all terms together theHiggs potential is
VH = (m2Hu
+ |µ|2)|Hu|2 + (m2Hd
+ |µ|2)|Hd|2 + (Bεab
HauH
bd + h.c.)
+1
8(g
2+ g
′2)(|Hd|2 − |Hu|2)2 +
1
2g2|H†
uHd|2
pre-SUSY2008 Higgs 15
We can make a comparison with the Higgs potential of the general2HDM and we should relate the coefficients λ1−6 to the presentparameters
λ2 = λ1
λ3 =1
8(g
2+ g
′2)− λ1
λ4 = λ1 −1
2(g
2+ g
′2)
λ5 = 2λ1 −1
2g′2
= λ6
m2Hu
+ |µ|2 = 2λ1v22 −
1
2m
2Z
m2Hd
+ |µ|2 = 2λ1v21 −
1
2m
2Z
B = −v1v2λ5 = − 1
2(4λ1 − g
′2)
Therefore, instead of 6 free parameter in the general 2HDM we have onlyTWO independent parameters in this Higgs sector. We can thereforepick two of them, usually one takes
tan β, mA0
All the other Higgs masses and the mixing angle can be expressed in
pre-SUSY2008 Higgs 16
terms of tan β and mA.
m2H+ = m
2A + m
2W
m2H0,h0 =
1
2
[m
2A + m
2Z ±
√(m2
A+ m2
Z)2 − 4m2
Zm2
Acos2 2β
]
cos 2α = − cos 2β
(m2
A −m2Z
m2H0 −m2
h0
)
sin 2α = − sin 2β
(m2
H0 + m2h0
m2H0 −m2
h0
)
where 0 ≤ β ≤ π/2, which implies that −π/2 ≤ α ≤ 0. These massrelations
mw ≤ mH+
mZ ≤ mH0
mh0 ≤ mA
mh0 ≤ mZ
The last relation guarantees a light Higgs boson.
pre-SUSY2008 Higgs 17
Higgs mass bound
On tree-level, the lightest CP-even Higgs boson has to be lighter thanthe Z boson. Searches at LEP1 and LEP2 have put a bound of 114.4GeV on mH . If the tree-level mass relations always hold, then the SUSYwould be ruled out. Fortunately, the radiative corrections to the Higgsboson mass is large.
m2h = m
2h(tree) + m
2h(loop)
m2h(tree) ≈ m
2Z −
4m2Zm2
A
m2A−m2
Z
cot β
m2h(loop) =
3m4t
4π2v2
[ln
(mt1
mt2
m2t
)+
|Xt|2m2
t1−m2
t2
ln
(m2
t1
mt2
)
+1
2
(|Xt|2
m2t1−m2
t2
)2 (2−
m2t1
+ m2t2
m2t1−m2
t2
ln
(m2
t1
m2t2
))]
where |Xt| = At − µ∗ cot β. Here v = 174 GeV.
The radiation correction is dominated by the stop loop. If the mixing is
pre-SUSY2008 Higgs 18
small, the correction is mainly due to the first term:
m2h(loop) ≈ 4400 ln(mt/mt)
It implies
mt1≈ mt exp
(m2
h −m2Z
4400GeV2
)
The minimum of mt is about 510 GeV in order to obtain mh > 115 GeV.
If |Xt| is large, then mt1will be much smaller than mt2
. This is a very
interesting scenario for the baryogenesis and searches at the LHC.
pre-SUSY2008 Higgs 19
Phenomenology of the MSSM or Model II Higgs bosons
• b → sγThe major contribution comes from the charged-Higgs loop of the2HDM The effective Hamiltonian at a scale of order O(mb) is
Heff = −GF√2
V∗
tsVtb
[ 6∑i=1
Ci(µ)Qi(µ) + C7γ(µ)Q7γ(µ) + C8G(µ)Q8G(µ)
].
