Phenomenology of Supersymmetric Gauge-Higgs Unification

1. Phenomenology of Supersymmetric Gauge-Higgs Unification Sylvain Fichet LPSC Grenoble Work in progress with Sabine Kraml (LPSC), Felix Brümmer (IPPP Durham) and Arthur Hebecker (Heidelberg)

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 ’03 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 ’00 hep-ph/0008103] • Radion T = field associated to extra dimension fluctuation • Compactification implies SUSY breaking : • (radion ) • (chiral compensator ) 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 ’03 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. ‘03 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] • For theory consistency : and

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 : + soft scalar parameters.

14. Phenomenology Scans and constraints 11 • Scans over and with 3rd generation soft scalar parameters : • Constraints : • Theoretical (verified in Suspect) : EWSB, CCB, tachyons • Experimental : • 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 mass bounds : too light LSP :

16. Scans and constraints Phenomenology 13 • Scan • With mass bounds : With all constraints : too light excess of DM LSP : lack of DM excl. by B-phys.

17. Phenomenology Scans and constraints 14 • Scan • With mass bounds : too light LSP :

18. Phenomenology Scans and constraints 15 • Scan • With mass bounds : With all constraints : too light LSP : excl. by B-phys. lack of DM

19. Phenomenology RMSB parameter space 16 • Scan • With mass bounds : • No points for ! • is , is not too large wrt

20. Phenomenology RMSB parameter space 17 • Scan • With all constraints : excess of DM excl. by B-phys. lack of DM

21. Phenomenology RMSB parameter space 18 • Scan • With mass bounds : • No points for ! • is , is not too large wrt

22. Phenomenology RMSB parameter space 19 • Scan • With all constraints : excl. by B-phys. lack of DM

23. Phenomenology Mass spectrum and decays 20 • Masses : • 3 possible LSPs • small 2 1 0

24. Phenomenology Mass spectrum and decays 21 • Masses : • 3 possible LSPs • small • SFOS dilepton 2 65 % 30 % 1 ~50 % 0

25. 22 • CONCLUSION : • SUSY GHU works,… • …have a particular mass spectrum, • … and have a good potential of discovery at LHC • (but probably not possible to discriminate it at LHC) • TO-DO LIST : • Analyze a complete model with realistic soft scalar parameters • (Burdman-Nomura) • Build an algorithm with iterations over , with a method of dichotomy

26. Thanks for your attention !

27. EXTRAS

28. Constraint with g-2

29. Examples of mass spectrum

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

31. 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

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

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

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

35. 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

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