Phenomenology of Supersymmetric Gauge-Higgs Unification

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

2. Theory Gauge-Higgs Unification 2 • What is Gauge-Higgs Unification ? • And with supersymmetry ? 4D spin 1 : gauge 4D spin 0 : Higgs [Review : 0704.0833 ] 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 orbifold SUSY GUTs • SUSY GUTs motivated by couplings unification • Extra dimensions motivated by doublet-triplet problem, GUT group breaking, proton decay • (5D SU(6) GHU [Burdman, Nomura hep-ph/0210257] ) • A top-down motivation : SUSY GUT with GHU can naturally come from classes of heterotic strings model.

4. Theory SUSY GUTs with Gauge-Higgs Unification 4 • Natural way to break SUSY? • With Radion Mediated SUSY breaking (RMSB) • [Chacko, Luty hep-ph/0008103] • Radion T = field associated to extra dimension fluctuation • Compactification implies SUSY breaking : • (radion ) • (chiral compensator : gravity effect) • with • Anomaly Mediation contributions are generated at one-loop

5. Theory SUSY GUTs with Gauge-Higgs Unification 5 • SUSY GUTs with Gauge-Higgs Unification and RMSB generically implies : • at the SUSY breaking scale. • Solves the mu-problem • Giudice-Masiero mechanism [Giudice, Masiero ‘88 Phys.Lett.B206:480-484] • Reminder :

6. Theory 5D complete realization : gauge-Higgs sector 6 • 5D SUSY GUT with SU(6) GHU[Burdman, Nomura hep-ph/0210257] • Radius T of the 5th dimension stabilized by an unknown mechanism : • and break the SU(6) adjoint : • 2 Higgs doublets

7. Theory 5D complete realization : gauge-Higgs sector 6 • 5D SUSY GUT with SU(6) GHU[Burdman, Nomura ’03 hep-ph/0210257] • Radius T of the 5th dimension stabilized by an unknown mechanism : • and break the SU(6) adjoint : • 2 Higgs doublets • It implies the high-scale relations : • Negative conclusions : • no EWSB • [Choi et al. hep-ph/0312178] • But one contribution was not taken into account !

8. Theory 5D complete realization : gauge-Higgs sector 7 • In odd number of dimension, a new term in the Lagangian is allowed : • the Chern-Simons term • e.g. in 5D non-susy : [Review : 0805.1778] • Fixed in a full theory, but here parametrized with free coefficient . • The high-scale relations become : • [Hebecker et al. 0801.4101, Brümmer et al. 0906.2957] • For theory consistency : and • Sign ambiguity :

9. Theory 5D complete realization : matter sector Bulk 3rd gen Gauge-Higgs 1,2nd gen Branes (4D) 8 • What about matter fields ? • Matter in the bulk, but can be confined if massive • 4D yukawas come from the overlap with Higgs field. • can generate mass hierarchy • for matter fermions

10. Theory 5D complete realization : matter sector Bulk 3rd gen Gauge-Higgs 1,2nd gen Branes (4D) 8 • What about matter fields ? • Matter in the bulk, but can be confined if massive • 4D yukawas come from the overlap with Higgs field. • can generate mass hierarchy • for matter fermions • What about soft scalar parameters ? • Only bulk matter couples • to SuSy breaking fields. • similar hierarchy for soft scalars : • , large, • others negligible.

11. Theory Summary Bulk 3rd gen Gauge-Higgs 1,2nd gen 9 • To sum up… • Orbifold SUSY GUT with GHU + RMSB • Model with 5D SU(6) GHU and Chern Simons term : • Confinement of matter fields controls • mass hierarchies (yukawas couplings) and • soft scalar parameters.

12. Phenomenology Spectrum calculation 10 • How to calculate the spectrum of such models ? • Use a spectrum calculator… (SuSpect) [hep-ph/0211331] • …but the pattern of input and constraints is different from other models : • Usually : and calculated from the 2 equations of Higgs potential minization, at each iteration. • But in our model : fixed from high scale relation…

13. Phenomenology Spectrum calculation 10 • How to calculate the spectrum of such models ? • Use a spectrum calculator… (SuSpect) [hep-ph/0211331] • …but the pattern of input and constraints is different from other models : • Usually : and calculated from the 2 equations of Higgs potential minization, at each iteration. • But in our model : fixed from high scale relation… • First solution : compute and at each iteration. • But unstable for ! (Potential fix : fixed point => dichotomy) • Second solution : Simply impose at high energy. • input parameters : … • + matter sector parameters (in the 5D model : 2 mixing angles and )

14. Phenomenology Scans and constraints 11 • 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]

15. Scans and constraints Phenomenology 12 Scan with • LSP : • red : • blue : • green : • Points excluded by B-physics or too light • ~ similar result with • No points for the 2 other combinations

16. RGE analysis Phenomenology 13 • Why such sign combinations ? • We have : • And dominated by • The overall sign is fixed by • For a given , only one is allowed. GHU RGE EWSB > 0

17. RGE analysis Phenomenology 13 • Why such sign combinations ? • We have : • And dominated by • The overall sign is fixed by • For a given , only one is allowed. • Which sign is selected depends on running. • is dominated by the gluino mass : • Roughly universal running • Only the initial value matters. GHU RGE EWSB > 0

18. RGE analysis Phenomenology 14 • If large and positive : • If small or negative :

19. Phenomenology RMSB parameter space 15 • RMSB parameters for the same points : • is , is not too large wrt • No points for !

20. Phenomenology Relic density 16 • Dark matter relic density : 3σ WMAP measurement • Assuming standard cosmology ! Not enough Good Too much !

21. Phenomenology Mass spectrum and decays 17 • Masses : • 3 possible LSPs • small 2 1 0

22. Phenomenology Mass spectrum and decays 17 • Masses : • 3 possible LSPs • small • SFOS dilepton 2 65 % 30 % 1 ~50 % 0

23. 18 • 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…) • Include a massive right-handed neutrino

24. Thanks for your attention !

25. EXTRAS

26. Constraint with g-2

27. Examples of mass spectrum

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

29. 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 Algorithm

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

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

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

33. 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

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