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6D Gauge-Higgs unification with custodial symmetry. Yutaka Sakamura (KEK) in collaboration with Yoshio Matsumoto ( Sokendai ) [arXiv:1407.0133] t o appear in JHEP. Introduction. Gauge-Higgs unification (GHU). [ Manton, 1979; Fairlie , 1979; Hosotani , 1983; … ]. =. Higgs. - PowerPoint PPT Presentation
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Summer Institute 2014@Fuji Yoshida
6D Gauge-Higgs unification with custodial symmetry
Yutaka Sakamura (KEK)in collaboration with
Yoshio Matsumoto (Sokendai)
[arXiv:1407.0133]to appear in JHEP
August 25, 2014
Summer Institute 2014@Fuji Yoshida
Introduction
August 25, 2014
Gauge-Higgs unification (GHU)
Higher-dim. gauge sym. protects the Higgs massagainst quantum correction.
Higgs
=
[Manton, 1979; Fairlie, 1979; Hosotani, 1983; …]
Simplest model• 5D U(3) model on S /Z (flat spacetime)
• 5D SO(5)xU(1) model on S /Z (warped spacetime)
1
1
2
2
[Scrucca, Serone, Silvestrini, Wulzer, 2004; … ]
[Agashe, Contino, Pomarol, 2005; … ]
2/13
Summer Institute 2014@Fuji YoshidaAugust 25, 2014
Wilson line phase :
The effective potential has quadratic terms (1 loop)quartic terms (tree)
[Agashe, Contino, Pomarol, 2005; …]
must be small, i.e.,
3/13
In this work, we consider 6D gauge-Higgs unification.
(determined at 1-loop level)
Summer Institute 2014@Fuji YoshidaAugust 25, 2014
Gauge group :simple group
The Weinberg angle is obtained by adjusting .
(gauge couplings)
In GHU, can deviate from 1 even at tree-leveldue to the mixing with the KK modes.
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Extra dimensions :
Introducing the custodial symmetry.
Summer Institute 2014@Fuji YoshidaAugust 25, 2014
[Agashe, Contino, Da Rold, Pomarol, 2006]
Rank 2
Rank 3
Custodial symmetry
Find candidates for a setup of realistic 6D GHU by means of the group-theoretical analysis.
Purpose
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Summer Institute 2014@Fuji YoshidaAugust 25, 2014
EW sym. is broken by a bidoublet Higgs:
Symmetry breakingRank 2
Rank 3
orbifold
(at the fixed point)
(at the fixed point)orbifold
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Summer Institute 2014@Fuji YoshidaAugust 25, 2014
SO(5) :
G :2
Rank 2
SU(4) :
SO(7) :
Sp(6) :
Rank 3
Irreducible decomposition
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Summer Institute 2014@Fuji Yoshida
where and .
August 25, 2014
T /Z orbifold2 N
Orbifold conditions
(N=2,3,4,6)
Cartan generator
Zero-mode conditions
roots of G
fixed points
8/13
Summer Institute 2014@Fuji YoshidaAugust 25, 2014
1
1
1
1
1
1
0
0
0
0
0
0
0
2
Number of Higgs bidoublets
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Summer Institute 2014@Fuji Yoshida
We focus on the third generation quarks.
August 25, 2014
Matter sector
6D fermion :6D chirality
4D chirality
This belongs to an irreducible rep. of G.
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Possible ‘s are restricted by the condition for the VEV alignment of .
Summer Institute 2014@Fuji YoshidaAugust 25, 2014
VEVs must be aligned as .
Higgs bidoublet :
VEV alignment
The alignment can be achieved if
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Summer Institute 2014@Fuji Yoshida
1. The corresponding weights are related as
2. have zero-modes in , and have zero-modes in .
August 25, 2014
Conditions for the VEV alignment
Among the representations such that ,only of SU(4) satisfies the above conditions.
Top Yukawa
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Summer Institute 2014@Fuji YoshidaAugust 25, 2014
of SU(4)
By orbifolding,
Only on T /Z , there is a choice of the orbifold conditionsthat satisfy the condition 3.
2 3
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Tree-level mass relations:
Summer Institute 2014@Fuji Yoshida
Summary• We considered necessary conditions for Gauge-Higgs unification on T /Z with custodial symmetry. • The requirements we demanded are
August 25, 2014
A Scalar bidoublet zero-mode exists.
2 N
• The best candidate is , and .
provides a right size group factor for the top Yukawa coupling.
The bosonic sector is symmetric under .
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The top and bottom quarks are coupled to through .
Summer Institute 2014@Fuji YoshidaAugust 25, 2014
If
we obtain
includes
includes ,
If and only has zero-modes,
we obtain
After integrating out unnecessary modes,
Yukawa couplings
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Summer Institute 2014@Fuji YoshidaAugust 25, 2014
Weight
simple rootZero-mode conditions
integer
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