The decay rate of B → Xsγ normalized to the experimentalsemileptonic decay rate is
Γ(B → Xsγ)
Γ(B → Xceνe)=|V ∗tsVtb|2|Vcb|2
6 αem
πf(mc/mb)|C7γ(mb)|2 ,
where f(z) = 1− 8z2 + 8z6 − z8 − 24z4 ln z. The Wilson coefficientC7γ(mb) is
C7γ(µ) = η1623 C7γ(MW ) + 8
3
(η
1423 − η
1623
)C8G(MW ) + C2(MW )
8∑i=1
hiηai ,
where η = αs(MW )/αs(µ). The coefficients Ci(MW ) at the leading
pre-SUSY2008 Higgs 20
order in 2HDM II are
Cj(MW ) = 0 (j = 1, 3, 4, 5, 6) ,
C2(MW ) = 1 ,
C7γ(MW ) = −A(xt)
2− A(yt)
6cot
2β − B(yt) ,
C8G(MW ) = −D(xt)
2− D(yt)
6cot
2β − E(yt) ,
where xt = m2t /M
2W , and yt = m2
t /m2H± .
The experimental data on b → s γ rate in 2003 was
B(b → s γ)|exp = 3.88± 0.36(stat)± 0.37(sys)+0.43−0.28(theory) .
The SM prediction is
B(b → s γ)|SM = (3.64± 0.31)× 10−4
,
which agrees very well the data. The constraint on new physicscontribution is, explicitly,
∆B(b → s γ) ≡ B(b → s γ)|exp − B(b → s γ)|SM = (0.24+0.67−0.59)× 10
−4,
pre-SUSY2008 Higgs 21
1 10 100tan β
300
600
900
1200
1500
1800
95%
C.L
. lim
it on
mH
+
(GeV
)
b−>sγ, B−B−
mixing
b−>sγ only
KC, Kong 2003
pre-SUSY2008 Higgs 22
• B0 −B0
The quantity that parameterizes the B0 −B0 mixing is
xd ≡∆mB
ΓB
=G2
F
6π2|V ∗td|2|Vtb|2f
2B BB mBηBτB M
2W (IWW + IWH + IHH) ,
IWW =x
4
[1 +
3− 9x
(x− 1)2+
6x2 log x
(x− 1)3
],
IWH = xy cot2β
[(4z − 1) log y
2(1− y)2(1− z)− 3 log x
2(1− x)2(1− z)+
x− 4
2(1− x)(1− y)
],
IHH =xy cot4β
4
[1 + y
(1− y)2+
2y log y
(1− y)3
],
with x = m2t /M2
W , y = m2t /m2
H± , z = M2W /m2
H± .
xd = 0.755± 0.015 .
We use the following input parameters |VtbV ∗td| = 0.0079± 0.0015,
f2BBB = (198± 30 GeV)2(1.30± 0.12), mB = 5279.3± 0.7 MeV, ηB = 0.55, and
τB = 1.542± 0.016 ps. Note that the value of |VtbV ∗td| is in fact determined by
the measurement of xd.
pre-SUSY2008 Higgs 23
• g − 2The data and the calculations of the SM in 2003 was
∆aµ ≡ aexpµ − a
SMµ = 426± 165× 10
−11(2.6σ)
At the present moment, the deviation is (Hagiwara et al. 2007)
∆aµ = (276± 81)× 10−11
(3.3σ)
For 2HDM: all higgs bosons contribute to aµ at one-loop level.
ν
H+
h, H, A
µ µ
γ
γµ µ
∆ahµ '
m2µ
8π2m2h
(gmµ
2mW
sin α
cos β
)2 (− 7
6− ln(m
2µ/m
2h)
)
pre-SUSY2008 Higgs 24
∆aHµ '
m2µ
8π2m2H
(gmµ
2mW
cos α
cos β
)2 (− 7
6− ln(m
2µ/m
2H)
)
∆aAµ ' −
m2µ
8π2m2A
(gmµ
2mW
tan β
)2 (− 11
6− ln(m
2µ/m
2A)
)
∆aH+µ '
m2µ
8π2m2H+
(gmµ
2mW
tan β
)2(− 1
6− 1
12
m2µ
m2H+
)
Dominated by small h and A.
