Higgs sector of NMSSM in the light of Higgs Discovery

Higgs sector of NMSSM in the light of HiggsDiscovery

Jacky KumarCollaboration :Monoranjan Guchait

Tata Institute of fundamental research

December 11, 2014

Jacky Kumar , Collaboration :Monoranjan Guchait, Tata Institute of fundamental research Higgs sector ofNMSSM in the light of Higgs Discovery slide 1 /34

Content:

• Higgs Discovery and NMSSM• 125.7 GeV Higgs in NMSSM

• LHC constraint and its impact on parameter space• Conclusion


Motivation: Higgs Discovery and NMSSM

Higgs Discovery: LHC hasfound a Higgs like particle.

Mass : 125.7GeV

CMS : µ = 1.00± 0.13

=⇒ Consistent with Standardmodel but some discrepancy is still

allowed.

But SM suffers from Naturalnessproblem, need some mechanism tocancel the quadratic divergences,and possibility of the found Higgsas non-standard Higgs is not ruled

out .

Possible solution isSupersymmetry:

So one possibility is this can beMSSM Higgs.

But it is difficult to get 125.7GeV value in MSSM because:

In decoupling limit, upperbound on mh:

m2h = m2

Z cos2 2β + δ2t

δ2t comes from top squarks/ top

quark loops

At large tanβ it requiresδt ∼ 85 GeV

To achieve this value we need.......


Motivation: Higgs Discovery and NMSSM

Heavy top squarks or largemixing in stop mass matrix:

But these give largecontributions to quadratic term

of Higgs potential δm2Hu

=

− 3y 2t

8π2

(m2

Q3+ m2

u3+ |A2

t |)

ln Λmt

If m2Hu

becomes too largeparameters of the theory has tobe tuned to get correct scale of

EWSB .

This motivated us to studynon-minimal models.

[L.Hall et al. 1112. 2703]

One such model isNext-to-Minimal-

supersymmetric-Standard-modelabbreviated as NMSSM:

It was originally introduced tosolve µ problem of MSSM.

But it has importance in thecontext of Higgs discovery,

because it also offers 125.7 GeVHiggs mass..


Introduction to NMSSM

MSSM: two Higgs doublets

H1 =

[Ho

1

H−1

],H2 =

[H+

2

H02

]NMSSM: two Higgs doublets + one singlet

H1 =

[Ho

1

H−1

],H2 =

[H+

2

H02

], S

NMSSM: → solves µ problem→ easy to accommodate 125.7 GeV Higgs boson found at LHC

S → addition of CP even scalar→ addition of CP odd scalar→ addition of neutralino


µ problem : Superpotential MSSM and NMSSM :MSSM:

WMSSM = µ.H1.H2 − hdH1.Q D − huQ.H2 U − heH1.L E

Expected µ(since dimensionful parameter) ∼ either zero or planck scaleCorrect phenomenology demand, µ ∼ EW sacle : that is known as µproblemNMSSM:

WMSSM = λH1.H2 S + 12κS

3 − hdH1.Q D − huQ.H2 U − heH1.L E

No dimensionful parameter and when S gets v.e.v,

µeff = λvs


NMSSM scalar potential and Parameters dependence :

V = VF + VD + Vsoft ,

VF = |λS |2(|Hu|2 + |Hd |2) + |λHuHd + κS2|2

VD = 18 g

2(|Hd |2 − |Hu|2)2 + 12g

2|H†uHd |2

Vsoft = m2Hu|Hu|2 + m2

Hd|Hd |2 + m2

S |S |2 +[λAλSHuHd + 1

3κAκS3 + h.c

]3 scalars: h1, h2, h3, 2 pseudo scalars a1, a2, 2 charged H±

Couplings: λ, κ

Soft parameters: Aλ,Aκ

Related to v.e.v: tanβ, µeff

Radiative Corrections: m2Q ,m

2u,m

2d ,Au,Ad


Upper bound on Higgs mass :

