# Presentation: 350411

## Higgs mass in the gauge-Higgs unification theory 

- Higgs mass in the gauge-Higgs unification theory

- Naoyuki Haba

**LCW05  SLAC (3/18/05-3/22/05)**

- (tokushima univ.)

## Plan of talk

- 1. Introduction
- 2. gauge-Higgs unification
-       -----*SU*(3)×*SU*(3), *SU*(6) models-----
- 3. dynamical EW symmetry breaking I
**        ****NH, Y. Hosotani, Y. Kawamura and T. Yamashita,  Phys.Rev.D70:015010, 2004 **
**        ****NH and T. Yamashita, JHEP 0402:059,2004**
- 4. dynamical EW symmetry breaking II
-         **NH and T. Yamashita, ****JHEP 0404 (2004) 016**** **
- 5. Higgs mass and phenomenology
**     ****NH, K.Takenaga and T.Yamashita, Phys.Rev.D71:025006,2005**
**     ****NH, K.Takenaga and T.Yamashita, hep-ph/0411250**
- 6. summary and discussion

## 1. Introduction

- 1-1. motivation
- 1-2. notation

## 1-1: motivation

- ☆ higher dimensional gauge theory:
-     scalar A5 in 4D effective theory ← extraD component
-       → _**identify Higgs field**_

**Origin of adjoint Higgs which break SU(5)**
- dynamics of 5D gauge theory

- “Hosotani mech.”

- μ

- ex.

- _1-1: motivation_

## 1-1: motivation

- _1-1: motivation_

- ☆ higher dimensional gauge theory:
-     scalar A5 in 4D effective theory ← extraD component
-       → _**identify Higgs field**_

**⇒ ****origin of Higgs doublets **

**⇒ ****origin of Yukawa int.**

- μ

- ex.

**Gauge-Higgs unification**

- “Higgs doublet” mass is finite!  (~1/R)

**5D gauge inv.**

## 1-2: notation

- _1-2: notation_

## 1-2: notation

- _1-2: notation_

## 2. gauge-Higgs unification

-    --- *SU*(3)×*SU*(3) model & *SU*(6) model---

- 2-1. *SU*(3)×*SU*(3) model
- 2-2. *SU*(6) model
- 2-3. SUSY

## 2-1. SU(3)c×SU(3)W model 

- _2-1. __*SU*__(3)__c__×__*SU*__(3)__W__ model_

- in base of

- (Kubo,Lim,Yamashita,
- Hall,Nomura,Smith,
- Burdman,Nomura,....)

## in base of

- Higgs doublet

- Higgs doublet

- _2-1. __*SU*__(3)__c__×__*SU*__(3)__W__ model_

- (Kubo,Lim,Yamashita,
- Hall,Nomura,Smith,
- Burdman,Nomura,....)

## 2-2. SU(6) GUT

- _2-2. __*SU*__(6) GUT_

- (Hall,Nomura,Smith,
-  Burdman,Nomura)

- in base of

## 2-2. SU(6) GUT

- Higgs doublet

- Higgs doublet

- _2-2. __*SU*__(6) GUT_

- (Hall,Nomura,Smith,
-  Burdman,Nomura)

- in base of

## 2-3. 5D N=1 SUSY

- _2-3. 5D N=1 SUSY_

_***5D N=1 SUSY***_

**odd dim.=vector-like**

***⇔****** ***_***4D N=***__***2***__*** SUSY***_

- Yukawa int. !!

**g****~****y****top****~****0.7 at GUT**

## 3. dynamical EW symmetry breaking I

- 3-1. *SU*(3)×*SU*(3) model
- 3-2. *SU*(6) model
- 3-3. SUSY version

**NH, Y. Hosotani, Y. Kawamura and T. Yamashita,  Phys.Rev.D70:015010, 2004 **
**NH and T. Yamashita, JHEP 0402:059,2004**

## search min. of

_**infinite sum of KK mode**_ →**effective potential,**
-            (**when SUSY → vanish! → **_**Scherk-Schwarz breaking)**_

- → Higgs VEV

- Now let us consider the quantum correction! in theory

## no sym. breaking!

**effective potential:**

- a:dim-less

- _3-1.__*SU*__(3)__c__×__*SU*__(3)__W__ model_

## Not Good!

- if vacuum is at y=πR

- at ~1/R

**effective potential:**

- vacuum should be at

##       introduce 

-       introduce
- extra fields in bulk

**There is d.o.f. of **

**effective potential:**

- fermion (adj. & fund.)  scalar (fund.)

## effective potential:

**effective potential:**

## vev: O(100)GeV

**effective potential:**

**bulk extra field effect is important!**

## bulk extra field effect is important! 

**effective potential:**

**bulk extra field effect is important!**

## 3-2.SU(6) GUT 

- _3-2.__*SU*__(6) GUT_

**not good! → introducing extra fields in bulk**

## introduce extra bulk fields →

- introduce extra bulk fields →

## introduce extra bulk fields →

- introduce extra bulk fields →

## 3-3.SUSY version

- Imposing different BC for fermion and boson → SUSY br.

- _☆ __Scherk-Schwarz SUSY breaking_

-    twist  of

- soft mass

- _3-3.SUSY version_

- SUSY must be broken, or V=0!

- _☆ __soft scalar mass for bulk fields (later)_

## gauge

-                                                                                    β~0.1
-     _bulk matter:  N__f__(±)__ fund. & N__a__(±)__ adjo. super-feilds_
-     examples:

- quarks/
- leptons

- How is Yukawa?

- quarks/leptons in bulk  →

- Yukawa from 5D gauge int.

