C. S. Lim

The Gauge hierarchy problem and higher dimensional gauge theories

We report on an attempt to solve the gauge hierarchy problem in the framework of higher-dimensional gauge theories. Both classical Higgs mass and quadratically divergent quantum correction to the mass are argued to be vanished. Hence the hierarchy problem in its original sense is solved. The remaining finite mass correction is shown to depend crucially on the choice of boundary condition for matter fields, and a way to fix it dynamically is presented. We also point out that on the simply-connected space S2 even the finite mass correction vanishes.

A prediction for dΓ(b→sℓℓdq2 including the long-distance effects

Abstract We point out that both long- and short-distance effects of b→ s l l (l= e , μ) can be computed. The long-distance contribution, mainly due to Ψ and Ψ′ resonances, is shown to give a dominant contribution to Br(b → s l l ). This contribution is predicted to be Br(b → s Ψ→ sl l =0.59×10 −3 , Br(b → sΨ ′→ sl l )=2.5×10 −5 . The long-distance effect also causes a remarkable deviation of the q 2 (q 2 : invariant l l mass-squared ) distribution from what is expected from the short-distance effect alone.

The Hosotani mechanism in bulk gauge theories with an orbifold extra space S**1 / Z(2)

We pursue the possibility of the scenario in which the Higgs field is identified with the extra-space component of a bulk gauge field. The space–time we take is M4 ⊗ S1/Z2. We show that a nontrivial Z2-parity assignment allows some of the extra-space component to have radiatively induced vev, which strongly modifies the mass spectrum and gauge symmetry of the theory, realized by orbifolding. In particular we investigate the dynamical mass generation of zero-mode fermion and spontaneous gauge symmetry breaking due to the vev. The gauge theories we adopt are a prototype model SU(2) and SU(3) model, of special interest as the realistic minimal scheme to incorporate the standard model SU(2) × U(1).

Natural suppression of flavour-changing neutral currents in supersymmetric gauge theories

Abstract Induced flavour-changing neutral currents (FCNC) in supersymmetric unified theories are investigated both in models with the standard SU(2)L × U(1) gauge symmetry and in models with an extra Ũ(1) gauge symmetry. Supersymmetric extension of the natural flavour conservation laws for neutral currents is obtained by adding a condition regarding the assumed type of supersymmetry breaking. This condition ensures no direct flavour-changing couplings of neutral gauge-Higgs fermions and at the same time is necessary and sufficient for the natural suppression of the induced FCNC. It is found that in the class of models satisfying the new condition the contribution of the scalar partners of quarks to the induced strangeness-changing neutral current is comparable to that of the quarks in K L → π π , while it is negligibly small in KL − KS mass difference.

Six Dimensional Gauge-Higgs Unification with an Extra Space S**2 and the Hierarchy Problem

We calculate one-loop radiative correction to the mass of Higgs identified with the extra space components of the gauge field in a six-dimensional massive scalar QED compactified on a two-sphere. The radiatively induced Higgs mass is explicitly shown to be finite for arbitrary bulk scalar mass M . Furthermore, the remaining finite part also turns out to vanish, at least for the case of small M , thus suggesting that the radiatively induced Higgs mass exactly vanishes, in general. The non-zero “Kaluza–Klein” modes in the gauge sector are argued to have a Higgs-like mechanism and quantum mechanical N =2 supersymmetry, while the Higgs zero modes, as supersymmetric states, have a close relation with monopole configuration.

Towards a realistic grand gauge-Higgs unification

Abstract We investigate a 5D SU ( 6 ) grand gauge-Higgs unification model compactified on an orbifold S 1 / Z 2 . Ordinary quarks and leptons, together with right-handed neutrinos, are just accommodated into a minimal set of representations of the gauge group, without introducing any exotic states in the same representations. The proton decay turns out to be forbidden at least at the tree level. We also find a correct electroweak symmetry breaking SU ( 2 ) L × U ( 1 ) Y → U ( 1 ) em is easily realized by introducing suitable number of adjoint fermions.

Finite anomalous magnetic moment in the gauge-Higgs unification

We show that the anomalous magnetic moment of fermion in the gauge-Higgs unification is finite in any spacetime dimensions, which is a new predictive physical observable similar to the Higgs mass.

Pseudo Dirac scenario for neutrino oscillations

We argue how the pseudo Dirac scenario for neutrinos leads to rich neutrino oscillation phenomena, including oscillation inside each generation. The pseudo Dirac scenario is generalized by incorporating generation mixings and formulas for the various neutrino oscillations are derived. As an application we compare the formulas with the corresponding data. We find that the observed pattern of mixings, such as almost maximal mixing in the atmospheric neutrino oscillation, is naturally explained in the generalized pseudo Dirac scenario with small generation mixings. We, however, also point out that there remain some problems to be settled for this scenario to be viable. The possible theoretical framework to realize the pseudo Dirac scenario is also briefly commented on.

Neutron electric dipole moment in the gauge-Higgs unification

We study the neutron electric dipole moment (EDM) in a five-dimensional SU(3) gauge-Higgs unification compactified on M{sup 4}xS{sup 1}/Z{sub 2} space-time including a massive fermion. We point out that to realize the CP violation is a nontrivial task in the gauge-Higgs unification scenario and argue how the CP symmetry is broken spontaneously by the vacuum expectation value of the Higgs, the extra space component of the gauge field. We emphasize the importance of the interplay between the vacuum expectation value of the Higgs and the Z{sub 2}-odd bulk mass term to get physically the CP violation. We then calculate the one-loop contributions to the neutron EDM as the typical example of the CP violating observable and find that the EDM appears already at the one-loop level, without invoking the three-generation scheme. We then derive a lower bound for the compactification scale, which is around 2.6 TeV, by comparing the contribution due to the nonzero Kaluza-Klein modes with the experimental data.

An attempt to solve the hierarchy problem based on gravity-gauge-Higgs unification scenario

Abstract We discuss a possible scenario to solve the hierarchy problem, in which 4-dimensional bosonic fields with all possible integer spins, graviton, gauge boson and Higgs are unified in a framework of a gravity theory with extra dimensions. The Higgs is identified with the extra space component of the metric tensor. One-loop quantum effect on the Higgs mass-squared is explicitly calculated in a five-dimensional gravity theory compactified on S 1 . We obtain a finite calculable Higgs mass-squared without suffering from quadratic divergence, by virtue of general coordinate transformation invariance, which is argued to be guaranteed by the summation over all Kaluza–Klein modes running in the loop diagrams.