the flhiggs model f. bazzocchi sissa (trieste)

The flhiggs modelThe flhiggs model

F. BazzocchiF. BazzocchiSISSA (Trieste)SISSA (Trieste)

F.B., M. Fabbrichesi, hep-ph/0407358F.B., M. Fabbrichesi, hep-ph/0407358F.B., M. Fabbrichesi, hep-ph/0410107F.B., M. Fabbrichesi, hep-ph/0410107

FB, IFIC (Valencia) 2February 8, 2005

OutlineOutlineOutlineOutline

• 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

• 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


Fermions: a new Mendeleev’s periodic table?Fermions: a new Mendeleev’s periodic table?


Fermion

Masses

&

Hierachies

Mixing

Angles

Little Hierarchy

Higgs Sector

&

EWSB

Little

Higgs

Models

Horizontal

Flavor

Symmetries

The

Flhiggs

Model


Motivations for Little HiggsMotivations for Little Higgs

Their mass is a dimensionful parameter that is not protected by any symmetry

-40000

-30000

-20000

-10000

0

10000

20000

30000

40000

total tree top gauge higgs

m_h^2

Scalar fields Scalar fields


Higgs as a pseudo-Goldstone bosonHiggs 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

LL0 1L1

1But is not small in the SM:


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

LL0 1L1 2L2

collective symmetry breaking:


Another contest in which scalar can be Another contest in which scalar can be used….think for a moment to the quark used….think for a moment to the quark

mass matricesmass matrices

textures: a way to reduce the number of parameters

ε related to the vevs of some scalar

fields : the flavons

ε related to the vevs of some scalar

fields : the flavons

are parameters of order 1

are parameters of order 1


Horizontal flavor symmetry & RequestsHorizontal flavor symmetry & Requests

dynamically generated potential with the desired dynamically generated potential with the desired vacuumvacuum

stable scales, i.e., only small radiative corrections (no stable scales, i.e., only small radiative corrections (no fine tuning)fine tuning)

appropriate textures (from charges and vev) from appropriate textures (from charges and vev) from natural parametersnatural parameters

a little-Higgs inspired scenario

little flavons

[B, Bertolini, Fabbrichesi, Piai, hep-ph/0306184 and 0309182]


horizontal symmetry: gauged

little flavons: 2 doublets of opposite F-hypercharge

SU(2) U(1) F

at f the flavons arise as pseudo-Goldstone bosons

the VEVs break

to nothing

SU(2) U(1) F

Low-energy effective theoryLow-energy effective theory


What is the scale 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

1000 TeV

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

Suggestion :

what happen with a global flavor symmetry?

Suggestion :

what happen with a global flavor symmetry?


Flavor & EW Symmetry embedded in a Flavor & EW Symmetry embedded in a little Higgs inspired scenariolittle Higgs inspired scenario

dynamically generated potential dynamically generated potential stable scales, i.e., only small radiative corrections (no fine stable scales, i.e., only small radiative corrections (no fine

tuning)tuning) appropriate textures (from charges and vev) from natural appropriate textures (from charges and vev) from natural

parametersparameters hierarchy in vev’s explains that in mass matriceshierarchy in vev’s explains that in mass matrices flavon-Higgs scalar fields : the Flhiggsflavon-Higgs scalar fields : the Flhiggs flavor and alectroweak spontaneous breakingflavor and alectroweak spontaneous breaking protection also of the Higgs massprotection also of the Higgs mass

Requests

The flhiggs modelThe flhiggs model


High-energy effective theoryHigh-energy effective theory

9+1 massive gauge bosons4 massive complex scalars1 massive complex sextet4 triplets massless (PGB)

C W potential+

Plaquettes terms

C W from right-handed neutrinos

Potential for the triplets

Triplets acquire vev’s

9 massive gauge bosons2 complex and 11 real scalars

Textures

Gauge symmetries Global symmetry


Low-energy effective theoryLow-energy effective theory

Electroweak gauge symmetry :Electroweak gauge symmetry :

Global horizontal flavor symmetry :Global horizontal flavor symmetry :

Exotic gauge symmetry:Exotic gauge symmetry:

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 )

[SU(3)XU(1)]W X [U(1)]F is the littlest group that allows

• scalars in the fundamental• flavor and electroweak symmetry

breaking at different scales


Potential for the flhiggs (PGB)Potential for the flhiggs (PGB)

Gauge boson CW and Plaquette terms

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

The vevs break [SU(3)XU(1)]W X [U(1)]X X [U(1)]F into [U(1)]Q

Quadratic terms come from 1-loop logarithmic

contributions

Quadratic terms come from 1-loop logarithmic

contributions

All the parameters are expressed in terms of the

gauge coupling & plaquettes’ coefficients

All the parameters are expressed in terms of the

gauge coupling & plaquettes’ coefficients


Are the flavor and the electroweak scales

different ?

