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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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2 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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3 Weve found you, Higgs! Discovery of the Higgs(-like) boson in July, 2012

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4 Higgs? or Higgs-like? We need to look at it carefully. SM Higgs?

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5 Higgs Puzzle (20.7 fb -1, new)

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7 Unknown Higgs Forces 1.Higgs self-coupling How does the Higgs field acquire a VEV ? 1.Couplings to fermion (Yukawa coupling) How does the Higgs VEV give masses to fermions? SM?

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8 Ex.

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9 The lightest Higgs mass in MSSM Maximized at Higgs mass is predictive in MSSM.

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10 The lightest Higgs mass in MSSM Maximized at (Hall-Pinner-Ruderman, 1112.2703)

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11 (tree level) How about minimization condition?

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12 RGE solution: (tree level) Cancellation sensitivity

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13 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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14 Sensitive to the stop mass parameters RGEs Hypercharge weighted Trace of scalar masses

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16 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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17 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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18 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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19 3. BMSSM (Beyond MSSM) 4. Non-perturbative Higgs model

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20 Non-perturbative Higgs model Higgs fields are moduli of SUSY QCD. (Haba-Okada) Hypercolor

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21 SUSY QCD (Seiberg et al, 90s)

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22 Effective Lagrangian

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23 SUSY QCD version Integrating S out

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24 Dynamical Higgsino mass term (VEV-dependent)

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25 (Carena-Low-Wagner) (W loop)(Top loop) For chiral fermions: Higgs to diphoton decay width

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26 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 enhance the diphoton decay rate largely. Unstable solution The coupling may blow up just above the weak scale.

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27 Sketch of the issue

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28 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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29 Dynamical Higgsino mass term (VEV-dependent)

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30 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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31 Charged Higgs boson loop contribution : Destructive contribution There is VEV-independent mass (decoupling). It does not destabilize the Higgs potential.

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32 NP potentialSUSY breaking

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33 Merit: In MSSM, Demerit:

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34 Work in progress : Pair production of Higgsino is enhanced. Pair production of the Higgs boson is enhanced.

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37 Summary There are missing pieces for the Higgs forces. There are missing pieces for the Higgs forces. SUSY Higgs is discussed. SUSY Higgs is discussed. Non-perturbative Higgs model in SUSY QCD is proposed. Non-perturbative Higgs model in SUSY QCD is proposed. It can enhance the Higgs to diphoton decay width. It can enhance the Higgs to diphoton decay width. We look forward to more data to specify the Higgs forces. We look forward to more data to specify the Higgs forces.

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38 Possible extension of the model Third generation can be also moduli of SUSY QCD. Left-handed matter Right-handed matter

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40 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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41 tree averaged stop mass Little hierarchy by definition (Giudice-Rattazzi, Dutta-YM)

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42 Distribution of Little hierarchy Probability is not 1% yet.

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43 (Carena-Gori-Shah-Wagner, 1112.3336)

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45 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.

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