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The flhiggs model F. Bazzocchi SISSA (Trieste). F.B., M. Fabbrichesi, hep-ph/0407358 F.B., M. Fabbrichesi, hep-ph/0410107. Outline. introduction main features of the Little Higgs models main features of the Little Flavons model the Flhiggs model high energy effective theory

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The flhiggs model F. Bazzocchi SISSA (Trieste)

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The flhiggs modelF. BazzocchiSISSA (Trieste)

F.B., M. Fabbrichesi, hep-ph/0407358

F.B., M. Fabbrichesi, hep-ph/0410107


  • 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

Fermions: a new Mendeleev’s periodic table?

February 8, 2005




Higgs Sector



Little Hierarchy













A puzzle ?

February 8, 2005

Motivations for Little Higgs

Their mass is a dimensionful parameter

that is not protected by any symmetry

Scalar fields

February 8, 2005

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

The little-Higgs mechanism[Schmaltz, hep-ph/0210415]

collective symmetry breaking:

February 8, 2005

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

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

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

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?


Problem: electro-weak scale is around 10 TeV at most

February 8, 2005

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


The flhiggs model

February 8, 2005

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


February 8, 2005

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

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


Right-handed neutrinos CW (collective simmetry breaking no 1-loop quadratically divergent mass terms!!)

February 8, 2005

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


  • 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


protection of the

flhiggs masses


Collective symmetry breaking mechanism

Yukawa terms preserve SU(8) (or SU(9) ) subgroup of SU(10)

February 8, 2005

Yukawa Lagrangian (Quarks)

Breaks SU(10),

preserves AN SU(9)

(subgroup SU(10))

Breaks SU(10),

preserves ANOTHER


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

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


top-like heavy, top-like exotic light


The exotic top-like quarks mix into a heavy and a light combination



February 8, 2005

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


Decoupling of the extra charged leptons

Charged leptons

Dirac neutrinos mass matrix (a = flavor index)

Majorana R-H neutrinos mass matrix

February 8, 2005

Mass Matrices



February 8, 2005

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


Flavor sector


FCNC processes ( neutral kaon mixing )

relevant effective operators are suppresed by powers of m(ferm)/f

Low energy scale

February 8, 2005

Then … what is the scale f (Λ) ?


~ 30 TeV

Lightest neutral scalar boson (Higgs!) (not so light…)

heavy gauge bosons (9+1), heavy scalars (4+12), heavy fermions (also νR)


~ 3 TeV

mh0~ 300 GeV


extra gauge bosons (5+1), heavy fermions


~ 1 TeV

Lightest charged scalar boson

scalars (PGB) (15)

mh± ~ 560 GeV


EW SM gauge bosons (3), SM fermions

February 8, 2005


  • 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

Represenations and Charges Assignments



February 8, 2005

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

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