∆ahµ(one− loop) is positive
∆aAµ (one− loop) is negative
Two-loop Barr-Zee diagrams with heavy fermions.
pre-SUSY2008 Higgs 25
h;A f ff ` ` `
∆ahµ = − α2
4π2 sin2θW
m2µ λµ
M2W
∑f=t,b,τ
Nf
c Q2f λf f
(m2
f
m2h
),
∆aAµ =
α2
4π2 sin2θW
m2µ Aµ
M2W
∑f=t,b,τ
Nf
c Q2f Af g
(m2
f
m2A
)
Dominated by τ and b loops
∆ahµ(two− loop) is negative
pre-SUSY2008 Higgs 26
∆aAµ (two− loop) is positive
Since the deviation is positive, we want to make A0 light and the h0
heavy such that the overall contribution is positive and large enough.
10 100mA (GeV)
10−9
5.10−9
10−8
∆aµA
tanβ=60tanβ=45tanβ=30tanβ=15
1−loop + 2−looppseudoscalar A
ALLOWED
KC, Kong 2003
pre-SUSY2008 Higgs 27
• The ρ parameter constrains the spectrum of the 2HDM.Essentially, it prefers small mass splitting among the bosons.However, some level of fine-tuning among various contributionsare still valid.
• There have been numerous collider searches for Higgs bosons ofthe 2HDM or the MSSM, in both the LEP2 and Tevatron. Wedo not list here.
pre-SUSY2008 Higgs 28
Adding an extra Higgs singlet field
pre-SUSY2008 Higgs 29
The NMSSM Superpotential
Superpotential:
W = huQ Hu Uc − hdQ Hd Dc − heL Hd Ec + λS Hu Hd +1
3κ S3.
When the scalar field S develops a VEV 〈S〉 = vs/√
2, the µ term is
generated
µeff = λvs√2
It was motivated by the µ problem.
pre-SUSY2008 Higgs 30
Higgs Sector
Higgs fields:
Hu =
(H+
u
H0u
), Hd =
(H0
d
H−d
), S .
Tree-level Higgs potential: V = VF + VD + Vsoft:
VF = |λS|2(|Hu|2 + |Hd|2) + |λHuHd + κS2|2
VD =1
8(g
2+ g
′2)(|Hd|2 − |Hu|2)2 +
1
2g2|H†
uHd|2
Vsoft = m2Hu|Hu|2 + m
2Hd|Hd|2 + m
2S |S|2 + [λAλSHuHd +
1
3κAκS
3+ h.c.]
Minimization of the Higgs potential links M2Hu
, M2Hd
, M2S with VEV’s of
Hu, Hd, S.
pre-SUSY2008 Higgs 31
In the electroweak symmetry, the Higgs fields take on VEV:
〈Hd〉 =1√2
(vd
0
), 〈Hu〉 =
1√2
( 0
vu
), 〈S〉 =
1√2
vs
Then the mass terms for the Higgs fields are:
V =(H
+d H
+u
)M2
charged
(H−
d
H−u
)
+1
2
(=mH
0d =mH
0u =mS
)M2
pseudo
=mH0d
=mH0u
=mS
+1
2
(<eH
0d <eH
0u <eS
)M2
scalar
<eH0d
<eH0u
<eS
pre-SUSY2008 Higgs 32
We rotate the charged fields and the scalar fields by the angle β to project out the
Goldstone modes. We are left with
Vmass = m2H±H
+H−
+1
2(P1 P2)M2
P
(P1
P2
)+
1
2(S1 S2 S3)M2
S
S1
S2
S3
where
M2P 11 = M
2A ,
M2P 12 = M2
P 21 =1
2cot βs
(M
2A sin 2β − 3λκv
2s
),
M2P 22 =
1
4sin 2β cot
2βs
(M
2A sin 2β + 3λκv
2s
)− 3√
2κAκvs ,
with
M2A =
λvs
sin 2β
(√2Aλ + κvs
), tan βs =
vs
v
M2S 11 = M
2A +
(M
2Z −
1
2λ
2v2)
sin22β ,
M2S 12 = M
2S 12 = − 1
2sin 4β
(M
2Z −
1
2λ
2v2)
,
pre-SUSY2008 Higgs 33
M2S 13 = M
2S 31 = − 1
2cot βs cos 2β
(M
2A sin 2β + λκv
2s
),
M2S 22 = M
2Z cos
22β +
1
2λ
2v2sin
22β ,
M2S 23 = M
2S 32 =
1
2
(2λ
2v2s −M
2A sin
22β − λκv
2s sin 2β
)cot βs ,
M2S 33 =
1
4M
2A sin
22β cot
2βs + 2κ
2v2s + κAκvs/
√2− 1
4λκv
2sin 2β
The MSSM limit can be recovered by λ → 0 and cot βs → 0.
