PDF grand gauge-Higgs unification & doublet-triplet splitting - TWCU

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based on : based on :

• PRDPRD8484, 051701 (2011) (arXiv:1103.1234), 051701 (2011) (arXiv:1103.1234)

w/ K. Kojima w/ K. Kojima (Kyushu) (Kyushu) & K. Takenaga & K. Takenaga (Kumamoto Health Science)(Kumamoto Health Science)

• PRDPRD8484, 115016 (2011) (arXiv:1106.3229), 115016 (2011) (arXiv:1106.3229)

Toshifumi Yamashita

MISC, Kyoto Sangyo U.

Aichi Medical U. ^{愛知医科大学} 2012/3/14 @Kobe

2012/3/14 @Kobe

grand gauge-Higgs unification grand gauge-Higgs unification

& doublet-triplet splitting

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GUT-breaking via

Hosotani mechanism

Outline

 PRD84, 051701 (2011) w/ Kojima & Takenaga

• proposed this possibility:

grand gauge-Higgs unification

 PRD84, 115016 (2011)

• SUSY version : testable Doublet-Triplet splitting We may get a hint of the GUT-breaking @LHC.

light adjoint

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Plan

• Outline Outline

• quick review quick review

- DT splitting- DT splitting

- Hosotani mechanism- Hosotani mechanism

• grand GHU & DT splitting grand GHU & DT splitting

• low energy predictions low energy predictions

• summary summary

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• unifications of forces and of matter

• charge quantization

• stabilization of the weak scale

• gauge coupling unification (GCU)

SUSY GUTs

Higgs?

Proton decay?

 fascinating extension of SM

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DT Splitting problem

 SUSY SU(5) model

Fine-tuning of 10¹⁴!!

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 Solutions



DW mechanism SO(10) :

• Sliding Singlet mechanism

• Missing partner mechanism

• Dimopoulos-Wilczek (DW) mechanism

• GIFT mechanism (Higgs as pNG)

• orbifold GUT, etc.

missing VEV

DT Splitting problem

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Hosotani mechanism

• at first :

applied to GUT breaking (A₅ : adjoint) in models w/o chiral fermions

Y. Kawamura (2000-)

• after orbifold breaking :

mainly applied to the EW breaking

• chiral fermion

• fundamental repr.

GUT breaking in models w/ chiral fermion?

K.Kojima & K.Takenaga & T.Y.

symmetry breaking by a continuous Wilson loop

VEV of zero-mode of A₅

Y. Hosotani (1983)

gauge-Higgs unification

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Hosotani mechanism

 difficulty

• orbifold action projects out adjoint scalars

• this difficulty is shared w/ heterotic string - well studied, classified w/ Kac-Moody level

- ``diagonal embedding” method

Why can’t we use this in our pheno. models?

grand gauge-Higgs unification

due to the opposite orbifold BCs.

e.g. Ito et.al. ( T.Y.) PRD(2011), JHEP(2011)flux cmpt?

Cf. Kobayashi’s talk

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Plan

• Outline Outline

• low energy predictions low energy predictions

• summary summary

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 diagonal embedding

K.R.Dienes & J.March-Russel (1996)

ex)

•

latticized picture

similar to S¹ model

chiral fermions

has a zero-mode.

This provides a way to “introduce”

chiral fermions in S

¹

models!!

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 SU(5) example

SU(5) G_SM on a local minimum where

(inversely) missing VEV

T.Y. PRD (2011)

w/ appropriate bulk fermions

DT Splitting

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T.Y. PRD (2011)

5 :

grand GHU & DT splitting grand GHU & DT splitting

 basis transformation

(broken) gauge transformation w/

• BCs around are modified:

symmetry breaking by BCs,

as in the orbifold breaking

 “DT splitting”

“anti-periodic” 5 scalar massless doublet

ex)

@ tree level

SUSY

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T.Y. PRD (2011)

grand GHU & DT splitting grand GHU & DT splitting

 basis transformation

(broken) gauge transformation w/

• BCs around are modified:

ex)

 “DT splitting

“anti-periodic” 5 chiral massless doublet SUSY

5 :

symmetry breaking by BCs,

as in the orbifold breaking

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grand GHU & DT splitting grand GHU & DT splitting

 matter content

 bulk fields

• similar to S¹ model : vector-like

• couple to P_W : SU(5) incomplete multiplets

 boundary fields

• essentially 4D fields : chiral

• not couple to PW : SU(5) full multiplets H_u & H_d

chiral matter

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Plan

• Outline Outline

• low energy predictions low energy predictions

• summary summary

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low energy predictions low energy predictions

 light adjoint chiral multiplets

• A₅ is massless @tree level,

and acquires a mass of O(m_SB) via loop.

Its superpartners can have masses of O(m_SB).

We may observe .

 gauge coupling unification

• The adjoint matters : recovered w/

to remain perturbative

T.Y. PRD (2011)

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low energy predictions low energy predictions

 recovery of GCU

ex) additional matters for :

5 10 (in the bulk)

T.Y. PRD (2011)

- MSSM

- MSSM + adj

- MSSM + adj + add

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 phenomenology of adjoints

low energy predictions low energy predictions

• SU(3) is no longer asymptotically free, and remains strong @high energy squarks & octet become rather heavy.

• colorless fields may be produced @LHC.

• these may contribute to the higgs mass.

(SUSY) triplet/(doublet)/singlet Higgs model.

e.g.

NMSSM-like and/or through loop

M.Kakizaki, S.Kanemura, H.Tanigucji & T.Y.

: now working

Prelim y inar

heavier higgs

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• a (local) vacuum : SU(5) G_SM

summary

Hosotani-breaking of GUT symmetry

 PRD84, 051701 (2011) w/ K.Kojima & K.Takenaga

• proposed this possibility, grand gauge-Higgs unification.

 PRD84, 115016 (2011)

• SUSY version : DT splitting realized naturally

• general prediction : light adjoint chiral w/

may be tested @LHC

e.g. direct production of a weak triplet, heavy squarks & higgs