MSSM:

m2h = m2

z cos2 2β

+3m4

t

4π2v 2

[ln

(m2

T

m2t

)+

A2t

m2T

(1−

A2t

12m2T

)]Tree level bound 91 GeV ! Need

large radiative corrections toachieve 125.7 =⇒ either heavy

stops or large mixing

NMSSM:

m2h = m2

z cos2 2β + λ2v 2 sin2 2β

−λ2v 2

κ2(λ− κ sin 2β)2

+3m4

t

4π2v 2

[ln

(m2

T

m2t

)+

A2t

m2T

(1−

A2t

12m2T

)]Tree level bound 122 GeV ! Do

not have to rely on large radiativecorrections to achieve 125.7 =⇒

light stops allowed stops[U. Ellawanger et al. 0910.1785]

In our scan we found that even 200GeV stops can give desired Higgsmass. In this sense NMSSM is morenatural.


Higgs Spectrum:

Approximate solutions (large tanβ and largeMA) :

m2h1/2

=1

2

(m2

Z +1

2κvs(4κvs +

√2Aκ)

)

±

√[m2

Z −1

2κvs(4κvs +

√2Ak)

]2+ cot2 vs

[2λ2v2

s −M2A sin2 2β

]2m2

h3= m2

a2= m2

A

(1 +

1

2cot2 βs sin2 2β

)m2

a1= − 3√

2κvsAκ

mh± = m2A + M2

W −1

2(λv)2

[Miller et al. hep-ph/0304049]


λ, κ vs Higgs Mass :λ ∼ 0.25, κ ∼ 0.25, tan β ∼ 7,Aλ ∼ 550,Aκ ∼ −500, µ ∼ 122

At ∼ 3000,Ab ∼ 2000,mQ3= mu3

= md3= 1000

0

200

400

600

800

1000

0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26

Hig

gs M

ass(G

eV

)

λ

CP-evenCP-oddcharged

3GeV band

0

200

400

600

800

1000

0.2 0.3 0.4 0.5 0.6 0.7 0.8H

iggs M

ass(G

eV

)

κ


3GeV band

Note: at λ = 0.21, h2 becomes SM like and be-yond that mh1

falls down till it spoils the vacuumstability. This can explained from :

m2h1

+ m2h2

=

(m2

Z +1

2κvs (4κvs +

√2Aκ)

)Interesting: while h2 SM like Higgs,singlet like (hence can pass LEP con-straint) h1 can be very even few GeV!We keep this point in mind and look forthis kind of region - this we call our sce-nario Ia. Note: a1 is heavy here.


Aλ, Aκ vs Higgs Mass :

0

100

200

300

400

500

-500 -400 -300 -200 -100 0

Hig

gs M

ass(G

eV

)

Aκ(GeV)


3GeV band

0

200

400

600

800

1000

0 200 400 600 800 1000 1200 1400

Hig

gs M

ass(G

eV

)

Aλ(GeV)


3GeV band

Note: Vaccum stability stricts Aκ from below andabove. From above ma1

becomes -ve. From be-low mh1

becomes -ve. mh1and ma1

are inverselycorrelated. This can explained from :

m2h1

+ m2h2

=(

m2Z + 1

2κvs (4κvs +√

2Aκ))

m2a1

= −3√

2κvs Aκ

Interesting: We can tune Aκ to getvery light singlet like a1 (both for ei-ther h1 SM like (scenario II) or h2 SMlike(scenario Ib)) or h1 light(for h2 SMlike scenario I a) a1 light for Aκ ∼−10GeV and h1 light for Aκ ∼ −450GeV


125.7 GeV Higgs within NMSSM

• NMSSM can accommodate 125.7 Higgs, simultaneously satisfyingphenomenological constraints. Using NMSSMTools (U. Ellawanger etal.), considering all phenomenological constraints we identified the regionof parameter space where:

Ia) h2 is SM like , h1 is very light

Ib) h2 is SM like, a1 is very light

II) h1 is SM like , a1 very light.

