MSSM Higgs Sector with Explicit CP-Violation · The CP-Violating MSSM Phenomenological Aspects MSSM...

The CP-Violating MSSMPhenomenological Aspects

MSSM Higgs Sector with

Explicit CP-Violation

SHOAIB MUNIR

Instituto de Fısica, UNAM, Mexico

November 24, 2008

SHOAIB MUNIR MSSM Higgs Sector with Explicit CP-Violation

References

S. Hasslebach, S. Moretti, S. Munir, P. Poulose, Eur. Phys. J.C 54 (2008) 129. [arXiv:0706.4269 [hep-ph]].

S. Moretti, S. Munir, P. Poulose, Phys. Lett. B 649 (2007)206. [arXiv:hep-ph/0702242]

Outline

1 The CP-Violating MSSMMSSM Higgs SectorExplicit CP-Violation

Outline

1 The CP-Violating MSSMMSSM Higgs SectorExplicit CP-Violation

2 Phenomenological AspectsThe Di-photon Decay ModeSignatures of CP-Violation

MSSM Higgs SectorExplicit CP-Violation

The MSSM Higgs Sector

The simplest possible MSSM superpotential (with R-parity)

WMSSM = QHuhuUC + HdQhdD

C + Hd LheEC + µHuHd

The full Higgs potential can be written as

VH = m21|Hd |2 + m2

2|Hu|2 − m23ǫij(H

u + h.c.)

2 + g 21

8(|Hd |2 − |Hu|2)2 +

2 |H†dHu|2,

where m21 = |µ|2 + m2

1 , m22 = |µ|2 + m2

2 , m23 = Bµ

After EWSB, the two Higgs doublets are expanded around VEVs

Hu =1√2

vu + H0u + iP0

), Hd =

(vd + H0

d + iP0d

VH = m21|Hd |2 + m2

u + h.c.)

2 + g 21

8(|Hd |2 − |Hu|2)2 +

2 |H†dHu|2,

where m21 = |µ|2 + m2

1 , m22 = |µ|2 + m2

2 , m23 = Bµ

Hu =1√2

vu + H0u + iP0

), Hd =

(vd + H0

d + iP0d

VH = m21|Hd |2 + m2

u + h.c.)

2 + g 21

8(|Hd |2 − |Hu|2)2 +

2 |H†dHu|2,

where m21 = |µ|2 + m2

1 , m22 = |µ|2 + m2

2 , m23 = Bµ

Hu =1√2

vu + H0u + iP0

), Hd =

(vd + H0

d + iP0d

5 Higgs states; H±, h, H (mh < mH) and A

Holomorphic superpotential; no CP-violation at tree level

Explicit CP-violation can be radiatively invoked by complex SUSYparameters such as

the Higgs-Higgsino mass parameter µthe soft SUSY-breaking gaugino masses mλ

the soft bilinear Higgs mixing mass Bµthe soft trilinear Yukawa couplings Af

The universality condition leaves common phases for mλ and Aλ

One of the Higgs doublets and the gaugino fields λ rephased suchthat mλ and Bµ become real

Two physical CP-violating phases left: arg(µ) and arg(Af )

...continued

CP-violating phases introduce non-vanishing off-diagonal mixingterms in the Higgs mass matrix now given as

S M2SP

M2PS M2

where M2PS = (M2

SP)T ∝ I(µAf )M2

Higgs bosons do not carry any definite CP-parities; rotation fromthe Electroweak states to the mass eigenvalues is now carried out bya 3 × 3 real orthogonal matrix O as:

(φ1, φ2, a)T = O(H1, H2, H3)

instead of the usual 2 × 2 one with rotation angle α

...continued

CP-violating phases introduce non-vanishing off-diagonal mixingterms in the Higgs mass matrix now given as

S M2SP

M2PS M2

where M2PS = (M2

SP)T ∝ I(µAf )M2

Higgs bosons do not carry any definite CP-parities; rotation fromthe Electroweak states to the mass eigenvalues is now carried out bya 3 × 3 real orthogonal matrix O as:

(φ1, φ2, a)T = O(H1, H2, H3)

instead of the usual 2 × 2 one with rotation angle α

The Di-photon Decay ModeSignatures of CP-Violation

Higgs Decay into two Photons

Our primary focus is the di-photon decay channel as

According to the ATLAS TDR, σ × BR(H → γγ) rates of 10fb or so may yield visible signal eventsThe tail of the γγ background rapidly falls with increasinginvariant mass of the di-photon pair, hence the photondetection efficiency grows with the Higgs mass

It is one of the most promising channel for the discovery of a(neutral) Higgs boson at the LHC for moderate Higgs mass

τ+τ−

γγ Zγ

MH [GeV]50 100 200 500 1000

τ+τ−

γγ Zγ

MH [GeV]50 100 200 500 1000

τ+τ−

γγ Zγ

MH [GeV]50 100 200 500 1000

Effects of CP-Violation

In the di-photon decay mode, the effects of explicit CP-violationmanifest themsleves at the leading order in perturbation theory

The effective Lagrangian describing Higgs interactions

LHi f f = −∑

f =u,d,l

Hi f (gSHi f f

+ igPHi f f

where (gS , gP) = (Oφ1i/ cosβ,−Oai tan β) for f = (l , d)and (gS , gP) = (Oφ2 i/ sinβ,−Oai cotβ) for f = u

