Collaboration with Prof. Sin Kyu Kang and Prof. We-Fu Chang
arXiv:1111.5422 [hep-ph] submitted to JHEP
Slide 2
The Standard Model(SM) and Hierarchy problem Higgs mass
Solutions about the Hierarchy problem Brief introduction to Gauge
Higgs unification(GHU) A toy example 5D SU(3) GHU model on S 1 /Z
2. Problems in the toy model Goals Possible answers for these
problems Phenomenologically viable GHU models Higgs potential in 6D
Numerical results. Summary Jubin Park @YongPyong2012
Slide 3
A fundamental scalar field (Higgs) is introduced to explain
spontaneous symmetry breaking of gauge group of electroweak
symmetry. The same field is also responsible for masses of all
matter fields through Yukawa interactions. Standard Model
Slide 4
Jubin Park @YongPyong2012 The Higgs potential is written by
HAND. So the Higgs sector is very sensitive to the UV scale of the
theory Without symmetry protection, Moreover, Unknown origin
Hierarchy Problem
Slide 5
hh W,Z h h h h h top Jubin Park @YongPyong2012
Slide 6
Little(low mass) Higgs and Fine Tuning Higgs mass Needed Tree
Contribution Top Gauge Higgs = Cutoff scale = 10TeV Tree Jubin Park
@YongPyong2012
Slide 7
So we need incredible fine tuning to explain why the Higgs mass
(~Weak scale order) is so much lighter than other mass parameter
scales (Planck, GUT or Heavy Majorana scale) when we take the
Cutoff scale as P or G or H. This is not NATURAL. (NATURALNESS
problem) In order to solve the hierarchy problem naturally (without
fine tuning), we can expect that there exist at least the new
physics beyond the Standard Model if we accept the big-desert
between weak energy scale and P or G or H.. LEP and Tevatron have
probed directly up to a few hundred GeV, and indirectly between 1
and 10 TeV through the precision measurements. Jubin Park
@YongPyong2012
Slide 8
Weak scale Hadronization scale B physics scale 200 MeV5 GeV80
GeV172 GeV 10 TeV Energy scales 1 TeV Compactification scale Theory
cutoff scale 10 ^19 GeV 10 ^17 GeV Planck scale- strong gravity
GUT- coupling unification Heavy right-handed Majorana for Seesaw
Mechanism Jubin Park @YongPyong2012
Slide 9
h top h hh stop Cancellation condition: Supersymmetry
Slide 10
Composite Higgs - Little Higgs (from UV completion) -
Tecnicolor (new Strong-type interation) Extra dimension - Large
extra dimension (ADD) - Universal extra dimension (UED) - Small
extra dimension - With the warped spacetime (RS) Jubin Park
@YongPyong2012
Slide 11
- Higgsless no zero modes SM gauge bosons = First excited modes
- Gauge Higgs Unification(GHU) Jubin Park @YongPyong2012
Slide 12
- Gauge Higgs Unification SM gauge bosons = Zero modes Needs
Higgs mechanism in order to break the EWSB. but there is no Higgs
potential in 5D. or Hosotani mechanism. too low Higgs mass (or top
quark mass) with VEV which is proportional to 1/R. Jubin Park
@YongPyong2012
Slide 13
Unification of gravity (s=2) & electromagnetic (s=1)
Kaluza-Klein gravity theory Unified theory of gauge (s=1) &
Higgs (s=0) Gauge-Higgs unification 4D space-time 4D gauge-field
Higgs 5D gauge field extra dimension Higher dimensional Gauge
Theory The pioneer works of GHU : N.S. Manton, Nucl. Phys.
58(79)141. Y. Hosotani, Phys. Lett. B126 (83) 309 ``Hosotani
mechanism Jubin Park @YongPyong2012
Slide 14
Kaluza-Klein gravity theory Gauge-Higgs unification
Slide 15
In addition the scenario may also shed some light on the
arbitrariness problem in the interactions of Higgs. The quantum
correction to m H is finite because of the higher dimensional gauge
symmetry. An interesting solution to solve the hierarchy problem
without the supersymmetry. Advantage of the GHU Jubin Park
@YongPyong2012
Slide 16
Slide 17
We only focus on the zero modes, After we integrate out fifth
dimension, And rescale the gauge field, Jubin Park
@YongPyong2012
Slide 18
We can easily understand that these terms can give a
modification to the gauge couplings without big change of given
models. From the effective Lagrangian, we can expect this relation
Similarly, for the U(1) coupling Jubin Park @YongPyong2012
Slide 19
This number is completely fixed by the analysis of structure
constants of given Lie group (or Lie algebra) regardless of volume
factor Z if there are no brane kinetic terms in given models. Jubin
Park @YongPyong2012
Slide 20
Wrong weak mixing angle (,, ) No Higgs potential (to trigger
the EWSB). - may generate too low Higgs mass (or top quark) even if
we use quantum corrections to make its potential. Realistic
construction of Yukawa couplings Jubin Park @YongPyong2012
Slide 21
Stability of the electroweak scale (from the quadratic
divergences Gauge hierarchy problem) Higgs potential - to trigger
the electroweak symmetry breaking Correct weak mixing Jubin Park
@YongPyong2012
Slide 22
Wrong weak mixing angle - Brane kinetic terms - Violation of
Lorentz symmetry ( SO(1,4) -> SO(1,3) ) - Graded Lie algebra
(ex. ) - Using a non-simple group. an anomalous additional U(1) (or
U(1)s) Jubin Park @YongPyong2012
Slide 23
No Higgs potential (to trigger the EWSB). - Using a non-simply
connected extra- dimension ( the fluctuation of the AB type phase
loop quantum correction) - Using a 6D (or more) pure gauge theory.
- Using a background field like a monopole in extra dimensional
space. Jubin Park @YongPyong2012
Slide 24
To find phenomenologically viable models they demand following
4 constraints: (1) three massive gauge bosons W+,W, Z0 at the
electroweak scale (2) rho =1 at tree level (3) existence of
representations that can contain all Standard Model(SM) particle,
especially hyper charge 1/6. (4) correct weak mixing angle. Alfredo
Aranda and Jose Wudka, PRD 82, 096005 Jubin Park
@YongPyong2012
Slide 25
Simple roots cor. to SU(2) One cartan generator cor. to U(1)
Any GHU model can not explain correct weak mixing angle. Jubin Park
@YongPyong2012
Slide 26
SU(2) generators U(1) generator Jubin Park @YongPyong2012
Slide 27
We focus on the mass term, and the mixing angle, From previous
toy example, we can easily expect that our brane kinetic terms can
modify the coupling constants, that is, the mixing angle, Jubin
Park @YongPyong2012
Slide 28
Slide 29
Finally, we can get this relation ( with brane Kinetic terms ),
We can rewrite the equation with previous relation, Jubin Park
@YongPyong2012
Slide 30
All masses are smaller than 114.4 GeV. Jubin Park
@YongPyong2012