The flhiggs model F. Bazzocchi SISSA (Trieste)

1. The flhiggs modelF. BazzocchiSISSA (Trieste) F.B., M. Fabbrichesi, hep-ph/0407358 F.B., M. Fabbrichesi, hep-ph/0410107

2. Outline • introduction • main features of the Little Higgs models • main features of the Little Flavons model • the Flhiggs model • high energy effective theory • low energy effective theory • fermions and textures • constraints and phenomenology • conclusions February 8, 2005

3. Fermions: a new Mendeleev’s periodic table? February 8, 2005

4. Little Higgs Models Higgs Sector & EWSB Little Hierarchy The Flhiggs Model Fermion Masses & Hierachies Mixing Angles Horizontal Flavor Symmetries A puzzle ? February 8, 2005

5. Motivations for Little Higgs Their mass is a dimensionful parameter that is not protected by any symmetry Scalar fields February 8, 2005

6. Higgs as a pseudo-Goldstone boson SU(3) SU(2) Problem:Goldstone bosons are exactly massless Explicit breaking of SU(3) to make them into pseudo But is not small in the SM: February 8, 2005

7. The little-Higgs mechanism[Schmaltz, hep-ph/0210415] collective symmetry breaking: February 8, 2005

8. Another contest in which scalar can be used….think for a moment to the quark mass matrices textures: a way to reduce the number of parameters εrelated to the vevs of some scalar fields : the flavons  are parameters of order 1 February 8, 2005

9. Horizontal flavor symmetry & Requests • dynamically generated potential with the desired vacuum • stable scales, i.e., only small radiative corrections (no fine tuning) • appropriate textures (from charges and vev) from natural parameters a little-Higgs inspired scenario little flavons [B, Bertolini, Fabbrichesi, Piai, hep-ph/0306184 and 0309182] February 8, 2005

10. Low-energy effective theory horizontal symmetry: gauged little flavons: 2 doublets of opposite F-hypercharge the VEVs break to nothing at f the flavons arise as pseudo-Goldstone bosons February 8, 2005

11. What is the scale  ? • Bounds from FCNC, parity violation etc. induced by tree-level gauge exchange • Most stringent from neutral Kaon physics [Bazzocchi, hep-ph/0312nnn] • They depend on fermion charges under full symmetry Suggestion : what happen with a global flavor symmetry? TeV Problem: electro-weak scale is around 10 TeV at most February 8, 2005

12. Flavor & EW Symmetry embedded in a little Higgs inspired scenario • dynamically generated potential • stable scales, i.e., only small radiative corrections (no fine tuning) • appropriate textures (from charges and vev) from natural parameters • hierarchy in vev’s explains that in mass matrices • flavon-Higgs scalar fields : the Flhiggs • flavor and alectroweak spontaneous breaking • protection also of the Higgs mass Requests The flhiggs model February 8, 2005

13. High-energy effective theory Gauge symmetries Global symmetry 9+1 massive gauge bosons 4 massive complex scalars 1 massive complex sextet 4 triplets massless (PGB) C W potential + Plaquettes terms Triplets acquire vev’s 9 massive gauge bosons 2 complex and 11 real scalars C W from right-handed neutrinos Potential for the triplets Textures February 8, 2005

14. Low-energy effective theory Electroweak gauge symmetry : Global horizontal flavor symmetry : Exotic gauge symmetry: • [SU(3)XU(1)]WX [U(1)]F is the • littlest group that allows • scalars in the fundamental • flavor and electroweak symmetry • breaking at different scales Little Flavons-Higgs (PGB): 2 triplets of opposite flavor charge, no charged under U(1) X exotic (Φ1 & Φ2 ) Little X-scalars (PGB): 2 triplets of opposite X charge, No charged under U(1)F flavor (Φ3 & Φ4 ) February 8, 2005

