 Collaboration with Prof. Sin Kyu Kang and Prof. We-Fu Chang arXiv: [hep-ph] submitted to JHEP

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

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

Jubin 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

hh W,Z h h h h h top Jubin

‘Little’(low mass) Higgs and Fine Tuning Higgs mass Needed Tree Contribution Top Gauge Higgs = Cutoff scale Λ = 10TeV Tree Jubin

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 Λ 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

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

h top h hh stop Cancellation condition: Supersymmetry

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

- Higgsless no zero modes SM gauge bosons = First excited modes - Gauge Higgs Unification(GHU) Jubin

- 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

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

Kaluza-Klein gravity theory Gauge-Higgs unification

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

We only focus on the zero modes, After we integrate out fifth dimension, And rescale the gauge field, Jubin

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

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

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

Stability of the electroweak scale (from the quadratic divergences – Gauge hierarchy problem) Higgs potential - to trigger the electroweak symmetry breaking Correct weak mixing Jubin

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

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

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, Jubin

Simple roots cor. to SU(2) One cartan generator cor. to U(1) Any GHU model can not explain correct weak mixing angle. Jubin

SU(2) generators U(1) generator Jubin

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

Finally, we can get this relation ( with brane Kinetic terms ), We can rewrite the equation with previous relation, Jubin

All masses are smaller than GeV. Jubin