in preparation

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Symmetry Restoration at High Temperature for
Little Higgs Models?

• (in preparation)
• Amine AHRICHE
• Laboratory of Theoretical Physics,
• University of Jijel,
• Algeria

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Outline

• Hierarchy problem Little Higgs Models.
• Symmetry Breaking and No-Restoration at High
  Temperature.
• Thermal Effects and Symmetry Restoration.
• Conclusions.

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Hierarchy problem of SM Little Higgs Models

• The SM has been very successful, but Hierarchy
  Problem, Mass Origin, Number of Generations, Dark
  Matter, Neutrino Mass, Matter-antimatter
  asymmetry ..etc

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Hierarchy problem of SM Little Higgs Models

• The SM has been very successful, but Hierarchy
  Problem, Mass Origin, Number of Generations, Dark
  Matter, Neutrino Mass, Matter-antimatter
  asymmetry ..etc

• The Hierarchy Problem

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Hierarchy problem of SM Little Higgs Models

• The SM has been very successful, but Hierarchy
  Problem, Mass Origin, Number of Generations, Dark
  Matter, Neutrino Mass, Matter-antimatter
  asymmetry ..etc

• The Hierarchy Problem

But ??MPl !!!
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• Little Higgs (Higgs as a Pseudo-Goldstone boson)

Georgi, Pais (1974) Georgi, Dimopoulos, Kaplan
(1984) Arkani-Hamed, Cohen, Georgi (2001)

• A vev f in new sector with spontaneously broken
  global symmetry
• Scalars are present because of the Goldstone
  theorem
• Scalar potential by radiative corrections
• Top sector triggers EWSB

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• Little Higgs (Higgs as a Pseudo-Goldstone boson)

Georgi, Pais (1974) Georgi, Dimopoulos, Kaplan
(1984) Arkani-Hamed, Cohen, Georgi (2001)

• A vev f in new sector with spontaneously broken
  global symmetry
• Scalars are present because of the Goldstone
  theorem
• Scalar potential by radiative corrections
• Top sector triggers EWSB

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• Little Higgs (Higgs as a Pseudo-Goldstone boson)

Georgi, Pais (1974) Georgi, Dimopoulos, Kaplan
(1984) Arkani-Hamed, Cohen, Georgi (2001)

• A vev f in new sector with spontaneously broken
  global symmetry
• Scalars are present because of the Goldstone
  theorem
• Scalar potential by radiative corrections
• Top sector triggers the EWSB

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• How to construct a Little Higgs Model
• Extend gauge theory SM x G ? SM (like Z
  models)
• Enlarge global symmetry SM x G is embedded in
  a larger symmetry H (like the custodial symmetry
  in the SM)
• Extend top sector New vector-like quark(s)
  coupled to both SM and G

Global broken symmetry Extended Gauge Theory
New fields New interactions
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The Littlest Higgs
Arkani-Hamed et al.(2002)

• The Littlest Higgs is a non-linear s-model based
  on a global SU(5) symmetry which is spontaneously
  broken to SO(5) at the scale f 1 TeV.

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The Littlest Higgs
Arkani-Hamed et al.(2002)

• The Littlest Higgs is a non-linear s-model based
  on a global SU(5) symmetry which is spontaneously
  broken to SO(5) at the scale f 1 TeV.
• An SU(2)U(1)2 subgroup of SU(5) is gauged,
  and is spontaneously broken to the diagonal
  SU(2)U(1) subgroup.

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The Littlest Higgs
Arkani-Hamed et al.(2002)

• The Littlest Higgs is a non-linear s-model based
  on a global SU(5) symmetry which is spontaneously
  broken to SO(5) at the scale f 1 TeV.
• An SU(2)U(1)2 subgroup of SU(5) is gauged,
  and is spontaneously broken to the diagonal
  SU(2)U(1) subgroup.
• New states that cancel the quadratic divergences
• Heavy top T
• Extra gauge bosons W , B
  ,
• Triplet ?

