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; … ]

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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.,

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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

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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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