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Exploring Supersymmetric Gauge-Higgs Unification: Phenomenology and Constraints

This review delves into the theory of Gauge-Higgs Unification with Supersymmetry, examining its appearance in various models and its implications for SUSY breaking mechanisms. It explores the 5D complete realization of Orbifold SUSY GUT with GHU and RMSB, discussing the high-scale parameters and how to calculate the spectrum of such models. Phenomenology scans and constraints are evaluated, including collider experiments and dark matter reliabilities, with a focus on mass spectrum and decays. Conclusions highlight the potential for discovery at the LHC and suggest future research directions.

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Exploring Supersymmetric Gauge-Higgs Unification: Phenomenology and Constraints

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  1. Phenomenology of Supersymmetric Gauge-Higgs Unification Sylvain Fichet LPSC Grenoble PhD supervisor : Sabine Kraml (LPSC) Collaboration : Felix Brümmer (IPPP Durham) and Arthur Hebecker (Heidelberg) Arxiv : 0906.2957

  2. Theory Gauge-Higgs Unification 2 • What is Gauge-Higgs Unification ? • And with supersymmetry ? [Review : 0704.0833 ] 4D spin 1 : gauge 4D spin 0 : Higgs 5D vector superfield 4D vector superfield & 4D chiral superfield 4D spin 1 : gauge 4D spin 0 : Higgs

  3. SUSY GUTs with Gauge-Higgs Unification Theory 3 • Where SUSY GHU can appear ? • In the low energy limit of heterotic strings models, and in orbifold SUSY GUTs. • Natural way to break SUSY ? • With Radion Mediated SUSY breaking (RMSB) • [Chacko, Luty ’00 hep-ph/0008103] • Radion T = field associated to extra dimension fluctuation • Compactification implies SUSY breaking : • (radion ) • (chiral compensator : gravity effect ) • Anomaly Mediation contributions are generated at one-loop

  4. Theory A 5D complete realization 4 • Orbifold SUSY GUT with GHU + RMSB implies generically : • We take the 5D SU(6) model [Burdman, Nomura ’03 hep-ph/0210257] • - Compactification scale : • Gauge-Higgs sector : • Matter sector : • Confinement of matter fields controls • mass hierarchies (yukawas couplings) and • soft scalar parameters. 2 Higgs doublets Bulk Brane(4D) 3rd gen Gauge-Higgs 1,2nd generation

  5. Theory 5D complete realization : gauge-Higgs sector 5 • The high scale parameters of the gauge-Higgs sector are : • [Hebecker et al. 0801.4101] • is the coefficient of the Chern-Simons term, fixed in a full theory but here parametrized. [Review : 0805.1778] • For theory consistency : and

  6. Phenomenology Spectrum calculation 6 • How to calculate the spectrum of such models ? • Use a spectrum calculator… (SuSpect) [hep-ph/0211331] • …appropriately modified : • Impose at high energy. • Stable an simple • Input parameters are : • and parameters of the matter sector. • In the ‘5D complete realization’, the matter sector depends on • 2 mixing angles : and

  7. Phenomenology Scans and constraints 7 • Scans over • with 4 sign combination : and • Constraints : • Theoretical (verified in Suspect) : EWSB, CCB, tachyons • Collider experiments : • Mass bounds from LEP [http://lepsusy.web.cern.ch/lepsusy/] • B-physics (2σ): • [CDF 0712.1708 hep-ex] • [HFAG hep-ex/0603003] • Dark matter (3σ): • [WMAP 0803.0586 astro-ph]

  8. Scans and constraints Phenomenology 8 Scan with • LSP : • red : • blue : • green : • Points excluded by B-physics or too light • ~ similar result with • No points for the 2 other combinations

  9. Phenomenology RMSB parameter space 9 • RMSB parameters for the same points : • is , is not too large wrt • No points for !

  10. Phenomenology Relic density 10 • Dark matter relic density : 3σ WMAP measurement • Assuming standard cosmology ! Not enough Good Too much !

  11. Phenomenology Mass spectrum and decays 11 • Masses : • 3 possible LSPs • small 2 1 0

  12. Phenomenology Mass spectrum and decays 11 • Masses : • 3 possible LSPs • small • SFOS dilepton 2 65 % 30 % 1 ~50 % 0

  13. 12 • CONCLUSION : • SUSY GHU works,… • …has a particular mass spectrum, • … and has a good potential of discovery at LHC • TO-DO LIST : • Discrimination among other models • See what happens in warped geometry (holographic models…) • See what happens with a massive right-handed neutrino

  14. Thanks for your attention !

  15. EXTRAS

  16. Examples of mass spectrum

  17. Fixed point vs dichotomy f(x) f(x) x x f(x)-x 2 3 1 x

  18. Choice of SuSy breaking model : high-scale boundary conditions GUT scale Phys. masses/couplings Check : EWSB EWSB scale Sparticles mass matrices diagonalization Check : Spectrum minization, compute or Mz scale SuSy finite corrections to τ, b, t & sparticles masses Low scale values modified iteration Exp. data & guess of The SuSpect Algorithm

  19. A mSUGRA example : Higgs Gauginos Sparticles Gluino dominated squark running Radiative EWSB

  20. Higgs sector Higgs potential (after some gauge rotations) : -potentiel bounded from below : -non-trivial minimum : Minimization : with

  21. Higgs sector • The bilinear parameter µ • The bilinear parameter B (susy breaking) • Higgs masses (susy breaking) with

  22. Interesting features of other RGES • Superpotential parameter corrections are proportional to the parameters themselves : • All susy-breaking parameters depend on gaugino masses . • Squark masses receive large negative corrections from the gluino mass : • mass receives large positive corrections from the top yukawa : with

  23. Couplings and sparticles masses • Yukawas • Trilinear couplings (susy breaking) • Sparticle masses (susy breaking)

  24. Why such sign combinations ? Big and positive At Small or negative At

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