pre-SUSY2008 Higgs 34
The charged Higgs mass:
M2H± = M
2A + M
2W − 1
2λ
2v2
The scalar Higgs bosons:The mass matrix M2
S is diagonalized by an orthogonal transformation
H3
H2
H1
= O
S1
S2
S3
In the approximation of large tan β and large MA, the physical scalarHiggs bosons masses are
m2H3
= M2A
(1 +
1
4cot
2βs sin
22β
),
m2H2/1
=1
2
[m
2Z +
κvs
2(4κvs +
√2Aκ)
±√(
m2Z− κvs
2(4κvs +
√2Aκ)
)2
+ cot2 βs
(2λ2v2
s −M2A
sin2 2β)2
]
pre-SUSY2008 Higgs 35
Pseudoscalar Higgs bosons
The pseudoscalar fields, Pi (i = 1, 2), is further rotated to mass basis A1 and A2,
through a mixing angle:
(A2
A1
)=
(cos θA sin θA
− sin θA cos θA
)(P1
P2
)
with
tan θA =M2
P 12
M2P 11 −m2
A1
=1
2cot βs
M2A sin 2β − 3λκv2
s
M2A−m2
A1
In large tan β and large MA, the tree-level pseudoscalar masses become
m2A2
≈ M2A (1 +
1
4cot
2βs sin
22β),
m2A1
≈ − 3√2
κvsAκ
pre-SUSY2008 Higgs 36
Parameters of NMSSM: NMHDECAY
Additional parameters other than the usual MSSM’s
λ, κ, Aλ, Aκ, µeff
Constraints inside the NMHDECAY (Ellwanger, Gunion, Hugonie):
• One-loop radiative corrections to Higgs potential
• b → sγ constraint
• Dark matter relic density constraint: [0.095, 0.112]
• LEP2 bounds
pre-SUSY2008 Higgs 37
A study of h → a1a1 → 4b in NMSSM (KC, Song, Yan RPL 2007)
NMSSM (A) NMSSM (B)
λ = 0.18, κ = −0.43 λ = 0.26, κ = 0.51
tan β = 29 tan β = 23
Aλ = −437 GeV Aλ = −222 GeV
Aκ = −4 GeV Aκ = −13 GeV
µeff = −143 GeV µeff = 144 GeV
mh1 = 110 GeV mh1 = 109 GeV
ma1 = 30 GeV ma1 = 39 GeV
B(h1 → a1a1) = 0.92 B(h1 → a1a1) = 0.99
B(a1 → bb) = 0.93 B(a1 → bb) = 0.92
gV V h1/gSMV V h = 0.99 gV V h1/gSM
V V h = −0.99
gtth1/gSMtth = 0.99 gtth1/gSM
tth = −0.99
gtta1/gSMtth = −2.4× 10−3 gtta1/gSM
tth = −1.2× 10−2
C24b = 0.80 C2
4b = 0.83
C24b ≡
(gZZh
gSMZZh
)2
× B(h → a1a1)× B2(a1 → bb)
pre-SUSY2008 Higgs 38
?: bench-mark point A-like
?: bench-mark point B-like
All evade the Higgs mass bound
pre-SUSY2008 Higgs 39
Further decay in h → a1a1
Further decay of a1 includes
h → a1a1 → (2γ, 2τ, 2b, 2g) (2γ, 2τ, 2b, 2g)
• If a1 is very light and so energetic that the two photons are very
collimated. It may be difficult to resolve them. Effectively, like
h → γγ.
