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

Gauge-Higgs Unification 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

SUSY GUTs with Gauge-Higgs Unification Theory SUSY GUTs with Gauge-Higgs Unification 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.

SUSY GUTs with Gauge-Higgs Unification 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

SUSY GUTs with Gauge-Higgs Unification 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 :

5D complete realization : gauge-Higgs sector 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

5D complete realization : gauge-Higgs sector 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 !

5D complete realization : gauge-Higgs sector 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 :

5D complete realization : matter sector Theory 5D complete realization : matter sector 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 Branes (4D) Gauge-Higgs 3rd gen 1,2nd gen Bulk

5D complete realization : matter sector Theory 5D complete realization : matter sector 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. Branes (4D) Gauge-Higgs 3rd gen 1,2nd gen Bulk

Theory Summary To sum up… Orbifold SUSY GUT with GHU + RMSB 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. Bulk Gauge-Higgs 3rd gen 1,2nd gen

How to calculate the spectrum of such models ? 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…

How to calculate the spectrum of such models ? 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 )

Phenomenology Scans and constraints Scans over 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]

Scans and constraints Phenomenology Scan with LSP : red : blue : 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

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

Why such sign combinations ? Phenomenology RGE analysis 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. > 0 EWSB RGE GHU

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

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

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

Mass spectrum and decays Phenomenology Mass spectrum and decays 17 Masses : 3 possible LSPs small 2 1

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

CONCLUSION : TO-DO LIST : SUSY GHU works,… 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

Thanks for your attention !

EXTRAS

Constraint with g-2

Examples of mass spectrum

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

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

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

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

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

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

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