Radiative EWSB in a Little Higgs Model Carl Schmidt Michigan State - - PowerPoint PPT Presentation

Radiative EWSB in a Little Higgs Model

Carl Schmidt

Michigan State University May 11, 2010 PHENO 2010 arXiv:1001.0584, R. Foadi, J. T. Laverty, CS, and J.-H. Yu

Motivation

Little Hierarchy: v2 << f 2 << Λ2

(0.25 TeV)2 (~1 TeV)2 (~10 TeV)2

Little Higgs (LH):

Collective Symmetry Breaking: If g1= 0 or g2= 0, H is a Goldstone Boson. => Quadratic divergences ~ Λ2 vanish at one loop

Higgs Potential: V = m2 |H|2 + λ |H|4

If potential is purely radiative, expect m2~g4f2, λ~g4 => v2 ~ -m2/λ2 ~ f2 => Too big! Typically, LH models introduce new operators to make λ larger. Plaquettes, mass terms, quartic terms

Motivation (cont’d)

Fermions: Collective Symmetry Breaking also Generic contribution to m2 from heavy top partner T:

Good: Gives negative contribution to m2. Necessary for symmetry breaking. Bad: Since mH

2 ~ -2m2, it gives contribution to Higgs mass

• f more than 1 TeV.

Still must have cancellation to get light Higgs.

=> Reconsider pure radiative EWSB

m2 = 3t

2

8 2 MT

2 ln 2

MT

2

The Model

Global Symmetry: SO(5)0 x SO(5)1→ SO(5) Gauge Symmetry: [SU(2) x U(1)]0 x [SU(2) x SU(2)]1

→ SU(2)L x U(1)Y

Collective Symmetry Breaking: If (g0L = g0R = 0) or (g1L = g1R = 0), H is a Goldstone Boson. => Quadratic divergences vanish at one loop

Related Models: 5-dimensional Gauge-Higgs Model (Medina, Shah, Wagner) Custodial Minimal Moose (Chang, Wacker)

Gauge Sector (Barbieri, Bellazzini, Rychkov, Varagnolo)

Heavy Gauge Bosons

MZ R

2 1 2 g0R 2 + g1R 2

( ) f 2

MWR

2

1

2 g1R 2 f 2

MZ L

2 1 2 g0L 2 + g1L 2

( ) f 2

MWL

2

1

2 g0L 2 + g1L 2

( ) f 2

WR ZR ZL WL g1L

2 = g1R 2 = 6

f =1 TeV

Higgs boson is only light scalar. All other GB’s from Σ are eaten.

(Also SM W and Z)

Fermions

QL and tR are in 5’s of SO(5):

• Dirac Fermions with missing SM partners
• Transform under SU(2)0LxU(1)0R
• χ is SU(2) doublet with charge +5/3, +2/3 fermions
• bR can be included in a 10 of SO(5), with more heavy fermions

Fermion mass terms:

L

A =

Q

• t
• L

A

R

A =

• t
• R

A

L

B =

• Q
• L

B

R

B =

• Q
• t
• R

B

Lmass = A f

L AR A B f L BR B 1 f L AEE R B + h.c.

Breaks SO(5)0 Preserves SO(5)1 Preserves SO(5)0 Breaks SO(5)1 Collective Symmetry Breaking => SO(5)1-breaking spurion E =

1

Heavy Fermions

MTA

2 A 2 + 1 2

( ) f 2

MTB

2 B 2 f 2

Mt

2 t 2v 2 /2

TA A = 1 = 2t B = 0.981t f =1 TeV TB t

Three fermion masses depend on Higgs field

1 t

2 = 1

1

2 + 1

A

2

Effective Potential

Possible to obtain EW scale v, because fermions give

m2 31

2

8 2 2B

2 A 2

( )ln 2

MTA

2

21

2A 2 f 2

1

2 1 2 3A 2 + 2B 2

( ) f 2

Higgs Boson Mass

f =10 TeV

g1L

2 = g1R 2 = 0.5, 2, 4

f =1 TeV

• Higgs boson is typically light.
• Mass insensitive to gauge couplings.

sint = 1 1

2 + A 2

Sensitivity to UV Physics

Possible to have separate fermion cutoffs, ΛA and ΛB Then: In fact, can make this precise:

• Make and complete Dirac multiplets (5s of SO(5) )
• Add new SU(2) doublet and singlet
• Add new mass term:

Gives above fermion contribution --- finite at one loop!

m2 31

2

8 2 2B

2 ln B 2

MTA

2 A 2 ln A 2

MTA

2

• Lmass = A
• Q

L AQR A Bt L B

• t

R B + h.c.

A B

• Q

L A

• t

R B

Compare to SUSY

Sensitivity to UV Physics

g1L

2 = g1R 2 = 2

f =1 TeV

Why is Higgs mass solution typically light? with

sint = 1 1

2 + A 2

A 4f , B 4f

• M H

2 2v 2

3t

4

4 2 1 4 ln MTA

2

Mt

2

+ F sint , MTA

2

MTB

2

( )

Electroweak Constraints

g1 = g1L = g1R

Bounds using universal electroweak parameters, S, T, Y, W Heavy fermion contributions still to be done ˆ ˆ

Conclusions

• Presented a Little Higgs model with Higgs Potential fully

radiatively-generated

• Cancellation in m2 occurs between two heavy fermion

contributions

• Higgs boson mass is generically light ( < 200 GeV )
• Higgs is the only light scalar
• Electroweak constraints considered, but more

phenomenology to be done