grand gauge-Higgs unification & its Higgs sector

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based on :

• PRD84, 051701 (2011) (arXiv:1103.1234)

w/ K.Kojima (Kyushu U.), K.Takenaga (Kumamoto Health Sci. U.)

• PRD84, 115016 (2011) (arXiv:1106.3229)

• arXiv:1312.7575 (to appear in PRD),

w/ M.Kakizaki, S.Kanemura, H.Tanigucji (U. of Toyama)

grand gauge-Higgs unification

& its Higgs sector

Toshifumi Yamashita

(Aichi Medical Univ.) 2014/3/26 @TWCU

Workshop 2014

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GUT-breaking via Hosotani mechanism

outline

= “grand gauge-Higgs unification”

 natural Doublet-Triplet (DT) splitting

 general prediction: light adjoints

We may get a hint of the GUT-breaking @LHC&LC.

K.Kojima, K.Takenaga & T.Y. (2011)

T.Y. (2011)

SUSY version (SGGHU)

M.Kakizaki, S.Kanemura, H.Taniguchi & T.Y. (2013) Cf) Lim&Maru(2007)

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plan

 Outline

 grand gauge-Higgs unification

 low energy effective theory

 Higgs sector

 summary

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grand gauge-Higgs unification

 The order parameter, , is valued on the group (instead of the algebra).

traceless special

(inversely) missing VEV

T.Y. (2011)

DT Splitting

symmetry breaking by a continuous Wilson loop

VEV of zero-mode of A₅ gauge-Higgs unification

 Hosotani mechanism

Y. Hosotani (1983)

Hosotani-san &

Maru-san’s talk

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 difficulty

• orbifold action projects out adjoint scalars

K.Kojima, K.Takenaga & T.Y. (2011)

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

- ^``diagonal embedding” method

We apply this in our pheno. models.

due to the opposite orbifold BCs.

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

Cf) Lim&Maru(2007)

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½

¾

½

¾

½

¾

½

¾

½

¾

 diagonal embedding

(in field theory)

ex)

•

“deconstruction”

similar to S¹ model

chiral fermions

has a zero-mode.

K.Kojima, K.Takenaga

& T.Y. (2011)

Hatanaka-san’s talk

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½

¾

½

¾

½

¾

½

¾

½

¾

 diagonal embedding

(in field theory)

ex)

•

“deconstruction”

similar to S¹ model

chiral fermions

has a zero-mode.

This provides a way to “introduce”

chiral fermions in S

¹

models!!

K.Kojima, K.Takenaga

& T.Y. (2011)

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 matter content

 bulk fields

• similar to S¹ model : vector-like

• couple to W.L. : SU(5) incomplete multiplets

 boundary fields

• essentially 4D fields : chiral

• not couple to W.L. : SU(5) full multiplets H_u & H_d

chiral matter

in contrast to the orbifold GUTs

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plan

 Outline

 Higgs sector

 summary

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low energy effective theory

• A₅ (= adjoint Higgs) is massless @tree level,

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

Its superpartners can have masses of O(m_SB).

Light adjoints, are predicted.

T.Y. (2011)

 low energy prediction

• ₂-symm. : (may be broken)

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 gauge coupling unification

• The adjoint matters : recovered w/

to remain perturbative

2 4 6 8 10 12 14 16

10 20 30 40 50 60

2 4 6 8 10 12 14 16

10 20 30 40 50 60

2 4 6 8 10 12 14 16

10 20 30 40 50 60

- MSSM

- MSSM + adj

- MSSM + adj + add

ex1) additional matters for :

T.Y. (2011)

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 phenomenology of adjoints

T.Y. (2011)

• SU(3) is not asymptotically free,

& remains strong @high energy

squarks & octet become rather heavy.

• colorless fields may be produced @LHC/LC.

• these may affect the higgs sector indirectly.

NMSSM-like contribution heavier higgs

e.g.

Higgs couplings are corrected at a few % level.

M.Kakizaki, S.Kanemura, H.Taniguchi & T.Y. (2013)

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plan

 Outline

 Higgs sector

 summary

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Higgs sector

 Higgs sector extended

• superpotential

2 more [CP even, CP odd, charged] modes.

H_u, H_d + S &

 no self couplings for S &

 & are related to the gauge couplings control the effects highly predictive

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• set @ GUT scale

Higgs sector

 RG running

• fix a model gauge coupling unification

• solve the RGEs

@ weak scale

ex1)

/ ( ) _{1 2 3}, ,

2 5 3 _S _S g λ_  λ  λ 

. , .

1 1 _S 0 25 λ_  　λ 

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T.Y. (2011)

• SU(3) is no longer asymptotically free,

& remains strong @high energy

squarks & octet become rather heavy.

• colorless fields may be produced @LHC/LC.

• these may affect the higgs sector indirectly.

NMSSM-like contribution heavier higgs

e.g.

Higgs couplings are corrected at a few % level.

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Higgs sector

& remains strong @high energy squarks & octet become heavy.

• top Yukawa mediates them to H_u. large

 fine tuning for EWSB

 large m_A, m_S,

• further tunings w/ inputs @GUT scale benchmark points with rich pheno.

• S( ) H_u H_d mediate it to S, & H_d.

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Higgs sector

 three Benchmark Points

(A) the SM-like Higgs boson is light (less-tuned) (B) the MSSM-like Higgs bosons are light

(C) the adjoints affect the SM-like Higgs couplings

tan β  3

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Higgs sector

 deviations of the SM-like Higgs couplings

(shifted)

30% 20% 10%

singlet mixing

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Higgs sector

 deviations of the SM-like Higgs couplings

30% 20% 10%

singlet mixing

same as NMSSM

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Higgs sector

 MSSM-like charged Higgs boson mass

. , .

1 1 _S 0 25 λ_  　λ 

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Higgs sector

 direct search?

Case (C)

MSSM-like &

singlet-like

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summary

 SUSY grand GHU

theoretically well motivated

 natural doublet-triplet splitting

 generally predicts light adjoint chiral matters the Higgs sector is extended, S &

 phenomenological study

 heavier Higgs mass

 distinguishable charged Higgs mass

 a few % deviations from the SM/MSSM can be a reasonable target of the ILC

T.Y. (2011)

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back up

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ex)

 basis transformation

(broken) gauge transformation w/

• BCs around are modified:

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ex)

 basis transformation

(broken) gauge transformation w/

• BCs around are modified:

symmetry breaking by BCs,

as in the orbifold breaking

 DT splitting

“anti-periodic” 5 chiral

T.Y. (2011)

massless doublet

5 :

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Higgs sector

& remains strong @high energy squarks & octet become heavy.

• top Yukawa mediates it to H_u. large

 fine tuning for EWSB

 large m_A, m_S,

• further tunings w/ inputs @GUT scale benchmark points with rich pheno.

• S( ) H_u H_d mediate it to S, & H_d.

• large rather heavy sleptons

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Higgs sector

 three Benchmark Points

(A) the SM-like Higgs boson is light (less-tuned) (B) the MSSM-like Higgs bosons are light

(C) the adjoints affect the SM-like Higgs couplings