15. Potential for the flhiggs (PGB) Gauge boson CW and Plaquette terms The vevs break [SU(3)XU(1)]W X [U(1)]X X [U(1)]F into [U(1)]Q All the parameters are expressed in terms of the gauge coupling & plaquettes’ coefficients Quadratic terms come from 1-loop logarithmic contributions Right-handed neutrinos CW (collective simmetry breaking no 1-loop quadratically divergent mass terms!!) February 8, 2005

16. Are the flavor and the electroweak scales different ? With the assumptions Conditions to be satisfied to have a minimum More conditions on the hessian… Expressions for VF and VW Field configuration chosen in the minimum …it is easy to have all the μ of the same order and VF / VW ~ 3 More other conditions on the parameters since we take VF = VX February 8, 2005

17. Fermions • Low-energy:[SU(3)]w triplets (antitriplets) [SU(3)]w singlets charged and uncharged under [U(1)]x (all charged Fl.) Why an exotic U(1) gauge symmetry ? in order to decouple the extra fermions (third component of the weak triplets) • High-energy:SU(10) decuplets (approximate global symmetry) Yukawa terms gauge (weak and exotic) and flavor invariant well defined textures protection of the flhiggs masses ? Collective symmetry breaking mechanism Yukawa terms preserve SU(8) (or SU(9) ) subgroup of SU(10) February 8, 2005

18. Yukawa Lagrangian (Quarks) Breaks SU(10), preserves AN SU(9) (subgroup SU(10)) Breaks SU(10), preserves ANOTHER SU(9) For each quark family we add 2 non exotic and 3 exoticcolouredWeyl fermions SU(3)w singlets and an exotic coloured SU(3)w triplet All the four scalar triplets are protected by the usual LH mechanism February 8, 2005

19. Quark Masses Considering all the family… 6X6 matrices almost block diagonalized The non-exotic top-like quarks mix into a heavy ( T ) and a light (top) combination top-like exotic heavy f top-like heavy, top-like exotic light VF The exotic top-like quarks mix into a heavy and a light combination Vw top February 8, 2005

20. SM leptons doublets embedded in SU(3)W triplets Yukawa lagrangian simpler (protection of the flhiggs masses only from νR and extra charged leptons) Majorana mass matrix for νL obtained through the see-saw mechanism Leptons Decoupling of the extra charged leptons Charged leptons Dirac neutrinos mass matrix (a = flavor index) Majorana R-H neutrinos mass matrix February 8, 2005

21. Mass Matrices Quarks Leptons February 8, 2005

22. Constraining the Model Extra neutral gauge boson (Z‘) : bounds on the ew currents (ρ,…) and mZ’ fix the U(1)w coupling and vF. Weak sector [SU(3)XU(1)]W Flavor sector [U(1)]F FCNC processes ( neutral kaon mixing ) relevant effective operators are suppresed by powers of m(ferm)/f Low energy scale February 8, 2005

23. Then … what is the scale f (Λ) ? Λ ~ 30 TeV Lightest neutral scalar boson (Higgs!) (not so light…) heavy gauge bosons (9+1), heavy scalars (4+12), heavy fermions (also νR) f ~ 3 TeV mh0~ 300 GeV Spectrum extra gauge bosons (5+1), heavy fermions VF ~ 1 TeV Lightest charged scalar boson scalars (PGB) (15) mh± ~ 560 GeV Vw EW SM gauge bosons (3), SM fermions February 8, 2005

24. Conclusions • We have given an example of flavor- electroweak gauge unification • The model is more constrained than the usual little-Higgs model because on bounds on weak and flavor physics • Explicit predictions for the new weak gauge bosons and scalars masses • Many new particles: most interesting experimental signatures for LHC coming from the scalar sector • The most characteristic prediction is a heavy Higgs boson February 8, 2005

25. Represenations and Charges Assignments Quarks Leptons February 8, 2005

26. What is natural? • Dirac:dimensionless parameters should be of order one • t Hooft: dimensionful parameters should be of the order of the largest scale in the problem, unless a symmetry arises in the limit of vanishing coupling the rules of the game February 8, 2005