• We ensured that the recent coupling measurements of scalar does notspoil our predictions.

Reduced couplings:

gNMSSMv = cvg

SMv , g

NMSSMu = cug

SMu

gNMSSMd = cdg

SMd , g

NMSSMg = cgg

SMg

gNMSSMγ = cγg

SMγ

Note: by SM like we mean that its couplings to fermions and bosons are same

(or close to) SM couplings and m = 125.7 GeVJacky Kumar , Collaboration :Monoranjan Guchait, Tata Institute of fundamental research Higgs sector of

NMSSM in the light of Higgs Discovery slide 12 /34

LHC constraints

LHC Constraints:

Mass of h1 or h2 should lie within :

122.7 ≤ mSMh ≤ 128.7

Scenario Ia: NSM Channels : BR(h1− > h1h1) , BR(h1− > χ01χ

01)

Scenario Ib: NSM Channels : BR(h1− > a1a1) , BR(h1− > χ01χ

01)

Scenario II: NSM Channels : BR(h1− > a1a1) , BR(h1− > χ01χ

01)

Sum of all non-standard model BR’s has to satisfy:

BRNS ≤ .58

For h1 or h2 to be SM like, its couplings should be as:

cv = 0.64− 1.26cu = 0.97− 2.28cd = 0.0− 1.31

cg = 0.51− 1.09cγ = 0.66− 1.37

[CMS-PAS-HIG-14-009]Jacky Kumar , Collaboration :Monoranjan Guchait, Tata Institute of fundamental research Higgs sector of


LHC constraints : Non Standard Branching fractions in Scenario I

h2SML

Non-Standard BR’s Before LHC After LHC

BR(h2 → a1a1) 39.1 30.8

BR(h2 → χ01χ

01) 28.9 28.9

BR(h2 → h1h1) 30.5 30.5


Impact of LHC constraint:Scenario I : h2 is SM like

Reduced couplings of h1

C h2u = S21

sin β

C h2d = S22

cos β

C h2v = sinβS21 + cosβS22 = ξ2

Standard Model limit:

Ideally C h2u = C h2

d = C h2v = 1

This limit has important consequences:S21 = sinβ, S22 = cosβ =⇒ ξ2 = 1

ξ2i = 1 =⇒ ξ1 = ξ3 = 0

i.e h1, h3 VBF channel is closed

Further∑ξ2

i .m2hi

= m2z (cos2 2β + λ2

g2 sin2 β) +rad . =⇒

m2h2

= m2z (cos2 2β + λ2

g2 sin2 β) + rad .

i.e Singlet Decouples. =⇒ h2 is purelydoublet like


Scenario I, Singlet Decouples

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

122 123 124 125 126 127 128 129

Sin

gle

t C

om

po

nen

t of h

2

mh2(GeV)

Excon+g-2Excon+g-2+LHC

Excon+g-2+Planck+LHC

• Light h2 would be mainly doublet like and will act as a SM like Higgs.


Scenario II, Doublet Component of h1 decouples: its consequences

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100 120 140

Sin

glet

Com

pone

nt o

f h1

mh1(GeV)

Excon+g-2Excon+g-2+LHC

Excon+g-2+Planck+LHC

• Around 125.7 GeV h1 is mainly doublet like, which is ruled out byLHC constraint =⇒ 2 SM like degenerate CP even Higgses of mass125.7 GeV are disallowed, Note : Singlet like h1 of mass 125.7 GeVstill allowed but would be difficult to produce because..


Scenario I : It decouples from VBF channel

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100 120 140

ch 1v

v

mh1(GeV)

excon+g-2+g-2+LHC

excon+LHC+Planck

• h1 of 125.7 GeV decouples from VBF channel.