Conditions to be satisfied to have a minimumConditions to be satisfied to have a minimum

Field configuration chosen in the minimumField configuration chosen in the minimumExpressions for VF and VWExpressions for VF and VW

More other conditions on the parameters since we take VF = VX

More other conditions on the parameters since we take VF = VX

With the assumptions With the assumptions

…it is easy to have all the μ of the same order and VF / VW ~ 3

…it is easy to have all the μ of the same order and VF / VW ~ 3

More conditions on the hessian…

More conditions on the hessian…


Fermions

Collective symmetry breaking mechanism

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

Low-energy: [SU(3)]w triplets (antitriplets)

[SU(3)]w singlets charged and

uncharged under [U(1)]x (all charged Fl.) High-energy: SU(10) decuplets

(approximate global symmetry)

protection of the

flhiggs masses

?

Why an exotic U(1) gauge symmetry

?

in order to decouple the extra fermions (third component of the weak triplets)

Yukawa terms gauge(weak and exotic)

and flavor invariant well defined

textures


Yukawa Lagrangian (Quarks)

Breaks SU(10), preserves AN SU(9)(subgroup SU(10))

Breaks SU(10), preserves ANOTHER

SU(9)

All the four scalar tripletsare protected by

the usual LH mechanism

For each quark family we add 2 non exotic and 3 exotic coloured Weyl

fermions SU(3)w singlets and an exotic coloured SU(3)w triplet


Quark Masses

The non-exotic top-like quarks mix into a heavy ( T ) and a light (top) combination

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

ff

Vw Vw

VFVF

toptop

top-like heavy, top-like exotic

light

top-like heavy, top-like exotic

light

top-like exotic heavy

top-like exotic heavy

Considering all the family…6X6 matrices almost block diagonalized

Considering all the family…6X6 matrices almost block diagonalized


Leptons

SM leptons doublets embedded in SU(3)SM leptons doublets embedded in SU(3)W W tripletstriplets Yukawa lagrangian simpler (protection of the flhiggs Yukawa lagrangian simpler (protection of the flhiggs

masses only from masses only from ννR and extra charged leptons)R and extra charged leptons) Majorana mass matrix for Majorana mass matrix for ννL obtained through the see-saw L obtained through the see-saw

mechanismmechanism

Dirac neutrinos mass matrix

(a = flavor index)

Dirac neutrinos mass matrix

(a = flavor index)

Majorana R-H neutrinos mass

matrix

Majorana R-H neutrinos mass

matrix

Charged leptons

Charged leptons

Decoupling of the extra charged

leptons

Decoupling of the extra charged

leptons


Mass Matrices

QuarksQuarksLeptonsLeptons


Constraining the Model

Weak sector

Flavor sector

[SU(3)XU(1)]W

Extra neutral gauge boson (Z‘) : bounds on the ew currents (ρ,…) and mZ’ fix the U(1)w coupling and vF.

[U(1)]F

FCNC processes ( neutral kaon mixing )

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

Low energy scale


Then … what is the scale f (Λ) ?

ff

Vw Vw

VFVF

ΛΛ

~ 1 TeV~ 1 TeV

~ 3 TeV~ 3 TeV

~ 30 TeV

~ 30 TeV

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

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

extra gauge bosons (5+1), heavy fermions

extra gauge bosons (5+1), heavy fermions

scalars (PGB) (15)scalars (PGB) (15)

EW SM gauge bosons (3), SM fermions

EW SM gauge bosons (3), SM fermions

mh0 ~ 300 GeVmh0 ~ 300 GeV

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

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

mh± ~ 560 GeVmh± ~ 560 GeV

Lightest charged scalar boson

Lightest charged scalar boson


Conclusions

We have given an example of flavor- electroweak gauge We have given an example of flavor- electroweak gauge unificationunification

The model is more constrained than the usual little-Higgs The model is more constrained than the usual little-Higgs model because on bounds on weak and flavor physicsmodel because on bounds on weak and flavor physics

Explicit predictions for the new weak gauge bosons and Explicit predictions for the new weak gauge bosons and scalars massesscalars masses

Many new particles: most interesting experimental Many new particles: most interesting experimental signatures for LHC coming from the scalar sectorsignatures for LHC coming from the scalar sector

The most characteristic prediction is a heavy Higgs boson The most characteristic prediction is a heavy Higgs boson


Represenations and Charges Assignments

QuarksQuarksLeptonsLeptons


What is natural?What is natural?

• Dirac:Dirac: dimensionless dimensionless parameters should be of order parameters should be of order oneone

• t Hooft: t Hooft: dimensionful dimensionful parameters should be of the order parameters should be of the order of the largest scale in the problem, unless a symmetry of the largest scale in the problem, unless a symmetry arises in the limit of vanishing couplingarises in the limit of vanishing coupling

the rules of the game

the flhiggs model f. bazzocchi sissa (trieste)

Documents

little flavonshiggs

global flavor symmetry

horizontal symmetry

exotic gauge symmetry

gauged little flavons

triplets triplets

flavor ew symmetry

little higgstheir mass