hhh Coupling in SUSY models after LHC run I

Mengchao Zhang (ITP,CAS,CHINA)Collaborators: J.M. Yang, C-P Yuan, L. Wu

2015.02.15

HPNP2015/TOYAMA UNIVERSITY

Outline

I Introduction

I hhh coupling in MSSM & NMSSM under current constraints

I hhh coupling relation to the measurements in future colliders

I Conclusion

Mengchao Zhang 2/19

Motivation and hhh Coupling in SM

I In order to describe the full Higgs sector, we need to know the

Higgs self-coupling.

I Multi-Higgs New Physics models always have very non-SM-like

Higgs self-coupling

I It’s important to show how large this deviation will be and whether

the future colliders could detect such deviation

Mengchao Zhang 3/19

Motivation and hhh Coupling in SM

SM Higgs sector:

L = (DµΦ)†(DµΦ)− V (Φ) (1)

V (Φ) =λ

4(Φ†Φ)2 − µ2Φ†Φ,Φ =

(φ+

φ0

)(2)

In Unitary gauge we have:

Φ =

(0

1√2

(v + h)

), v = 2

µ√λ

(3)

Then the tree-level potential will yield:

mh =

√λ

2v, λhhh =

3

2λv =

3m2h

v(4)

Consider the one loop top correction, we get:

λhhh =3m2

h

v− 3m4

t

π2v3(5)

Mengchao Zhang 4/19

Effective Potential Method

Vtree = m211Φ†

1Φ1 + m222Φ†

2Φ2 − [m212Φ†

1Φ2 + h.c .]

+1

8(g2

2 + g21 )(Φ†

1Φ1)2 +1

8(g2

2 + g21 )(Φ†

2Φ2)2

+1

4(g2

2 − g21 )(Φ†

1Φ1)(Φ†2Φ2)− 1

2g22 (Φ†

1Φ2)(Φ†2Φ1) (6)

Φ1 =

(H+

11√2

(v1 + H01 + iA0

1)

),Φ2 =

(H+

21√2

(v2 + H02 + iA0

2)

)(7)

In SUSY models, for example the MSSM, mH is not an inputparameters but a calculable quantity that mainly controlled by top andstop sector, and the tree-level couplings are fixed by gauge couplingsconstants. So one may expect a very different hhh coupling in SUSY.Let’s perform a simple estimation first.

Mengchao Zhang 5/19

Effective Potential Method

Correction to triple coupling is(simplified stop sector):

Γt,thhh =

3m4t

2π2v3

(3 ln

m2t

m2t

− 2

)(8)

So it seems we get a very large corrections from top/stop sector. But thetop/stop correction to Higgs mass is:

∆m2h =

3m4t

2π2v2ln

m2t

m2t

(9)

So if we shift the tree level Higgs mass to the one-loop level Higgs mass,the relationship we found in SM still hold.

W. Hollik, S. Penaranda. Eur. Phys. J. C 23, 163–172 (2002)

Mengchao Zhang 6/19

Effective Potential Method

As we’ve seen, the loop correction to hhh coupling may have a

corresponding part in the loop correction to Higgs mass. So the key point

in here is to treat the hhh coupling and Higgs mass in a consistent

way.

A convenient way to perform such a consistent calculation is the

effective potential method. The effective potential method can absorb

the dominant loop contribution into the effective couplings in low energy

scale and deal with the Higgs mass and coupling in the same accuracy.

Mengchao Zhang 7/19

Effective Potential Method

These infinity Feynman graphs series can be summed to a elegantexpression:

V(1) =3

16π2

{m4

t

(ln

m2t

µ2− 3

2

)−m4

t

(ln

m2t

µ2− 3

2

)}(10)

{expand the effective potential in SUSY scale

ignore the high dimensional operators

}⇒{

effective couplings in

low energy scale

}M. Carena, J.R. Espinosa, M. Quiros and C.E.M. Wagner. Phys.Lett. B355 (1995) 209-221Howard E. Haber and Ralf Hempfling.Phys.Rev. D48 (1993) 4280-4309Ellis J, Ridolfi G, Zwirner F. Physics Letters B, 1991, 257(1): 83-91.Okada Y, Yamaguchi M, Yanagida T.Progress of Theoretical Physics, 1991, 85(1): 1-5.

