DIVERGENCIES AND SYMMETRIES IN HIGGS-GAUGE UNIFICATION THEORIES

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DIVERGENCIES AND SYMMETRIES IN
HIGGS-GAUGEUNIFICATION THEORIES
Carla Biggio Institut de Física d'Altes
Energies Universitat Autonoma de Barcelona
based on CB Quirós, Nucl.Phys.B703 (2004) 199
hep-ph/0407348 (see also hep-ph/0410226)
XL Rencontres de Moriond ELECTROWEAK INTERACTIONS
UNIFIED THEORIES La Thuile (IT), 5-12/03/04
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Little Hierarchy Problem (LHP)
A possible motivation
Barbieri Strumia 00 Giudice 03
No fine-tuning ? ?SM 1 TeV
Precision tests ? ?LH 5-10 TeV
One order of magnitude of discrepancy LHP
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Supersymmetry (SUSY)
A possible solution
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Higgs-gauge unification
An alternative solution
Consider a gauge theory in a D-dimensional
space-time
4D Lorentz scalars ? Higgs fields !
Randjbar-Daemi, Salam Strathdee 83
4D Lorentz vector
they can acquire mass through the Hosotani
mechanism
Hosotani et al. 83-04
Higgs mass in the bulk is protected by
higher-dimensional gauge invariance
finite corrections (1/R)2 allowed
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Gauge theory in D dimensions
Invariant under gauge group G (SO(1,D-1))
Spacetime MD coord. xM (x?,yi)
Compactification on the orbifold M4xTd/Gorb
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Action of Gorb on the fields
acts on Lorentz indices
acts on gauge and flavour indices
unconstrained
fixed by requiring invariance of lagrangian
?
scalars vectors
it can be used to break symmetries
S1
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Gauge symmetry breaking _at_ yf
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Effective 4D lagrangian
Lf ? most general 4D lagrangian compatible with
symmetries _at_ yf
The symmetries _at_ yf are Gorb SO(3,1) Hf
K
All these are dimension FOUR operators ?
renormalize logarithmically
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another (worse) allowed term
is invariant under Gorb SO(3,1) Hf K ?
This is a dimension TWO operator ? quadratic
divergencies
D6 it seems it always exists

• D6 (QFT) Gersdorff, Irges Quirós 02
  Csaki, Grojean Murayama 02
• Scrucca, Serone,
  Silvestrini Wulzer 03 (SSSW03)
• D10 (strings) Groot-Nibbelink et al. 03

? How can we avoid this?
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another symmetry must be considered
But
CB Quirós, Nucl.Phys.B703 (2004) 199
The symmetries _at_ yf are Gorb SO(3,1) Hf
K Of
? Can this Of forbid the tadpole?
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The tadpole Fij and the symmetry Of
If OfSO(2) x then the Levi-Civita tensor
eij exists
?
is Of invariant
? TADPOLES ARE ALLOWED
If OfSO(p1) x SO(p2) x (pigt2) then the
Levi-Civita tensor is
? only invariants constructed with pi-forms are
allowed
? NO TADPOLES
Sufficient condition for the absence of localized
tadpoles
BQ04
Of is orbifold-dependent we studied the Td/ZN
case
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Orbifolds Td/ZN (d even)
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Conclusions
In Higgs-gauge unification theories (Higgs Ai)

• bulk gauge symmetry G prevents the Higgs from
  adquiring
• a quadratically divergent mass in the bulk
• shift symmetry K forbids a direct mass _at_ yf

If Hf U(1)a x can be radiatively
generated _at_ yf giving rise to a quadratically
divergent mass for the Higgs
Fija can be generated ? it is Of-invariant
such that
If OfSO(p1) x SO(p2) x (pigt2) ? NO
TADPOLES
If OfSO(2) x ? TADPOLES
Td/ZN (d even, Ngt2) if Nfgt2 ? OfSO(2) x
x SO(2) ? TADPOLES
Td/Z2 (any d) OfSO(d) ? TADPOLES ONLY FOR
d2 (D6)
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Outlook

• The absence of tadpoles is a necessary but not
  sufficient condition
• for a realistic theory of EWSB without SUSY
• Other issues
• REALISTIC HIGGS MASS
• Dgt6 (D5 no quartic coupling, D6
  tadpoles)
• Td/Z2 ? d Higgs fields ? non-minimal
  models
• ? we have to obtain only one SM Higgs
• even if this is achieved
• ? Higgs mass must be in agreement with LEP
  bounds
• FLAVOUR PROBLEM
• - matter fermions in the bulk coupled to a
  background
• which localizes them at different locations
• 
  Burdman Nomura 02
• - matter fermions localized and mixed with
  extra heavy