SUSY Higgs with Non-perturbative effects

Yukihiro Mimura (National Taiwan University)

Based on PLB718 (2013) 1441. Collaboration with N. Haba, K. Kaneta, and R. Takahashi Work in progress.

Seminar at Academia Sinica (2013.5.10)

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Menu Higgs discovery and Higgs puzzle

SUSY Higgs

Non-perturbative Higgs model in SUSY QCD

Feature of the model (Higgs to diphoton decay)

Summary

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We’ve found you,

Higgs!

Discovery of the Higgs(-like) boson in July, 2012

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Higgs? or Higgs-like?

We need to look at it carefully.

SM Higgs?

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Higgs Puzzle

(20.7 fb-1, new)

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Unknown “Higgs Forces”

1. Higgs self-coupling

How does the Higgs field acquire a VEV ?

2. Couplings to fermion (Yukawa coupling)

How does the Higgs VEV give masses to fermions?

SM?

SM?

8Ex.

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The lightest Higgs mass in MSSM

Maximized at

Higgs mass is predictive in MSSM.

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The lightest Higgs mass in MSSM

Maximized at

(Hall-Pinner-Ruderman, 1112.2703)

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(tree level)

How about minimization condition?

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RGE solution:(tree level)

Cancellation sensitivity

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However, in Radiative EWSB scenario, becomes zero at a scale.

(Note : RGEs are homogeneous equation, and thus, the solution is overall-scale invariant.)

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Sensitive to the stop mass parameters

RGEs

Hypercharge weightedTrace of scalar masses

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Good news & Bad news for 125 GeV Higgs

Good news :

Consistent with no sign in direct search

Bad news: Stop mass and/or mixing have to be large, and radiative EWSB breaking is sensitive to them.

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Good news & Bad news for 125 GeV Higgs

Good news :

Consistent with no sign in direct search

Bad news: Stop mass and/or mixing have to be large, and radiative EWSB breaking is sensitive to them.

No EWSB

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One may extend the SUSY SM.

1. NMSSM

2. Add vector-like matter which couples to the Higgs field.

Coleman-Weinberg potential can enhance the Higgs mass (via VEV-dependent masses).

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3. BMSSM (Beyond MSSM)

4. Non-perturbative Higgs model

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Non-perturbative Higgs model

Higgs fields are moduli of SUSY QCD.

(Haba-Okada)

Hypercolor

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SUSY QCD (Seiberg et al, 90’s)

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Effective Lagrangian

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SUSY QCD version

Integrating S out

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Dynamical Higgsino mass term(VEV-dependent)

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(Carena-Low-Wagner)

(W loop) (Top loop)

For chiral fermions:

Higgs to diphoton decay width

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Constructive contribution to W loop is needed.

VEV-dependent contribution to the new particle mass must reduce its mass.

A sizable contribution is needed to enhancethe diphoton decay rate largely.

Unstable solution

The coupling may blow upjust above the weak scale.

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Sketch of the issue

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Sketch of the issue

For a < 0 (non-perturbatively) and M=0,it always provides a constructive contribution to W loop.

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Dynamical Higgsino mass term(VEV-dependent)

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Suppose that Higgsino loop is the only additional source.

Ratio of the decay amplitude from top quark loop and Higgsino loop

The decay amplitude is about 40% up!

Decay width can be twice as the one in SM.

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Charged Higgs boson loop contribution :

Destructive contribution

There is VEV-independent mass (decoupling).

It does not destabilize the Higgs potential.

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NP potential SUSY breaking

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Merit:

In MSSM,

Demerit:

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Work in progress :

Pair production of Higgsino is enhanced.

Pair production of the Higgs boson is enhanced.

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Summary

There are missing pieces for the “Higgs forces”.

SUSY Higgs is discussed.

Non-perturbative Higgs model in SUSY QCD is proposed.

It can enhance the Higgs to diphoton decay width.

We look forward to more data to specify the “Higgs forces”.

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Possible extension of the modelThird generation can be also moduli of SUSY QCD.

Left-handed matter

Right-handed matter

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minimal Supergravity (mSUGRA)/Constrained MSSM (CMSSM)

1. Unified Gaugino masses at GUT scale

2. Universal scalar mass (at Planck/GUT scale)

3. Scalar trilinear coupling (A-term)

4. Ratio of up- and down-type Higgs vev

5. Higgsino mass

( is fixed by the minimization of Higgs potential.)

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tree

averaged stop mass

Little hierarchy

by definition

(Giudice-Rattazzi, Dutta-YM)

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Distribution of Little hierarchy

Probability is not 1% yet.

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Good news & Bad news for 125 GeV Higgs

Good news :

Consistent with no sign in direct search

Bad news: Stop mass and/or mixing have to be large, and radiative EWSB breaking is sensitive to them.

No EWSB

We are OK!

You look uncomfortable.