Mengchao Zhang 8/19 We use too loop result.

hhh Coupling in MSSM and NMSSM

In order to illustrate the genuine SUSY effect on hhh coupling, it’s

convenient to define:

δhhh =λSM

hhh − λSUSYhhh

λSMhhh

= (3m2

h√2v− λSUSY

hhh )/3m2

h√2v

(11)

We will call the quantity ”triple coupling deviation”. This triple coupling

deviation is more suitable than the absolute value of triple coupling,

because the uncertainty in Higgs mass calculation have little impact to

this deviation.

{all non − SM particles mass →∞

}⇒{δhhh → 0

}(for conciseness, we don’t write m4

t term in here)

Mengchao Zhang 9/19

hhh Coupling in MSSM and NMSSM

MSSM Higgs sector dominantly decided by mA and tanβ. δhhh

dependency on mA and tanβ is the under graph (other parameters: all

the other soft mass and At are equal to mq3, and other A-terms are zero):

small tanb and light mA are wanted

Mengchao Zhang 10/19

hhh Coupling in MSSM and NMSSM

important part

Mengchao Zhang 11/19

hhh Coupling in MSSM and NMSSM

Similar to: Marcela Carena, Howard E. Haber, Ian Low, Nausheen R. Shah, Carlos E. M. Wagner. Phys.Rev. D91 (2015) 035003

Mengchao Zhang 12/19

hhh Coupling in MSSM and NMSSM

NMSSM give a solution of the µ-problem in MSSM by introducing a

Singlet Field. The Higgs part super potential of NMSSM is:

WHiggs = λSHu · Hd +κ

3S3 (12)

and the corresponding Higgs soft term is:

−Lsoft = m2Hu|Hu|2 + m2

Hd|Hd |2 + m2

S |S |2

+(λAλHu · Hd S +1

3κAκS3 + h.c.) (13)

In order to describe the NMSSM Higgs sector, we need six parameters:

λ, κ,Aλ,Aκ, tanβ, µeff = λs.(s is the vev of singlet Higgs field)

Such couplings can be very large:

λsss =√

2κ

(6κµeff

λ+√

2Aκ

), λuds = −λAλ√

2−√

2κµeff . (14)

and the mixing between singlet and SM-like Higgs – OHS is the most

relevant quantity.

Mengchao Zhang 13/19

hhh Coupling in MSSM and NMSSM

The new couplings in NMSSM are not fixed by gauge coupling and

can vary in a large range, so significant mixing OHS will induce a very

different Higgs triple coupling.

We use NMSSMTools to scan the parameter space.

Scan range:

0 < λ < 0.7,−0.7 < κ < 0.7, 200GeV < Aλ < 1TeV ,−500GeV <

Aκ < 500GeV , 1 < tanβ < 20, 100GeV < µ < 500GeV , 500GeV <

mq3 = mu3 = md3 < 2.5TeV , |At = Ab| < 6TeV .

Other soft mass are equal to 2TeV and other A-terms are equal to

zero.

Most relevant constrains: Higgs mass and Higgs signal strength in

2σ region. Higgs mass will strongly limit Higgs sector parameters and

Higgs signal strength will restrict OHS directly.

Mengchao Zhang 14/19

hhh Coupling in MSSM and NMSSM

huge deviation is a hintof another scalar in the neighbor

Mengchao Zhang 15/19

hhh Coupling Measurement in Future Colliders

mixing between SM − like Higgs

and non − SM Higgs

⇒ Chbb,Chγγ ... deviation

λhhh deviation

So there is a close relationship between Chbb,Chγγ ... and λhhh.

Precise measurement on Higgs couplings will confine λhhh.

Mengchao Zhang 16/19 Higgs working group report:1310.8361

hhh Coupling Measurement in Future Colliders

Mengchao Zhang 17/19

hhh Coupling Measurement in Future Colliders

Mengchao Zhang 18/19

Conclusions

Mengchao Zhang 19/19

hhh coupling deviation in MSSM: < 3%

hhh coupling deviation in NMSSM: > 50%

ILC(LumUp) measurement constraint to hhh coupling deviation in MSSM: < 0.3%

ILC(LumUp) measurement constraint to hhh coupling deviation in NMSSM: < 1.0%