Lecture 2: Weakly-coupled Higgs bosons Problems with the ...

46
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 Higgs bosons.

Transcript of Lecture 2: Weakly-coupled Higgs bosons Problems with the ...

Page 1: Lecture 2: Weakly-coupled Higgs bosons Problems with the ...

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.

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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.

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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.

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• Weakly-coupled models, e.g., supersymmetry. It predicts new scalars

such that they systematically cancel the quadratic divergences

H H

S

∆M2H =

λS

16π2

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.

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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

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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

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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.

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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.

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• 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

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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±

)=

(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+

)

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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)

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• 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.

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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+]

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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

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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

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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.

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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

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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.

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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

1423 − η

1623

)C8G(MW ) + C2(MW )

8∑i=1

hiηai ,

where η = αs(MW )/αs(µ). The coefficients Ci(MW ) at the leading

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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,

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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

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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.

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• 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)

)

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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.

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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

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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

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• 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.

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Adding an extra Higgs singlet field

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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.

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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.

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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

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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

2v2)

sin22β ,

M2S 12 = M

2S 12 = − 1

2sin 4β

(M

2Z −

1

2v2)

,

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M2S 13 = M

2S 31 = − 1

2cot βs cos 2β

(M

2A sin 2β + λκv

2s

),

M2S 22 = M

2Z cos

22β +

1

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.

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pre-SUSY2008 Higgs 34

The charged Higgs mass:

M2H± = M

2A + M

2W − 1

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

]

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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

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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

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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)

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pre-SUSY2008 Higgs 38

?: bench-mark point A-like

?: bench-mark point B-like

All evade the Higgs mass bound

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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.

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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.

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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.

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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.

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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.

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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 ,

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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

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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.