• If the mixing angle is larger than 10−3 and a1 is heavier than a few
GeV, it can decay into τ+τ−. Thus, 4τs in the final state (Graham,
Pierce, Wacker 2006).
• If a1 is heavier than 2mb, a1 will dominately decay into bb.
• The gluon mode suffers from QCD background.
pre-SUSY2008 Higgs 40
Higgs Production at the LHC
• Gluon fusion gg → h → ηη → 4b suffers from huge QCD background.
• WW fusion qq → qqWW → qqh → qq(4b) also suffers from QCD
background.
• Wh, Zh associated production:
Wh → (`ν) + (4b) , Zh → (``) + (4b)
The charged lepton removes most QCD background.
• tth → (bW )(bW ) + (4b), combinatorial background.
Require at least one charged lepton and 4 b-tagged jets in the final state.
pre-SUSY2008 Higgs 41
Production and decay
We used MADGRAPH with the effective vertex gvvh to calculatethe signal cross sections. Decay of the W/Z and h:
pT (`) > 15GeV, |η(`)| < 2.5 ,
pT (b) > 15GeV, |η(b)| < 2.5 , ∆R(bb, b`) > 0.4 ,
We employ a B-tagging efficiency of 70% for each B tag, and aprobability of 5% for a light-quark jet faking a B tag.
pre-SUSY2008 Higgs 42
Backgrounds
• It is possible for the photon in γ + nj background to fake an
electron in the EM calorimeter.
• The backgrounds from W + nj and Z + nj contribute at a very low
level and are reducible as we require 4 b-tagged jets in the final state.
• The background from WZ → `νbb is also reducible by the 4
b-tagging requirement.
• tt production with one of the top decay hadronically and the other
semi-leptonically. The jet from the W may fake a b jet.
• ttbb production, irreducible.
• W/Z + 4b production, irreducible.
pre-SUSY2008 Higgs 43
Event rates
Channels NMSSM (A) NMSSM (B) SLHµ (A) SLHµ (B)
W+h signal 3.13 fb 9.54 fb 1.27 fb 0.63 fb
W−h signal 2.35 fb 6.55 fb 0.87 fb 0.44 fb
Zh signal 1.05 fb 2.76 fb 0.36 fb 0.18 fb
Background
Channels cross sections (fb)
tt 172 (NMSSM & SLHµ)
ttbb 236 (NMSSM), 284 (SLHµ A), 429 (SLHµ B)
W + 4b 3.80 (NMSSM), 4.16 (SLHµ A), 4.63 (SLHµ B)
Z + 4b 3.85 (NMSSM & SLHµ)
ttbb background is enhanced by ttη production in SLH model.
pre-SUSY2008 Higgs 44
4bm50 100 150 200 250 300 350 400 450
(fb
/GeV
)4b
d m
σd
0
1
2
3
4
5
6
7
4bm50 100 150 200 250 300 350 400 450
(fb
/GeV
)4b
d m
σd
0
1
2
3
4
5
6
7 4 blν - l→pp 4 blν + l→pp
4 b-l+ l→pp t t →pp
b b t t →pp
Apply the invariant mass cuts:
mh − 15 GeV < M4b < mh + 15 GeV ,
pre-SUSY2008 Higgs 45
Significance of the signal
Total signal and background cross sections under the signal peak:
NMSSM (A) NMSSM (B) SLHµ (A) SLHµ (B)
signal 6.53 fb 18.85 fb 2.50 fb 1.25 fb
bkgd 4.83 fb 4.77 fb 13.83 fb 22.45 fb
S/√
B 29.7 86.3 6.7 2.6
S/√
B for L = 100 fb−1
pre-SUSY2008 Higgs 46
Impact of the channel Wh → Wa1a1 → `ν + 4b
• The emergence of the Higgs boson decay mode into two
pseudoscalar bosons can relieve the so-called little hierarchy problem
and reduce the LEP2 Higgs boson mass bound.
• It may affect the golden search modes (h → γγ, bb) of the Higgs
boson significantly.
• With the h → a1a1 → 4b, together with at least a charged lepton
from the W or Z boson decay, a significant Higgs boson signal is
observable at the LHC.
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