- extra matters

## 4. dynamical EW symmetry breaking II

- 4-1. *SU*(3)×*SU*(3) model
- 4-2. result

**NH and T. Yamashita, ****JHEP 0404 (2004) 016**** **

## 4-1. SU(3)c×SU(3)W model 

_**fund. rep. bulk matter**_

- SU(2) doublet

- SU(2) singlet

**fund. rep. → only down-sector Yukawa**
**               ****6 → up-sector**
**             ****10 → charged lepton sector**
**               ****8 → ν-sector**

- (Burdman-Nomura)

_**gauge sector**_

_**4-1. **__***SU***__**(3)**__**c**__**×**__***SU***__**(3)**__**W**__** model**_

- Yukawa** **

## effective potential:

## effective potential:

**effective potential:**

## vev: O(100)GeV

**effective potential:**

**bulk extra field effect is important!**

## examples: 

- examples:

- all 3-generation quarks/leptons in bulk

- set-up:

_*SU*__(3)__c__×__*SU*__(3)__W__ model_

_*SU*__(6) GUT_

- result:

_**4-2. result**_

## 5. Higgs mass & phenomenology 

- 5. Higgs mass & phenomenology

- 5-1. Mass spectrum
- 5-2. soft scalar mass
- 5-3. 3-point self coupling

**NH, K.Takenaga and T.Yamashita, Phys.Rev.D71:025006,2005**
**NH, K.Takenaga and T.Yamashita, hep-ph/0411250**

## 5-1. Mass spectrum

_**5-1. Mass spectrum**_

- 5D gauge kinetic term→4D Higgs kinetic term

- ● However,

- , so we assume wall-localized kinetic terms,

- , which do not respect SU(3) symmetry, are dominant as

- g42 > λ-1,  (we take g4~1), and expect

- ● additional U(1)’

## SUSY case

_**SUSY case**_

- D-flat (μ=0)

**NH, K.Takenaga,T.Yamashita, Phys.Rev.D71:025006,2005**

## ☆

- D-flat (μ=0)

**twist of**

**→****gaugino mass****~****higgsino mass****~****β/R**
**    ****(no soft scalar masses)**

-     (**radiative induced mass****~*****O*****(100)GeV)**
- ☆ gauginos mass~higgsinos mass~β/R

_**Mass Spectrum**_

## ● introducing soft scalar mass, m (z=mR) in addition to SS

*SU*(3) × *SU*(3) model

- ● introducing soft scalar mass, *m *(*z=mR*) in addition to SS

***similar effect of large β***

_**5-2. soft scalar mass**_

## SU(3) × SU(3) model

_*SU*__(3) × __*SU*__(3) model_

- introducing soft scalar mass, *m *(*z=mR*)

_*SU*__(6) model_

*O*(1) # bulk fields are OK for DSB

**(NH, K.Takenaga and T.Yamashita, hep-ph/0411250)**

## tend to be small comparing to SM 

_**☆ **__**higher order operators**_

- a few TeV → suppression scale → suppressed enough

_**☆ **__**effective 3-point coupling**_

- deviation from SM

- tend to be small comparing to SM

_**5-3. 3-point self coupling**_

## 6. summary and discussion

##  Higgs mass is finite! (5D gauge invariance)

**gauge-Higgs unification=origin of Higgs doublets & Yukawa int.**

- → doublet Higgs

- → Yukawa ints.

-  **Higgs mass is finite! (5D gauge invariance)**

-    1 loop effective potential of Higgs doublets (*A*5)
-     in *SU*(3)×*SU*(3) model & *SU*(6) GUT (*q/l*: blane & bulk)
-                                             **↓**
**  **_**EW DSB can be possible by extra bulk matters**_ (suitable # & rep.)

- ☆
-     (**radiative induced mass****~*****O*****(100)GeV)**
- ☆ extra bulk fields~*O*(100) GeV
- ☆
- ☆ gauginos mass~higgsinos mass~β/R

_**summary**_

## ☆ SUSY br.    gaugino ⇔ higgsino 

- _☆ __SUSY br._    gaugino ⇔ higgsino

- at tree level at 1/R

- radiative br. is possible?
- investigate by including gravity effects

**(Choi, N.H., Jeong, Okumura, Shimizu, Yamaguchi, ****JHEP 0402:037,2004****)                                    **

**another approach of EW symmetry breaking in gauge-Higgs unification: **

- (Burdman,Nomura)

## problems

- (1): Winberg angle
-      ←● small brane-localized Higgs kinetic term
-                             bulk gauge coupling > brane-localized g.c.
-                                      (*g**4*~*O*(1), *(M*****R)**1/2*≫1 (*M****≫1*/R*))
-                         ● additional *U*(1)*’*
- (2): proton decay suppression for TeV scale compactification
-                      ← *U*(1)B
- (3): general soft masses in SUSY etc
-                      ← how to calculate deviation from *tanβ*=1 (D-flat) ?

## ☆ 5D E6, E7 GUTs on 

- _☆ __5D __*E*__*6*__*, E*__*7*__ GUTs_ on

-  *E**6*:   bulk matters **⇒ adjoint & fund.**
-   *E**7*:   bulk matters **⇒ adjoint **

**fermion mass hierarchy & flavor mixings****← wall-localized extra fields effects**

**(NH and Y. Shimizu, Phys.Rev.D67:095001,2003, Erratum-ibid.D69:059902,2004)**

_**related studies**_

## V (p=0) → position independent potential

- integrate it

**calculating one loop effective potential**

*V* (*p=0*) → position independent potential
-      →  *V*eff (vev)      (SUSY→zero!)

- background field gauge

- 1 loop

- Now let us consider the quantum correction! in theory

## Q:

- is really physical ?

**cf.        is not, it’s gauged away.**

_***Wilson line d.o.f.***_

- cf. Hosotani mech.

## bulk extra field effect is important! 

**effective potential:**

**bulk extra field effect is important!**