Scenario I, h2 being SM like, mh1 vs ma1 , λ vs Aκ

0

20

40

60

80

100

120

140

0 50 100 150 200

mh

1(G

eV

)

ma1(GeV)

excon+g-2excon+g-2+LHC

excon+g-2+LHC+Planck 0.1

0.2

0.3

0.4

0.5

0.6

0.7

-600 -500 -400 -300 -200 -100 0 100 λ

Aκ

Legend

left h1 light right a1 lighth1 GM2+Pa1 GM2+Ph1 GM2+P+La1 GM2+P+L

• mh1 and ma1 are inversely correlated.• Aκ separates out region of parameter space for scenario Ia and Ib.


Scenario I, h2 being SM like, mst1 vs At

0

200

400

600

800

1000

1200

1400

-4000 -3000 -2000 -1000 0 1000 2000 3000 4000

mst 1

(GeV

)

At(GeV)

Legend

+g-2+g-2+Planck

+LHC

• For light top squarkslarge mixing is not neces-sary to get the value of125.7 GeV.


LHC constraints : Non Standard Branching fractions Scenario II

h1SML

Non-Standard BR’s Before LHC After LHC

BR(h1 → a1a1) 26.2 26.2

BR(h1 → χ01χ

01) 26.0 26.0


Impact of LHC constraint:Scenario II : h1 is SM like

Reduced couplings of h1

C h1u = S11

sin β

C h1d = S12

cos β

C h1v = sinβS11 + cosβS12 = ξ1

Standard Model limit:

Ideally C h1u = C h1

d = C h1v = 1

This limit has important consequences:S11 = sinβ, S12 = cosβ =⇒ ξ1 = 1

ξ2i = 1 =⇒ ξ2 = ξ3 = 0

i.e h2, h3 VBF channel is closed

Further∑ξ2

i .m2hi

= m2z (cos2 2β + λ2

g2 sin2 β) +rad . =⇒

m2h1

= m2z (cos2 2β + λ2

g2 sin2 β) + rad .

=⇒ S13 = 0 i.e Singlet Decouples


Scenario II:For C h2v vs mh2

Note:As expected mh2 of mass near125 GeV (i.e doublet like ) is tightlyconstrained LHC means only sin-glet like second lightest Higgs afterLHC? constraint.


Scenario II:For h1 SM like, mh2 vs ma1 , mst1 vs At

• For light top squarks, largemixing is not necessary


LHC phenomenology: In progress

For Scenario Ia, NMSSM predicts a singlet like CP even scalar : few GeV to129 GeV.

For Scenario Ib, NMSSM predicts a singlet like CP odd scalar : few GeV to 500GeV.

For Scenario II, NMSSM predicts a singlet like CP odd scalar : few GeV to 500GeV.

How to produce them ? This could be possibly produced in h2 → xxDifficult to produce directly since they are singlet like. Predominant decaymodes of x ≥ 10.5 GeV: x → bb x = h1 or a1.


Conclusion

In context of Higgs Discovery NMSSM is more natural

model as compare to MSSM and solves the µ problem

of MSSM.

LHC constraints do not destroy the well known fact that in

NMSSM it is possible to have light stops without necessarily

having maximal mixing .

NMSSM predicts very light CP even as well as CP scalar,

so has quite interesting phenomenology for LHC.

2 degenerate SM like Higges are not allowed after putting

LHC constraints.

