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)
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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Discovery of the Higgs(-like) boson in July, 2012
We’ve found you,
Higgs!
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Higgs? or Higgs-like?
SM Higgs?
We need to look
at it carefully.
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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 ?
SM?
1. Couplings to fermion (Yukawa coupling)
How does the Higgs VEV give masses to fermions?
SM?
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Ex.
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Higgs mass is predictive in MSSM.
The lightest Higgs mass in MSSM
Maximized at
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The lightest Higgs mass in MSSM
Maximized at
(Hall-Pinner-Ruderman, 1112.2703)
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How about minimization condition?
(tree level)
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(tree level)
RGE solution:
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 weighted
Trace 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.
Hypercolor
(Haba-Okada)
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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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Higgs to diphoton decay width
(Carena-Low-Wagner)
(W loop)
(Top loop)
For chiral fermions:
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Constructive contribution to W loop is needed.
 VEV-dependent contribution to the new
particle mass must reduce its mass.
Unstable solution
 A sizable contribution is needed to enhance
the diphoton decay rate largely.
The coupling may blow up
just 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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Ratio of the decay amplitude from top quark loop and
Higgsino loop
Suppose that Higgsino loop is the only additional source.
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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In MSSM,
Merit:
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 model
Third 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
by definition
Little hierarchy
(Giudice-Rattazzi, Dutta-YM)
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Distribution of Little hierarchy
Probability is not 1% yet.
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(Carena-Gori-Shah-Wagner, 1112.3336)
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Good news & Bad
news for 125 GeV Higgs
We are OK!
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
You look uncomfortable.
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