An MSSM Higgs decays into two photons as

h,H,A f, χ±

h,H W,H±, f

W,H±, f

LHi f f = −∑

f =u,d,l

Hi f (gSHi f f

+ igPHi f f

An MSSM Higgs decays into two photons as

h,H,A f, χ±

h,H W,H±, f

W,H±, f

LHi f f = −∑

f =u,d,l

Hi f (gSHi f f

+ igPHi f f

Code and Parameters

Code: CPSuperH; computes decay widths and BRs of the MSSMHiggses as well as their total widths at their respective pole massesor effective potential masses

MSSM inputs for the code includeMH± , tan β, µ, φµ, M(1,2,3), φ(1,2,3), M(Q3,U3,D3,L3,E3)

, Af , φAf

φAf= 0 and φµ varied

Variation in the Higgs masses and γγ BR in different regions of theparameter space with varying CP-violating phases

Collider constraints on loop (s)particle masses

Aim: Searching regions in the parameter space where the variationin BR due to CPV phases is maximized

Code and Parameters

, Af , φAf

Code and Parameters

, Af , φAf

Code and Parameters

, Af , φAf

Code and Parameters

, Af , φAf

Code and Parameters

, Af , φAf

Code and Parameters

, Af , φAf

Comparison of γγ BRs

92 96 100 104 108 112 116 120 124 128MH1

ϕµ=20o

ϕµ=40o

ϕµ=60o

ϕµ=80o

ϕµ=100o

ϕµ=120o

ϕµ=140o

ϕµ=160o

•R iφµ

BR(i,n)φ

−BR(i,n)0

n BR(i,n)0

tan β: 1–60;

|µ|: 100–2000 GeV;

φµ: 0◦–160◦;

MH± : 100–500 GeV;

M2: 100–500 GeV;

M(Q3,U3,D3,L3,E3):

100–2000 GeV;

|Af|: 100–2000 GeV;

φAf: 0;

M1: 100 GeV;

M3: 1 TeV

Mean Percentage Deviation

92 96 100 104 108 112 116 120 124 128MH1

ϕµ=20o

ϕµ=40o

ϕµ=60o

ϕµ=80o

ϕµ=100o

ϕµ=120o

ϕµ=140o

ϕµ=160o

•R i′

n |BR(i,n)φ

−BR(i,n)0 |

n BR(i,n)0

∼ 70%

for φµ = 160◦;

∼ 30%

for φµ = 40◦;

MH1= 104 GeV

• Not possible

to see whether

there is a rise

in BRφµwrt BR0

or fall

Some Sample Points

0.0005

0.0015

0.0025

116 118 120 122 124MH1 (GeV)

BR (H1 −> γγ)

ϕµ=0o

90o 180o

• A drop in BR when noneof the sparticles is light;main contribution comes fromthe modified couplings of theSM particles to the Higgsesas a result of the mixing betweendifferent CP-states

Some Sample Points

0.0005

0.0015

0.0025

116 118 120 122 124MH1 (GeV)

BR (H1 −> γγ)

ϕµ=0o

90o 180o

• A drop in BR when noneof the sparticles is light;main contribution comes fromthe modified couplings of theSM particles to the Higgsesas a result of the mixing betweendifferent CP-states

0 20 40 60 80 100 120 140 160 180

ϕµ (in deg)

• Variation in Higgs massMass of H1 as a function of φµ.Solid line corresponds to the case whennone of the sparticles going into theloops is light while dashed linerepresents the case when the t1is light (of order 200 GeV)

Contribution due to Sparticles

0.0005

0.0015

0.0025

116 118 120 122 124MH1 (GeV)

BR (H1−> γγ)

ϕµ=180o90o 0o

0 20 40 60 80 100 120 140 160 180

ϕµ (in deg)

• Rise in

BRCPV when

the t1 is

light due to

maximum vari-

ation in its

own mass

Contribution due to Sparticles

0.0005

0.0015

0.0025

116 118 120 122 124MH1 (GeV)

BR (H1−> γγ)

ϕµ=180o90o 0o

0 20 40 60 80 100 120 140 160 180

ϕµ (in deg)

• Rise in

BRCPV when

the t1 is

light due to

maximum vari-

ation in its

own mass

0.0005

0.0015

0.0025

116 118 120 122 124

MH1 (GeV)

ϕµ=0o

90o180o

0 20 40 60 80 100 120 140 160 180

ϕµ (in deg)

• Negligible

variation when

the b1 has

mass close

to the

lower bound;

O(300 GeV)

Progress and Plans

Calculating the effects of CP-Violation in the production process:

q, q1,2

The propagator matrix to be calculated initially at one loop level

CP-violating phases enter at each vertex - significant deflection inthe production cross section from anticipated

The only observables in the process are the Higgs cross sections andmasses

To reduce CPV effects, the Higgs-strahlung production mode couldbe used as a precedent

Progress and Plans

q, q1,2

Progress and Plans

q, q1,2

Progress and Plans

q, q1,2

Progress and Plans

q, q1,2

MSSM Higgs Sector with Explicit CP-Violation · The CP-Violating MSSM Phenomenological Aspects MSSM...

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