Thanks for your attention.Jacky Kumar , Collaboration :Monoranjan Guchait, Tata Institute of fundamental research Higgs sector of


Backup

Range of parameter scanned

Specific to Higgs sector

λ ∼ 0.1− 0.8

κ ∼ 0.1− 0.8

tanβ ∼ 1.5− 30

µ(GeV ) ∼ 100− 2000

Aλ(GeV ) ∼ 0− 1000

Aκ(GeV ) ∼ −600, 100

Fixed parameters(GeV)

AD3 = 2000,mD3 = 1000

AE1 = AE2 = 0, AE3 = 1000

mL1 = mL2 = 100,mL3 = 1000

mE1 = mE2 = 100,mE3 = 1000

mQ1 = mQ2 = mU1 = mU2

= mD1 = mD2 = 1000

M3 = 1200

Gaugino mass parameters (GeV)

M1 ∼ 50− 500

M2 ∼ 50− 500

Third generation (GeV)

At ∼-4000 ,4000

MQ3 ∼ 500 -3000

mU3 ∼ 500- 3000Jacky Kumar , Collaboration :Monoranjan Guchait, Tata Institute of fundamental research Higgs sector of


Good range of parameters

Parameter h1SML,ma1 ≤mh1

2h2SML,mh1 ≤

mh22

h2SML ,ma1 ≤mm2

2

λ 0.1 - 0.7 0.2-0.7 0.35-0.7

κ 0.1 - 0.65 0.1-0.24 0.1-0.18

tanβ 1.5-21 3-14 4-13

µ(GeV) 118 - 1993 150-398 150-231

Aλ(GeV) 0 - 1999 564-1961 858-1991

Aκ (GeV) -100 - (+11) -515 - (-146) -52-(+22)

Table: Range of parameters subject toall experimental constraints


The Higgs Sector of NMSSM

Re[ H01 ,H

02 ,S ] gives 3× 3 CP even Higgs mass matrix ,

Diagnalization: hi = SijHrj =⇒ 3 CP even Higgses

Imm[ H01 ,H

02 ,S ] gives 3× 3 CP odd Higgs mass matrix ,

Roation : Ai = RβSIH I

j , Ai = [A,G ,S ]

Dropping the Goldston mode A′

i = [A,S ]

Diagnalization: ai = PijA′

j =⇒ 2 CP odd Higges

H+ = [H+2 ,H

+1 ] gives 2× 2 chagrged Higgs mass matrix

Diagnalization: H+i = Rβij H

+j , H+

i = [H+,G+]

Dropping the Goldston mode G+ =⇒ 2 Charged Higgses


0

200

400

600

800

1000

2 4 6 8 10 12 14 16

Hig

gs M

ass(G

eV

)

tanβ


3GeV band

0

200

400

600

800

1000

1200

1400

100 200 300 400 500 600 700 800 900 1000H

iggs M

ass(G

eV

)

µ(GeV)


3GeV band


Couplings and Non-Standard BRconstraints from LHC(New)

BRNS ≤ .58

cv = 0.64− 1.26cu = 0.97− 2.28cd = 0.0− 1.31

cg = 0.51− 1.09cγ = 0.66− 1.37

Theoretical constraints

• Positivity of m2h1,m2

a1,m2

h+ i.e vaccum

stability

• Problem in integration of RGEs

• Convergence problem

• λ, tan β or µ = 0


Scenario I:For h1 SM like, Couplings of a1

• This explains why very light a1 haspassed LEP bound in our scans. Becausea1 is inert for fermions.


LHC constraints : Scenario I

0.8

0.85

0.9

0.95

1

1.05

0.8 0.85 0.9 0.95 1 1.05

cuh

2

cvh2

Excon+g-2+PlanckExcon+g-2+Planck+LHC

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0.8 0.85 0.9 0.95 1 1.05

cdh

2

cvh2



LHC constraints : Scenario II

0.95

0.96

0.97

0.98

0.99

1

1.01

0.95 0.96 0.97 0.98 0.99 1 1.01

cuh

1

cvh1


0.9

0.95

1

1.05

1.1

0.95 0.96 0.97 0.98 0.99 1 1.01 1.02

cdh

1

cvh1



LHC constraints : Scenario II

0.9

0.95

1

1.05

1.1

0.95 0.96 0.97 0.98 0.99 1 1.01 1.02

cdh

1

cvh1



Higgs sector of NMSSM in the light of Higgs Discovery

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