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• Global symmetry breaking SU(5)? SO(5)
• 
  24 - 10 14 Goldstone bosons
• 4 are eaten by SU(2)U(1)2? SU(2)U(1)SM
• 10 are remaining 4Higgs doublet 6
  Complex triplet

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(No Transcript)
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Lagrangian
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Lagrangian
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Lagrangian
Collective breaking at ?4pf
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Lagrangian
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Lagrangian
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Lagrangian
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Symmetry Breaking and No-Restoration at High
Temperature
Since , no EWSB!! but when including
1-loop corrections
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Symmetry Breaking and No-Restoration at High
Temperature
Since , no EWSB!! but when including
1-loop corrections
Espinosa et al., PRD72, 043520 (2005)
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Symmetry Breaking and No-Restoration at High
Temperature
Since , no EWSB!! but when including
1-loop corrections
Espinosa et al., PRD72, 043520 (2005)
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At finite temperature, the scalar potential is
given by
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At finite temperature, the scalar potential is
given by
Espinosa et al., PRD72, 043520 (2005)
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At finite temperature, the scalar potential is
given by
Espinosa et al., PRD72, 043520 (2005)
The symmetry is not restored at high temperature
as in other gauge theories no Phase
transition, no cosmological consequences..!!
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What is the explanation of this behavior? The
reason is that the thermal corrections are
computed from the same diagrams that contribute
to the mass corrections.
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What is the explanation of this behavior? The
reasons is that the termal corrections are
computed from the same diagrams that contribute
to the mass.

• The 1-loop thermal corrections make the potential
  more negative at very high temperature instead of
  relax it to positve values because
• Yukawa correction is larger than tree-level
  especially for ?4pf.
• The Yukawa thermal corrections become more
  significant instead of getting suppressed at high
  temperatures.
• Is there any solution!!

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Is ?4pf really the collective symmetry breaking
scale?
Unitarity suggests ?(3-4)f
S. Chang H.-J. He, PLB 586 (2004) 95
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Is ?4pf really the collective symmetry breaking
scale?
Unitarity suggests ?(3-4)f
S. Chang H.-J. He, PLB 586 (2004) 95
Study of scalar loops suggests
J.R. Espinosa J.M. No, JHEP01(2007)006
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Is ?4pf really the collective symmetry breaking
scale?
Unitarity suggests ?(3-4)f
S. Chang H.-J. He, PLB 586 (2004) 95
Study of scalar loops suggests
J.R. Espinosa J.M. No, JHEP01(2007)006
If we put
, at the minimum hpf/2 ,
we get ?(1.5-3)f
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Is ?4pf really the collective symmetry breaking
scale?
Unitarity suggests ?(3-4)f
S. Chang H.-J. He, PLB 586 (2004) 95
Study of scalr loops suggests
J.R. Espinosa J.M. No, JHEP01(2007)006
If we put
, at the minimum hpf/2 ,
we get ?(1.5-3)f
The Little Higgs breaking scale should be ?lt 4pf
Are there any interactions that were not taken
into account?
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Thermal Effects and Symmetry Restoration
Due to the non-linear nature of the scalar fields
Yes
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Yes
Due to the non-linear nature of the scalar fields
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Yes
Due to the non-linear nature of the scalar fields
May be important for Tf
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Yes
Due to the non-linear nature of the scalar fields
May be important for Tgtf
Then we consider higher-loops dominant
T-dependant contributions by replacing
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0th order
Scalars
Gauge fields
Fermions
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mth order
Scalars
Gauge fields
Fermions
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Thermal Masses
Scalars
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Thermal Masses
Scalars
Gauge fields
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Thermal Masses
Scalars
Gauge fields
Fermions
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Effective Potential
But ?ltlt4pf
Espinosa et al., PRD72, 043520 (2005)
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Effective Potential
0.3
0.2
?4pf
0.1
0
-0.1
V/f4
-0.2
-0.3
-0.4
-0.5
-0.6
-1
-0.5
0
0.5
1
h/pf
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Effective Potential
0.3
?1.2f
0.2
0.1
0
V/f4
-0.1
-0.2
-0.3
-0.4
-1
-0.5
0
0.5
1
h/pf
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Effective Potential
0.18
0.16
?1.2f, Tf
0.14
0.12
0.1
V/f4
0.08
0.06
0.04
0.02
0
-0.02
-1
-0.5
0
0.5
1
h/pf
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Conclusion

• The symmetry nonrestoration reasons are
• 1- Large value of ?4pf
• 2- Yukawa thermal contributions are not
  suppressed.
• Solution
• 1- Natural values for ?f
• 2- Including higher order dominant thermal
  corrections.
• Values of cm terms suggest ?f (we should care
  for Tf only)
• Then one can ivestigate the the EWPT nature in LH.

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Thank You