Two loop finiteness of Higgs mass and potential in the gauge-Higgs unification

The zero mode of an extra-dimensional component of gauge potentials serves as a 4D Higgs field in the gauge-Higgs unification. We examine QED on $M^4 \times S^1$ and determine the mass and potential of a 4D Higgs field (the $A_5$ component) at the two loop level with gauge invariant reguralization. It is seen that the mass is free from divergences and independent of the renormalization scheme.Comment: 18 pages, 1 figur

On Gauge Symmetry Breaking via Euclidean Time Component of Gauge Fields

We study gauge theories with/without an extra dimension at finite temperature, in which there are two kinds of order parameters of gauge symmetry breaking. The one is the zero mode of the gauge field for the Euclidean time direction and the other is that for the direction of the extra dimension. We evaluate the effective potential for the zero modes in one-loop approximation and investigate the vacuum configuration in detail. Our analyses show that gauge symmetry can be broken only through the zero mode for the direction of the extra dimension and no nontrivial vacuum configuration of the zero mode for the Euclidean time direction is found.Comment: 22 pages, 6 figures, references and typos corrected, version to appear in PR

Large Gauge Hierarchy in Gauge-Higgs Unification

We study a five dimensional SU(3) nonsupersymmetric gauge theory compactified on $M^4\times S^1/Z_2$ and discuss the gauge hierarchy in the scenario of the gauge-Higgs unification. Making use of calculability of the Higgs potential and a curious feature that coefficients in the potential are given by discrete values, we find two models, in which the large gauge hierarchy is realized, that is, the weak scale is naturally obtained from an unique large scale such as a grand unified theory scale or the Planck scale. The size of the Higgs mass is also discussed in each model. One of the models we find realizes both large gauge hierarchy and consistent Higgs mass, and shows that the Higgs mass becomes heavier as the compactified scale becomes smaller.Comment: 21 pages, no figures, version to appear in PR

Multi-Higgs Mass Spectrum in Gauge-Higgs Unification

We study an SU(2) supersymmetric gauge model in a framework of gauge-Higgs unification. Multi-Higgs spectrum appears in the model at low energy. We develop a useful perturbative approximation scheme for evaluating effective potential to study the multi-Higgs mass spectrum. We find that both tree-massless and massive Higgs scalars obtain mass corrections of similar size from finite parts of the loop effects. The corrections modify multi-Higgs mass spectrum, and hence, the loop effects are significant in view of future verifications of the gauge-Higgs unification scenario in high-energy experiments.Comment: 32 pages; typos corrected and a few comments added, published versio

Correct Effective Potential of Supersymmetric Yang-Mills Theory on M^4\times S^1

We study an ${\cal N}=1$ supersymmetric Yang-Mills theory defined on $M^4\times S^1$. The vacuum expectation values for adjoint scalar field in vector multiplet, though important, has been overlooked in evaluating one-loop effective potential of the theory. We correctly take the vacuum expectation values into account in addition to the Wilson line phases to give an expression for the effective potential, and gauge symmetry breaking is discussed. In evaluating the potential, we employ the Scherk-Schwarz mechanism and introduce bare mass for gaugino in order to break supersymmetry. We also obtain masses for the scalars, the adjoint scalar, and the component gauge field for the $S^1$ direction in case of the SU(2) gauge group. We observe that large supersymmetry breaking gives larger mass for the scalar. This analysis is easily applied to the $M^4\times S^1/Z_2$ case.Comment: 12 pages, 1 figur

Aspects of Phase Transition in Gauge-Higgs Unification at Finite Temperature

We study the phase transition in gauge-Higgs unification at finite temperature. In particular, we obtain the strong first order electroweak phase transition for a simple matter content yielding the correct order of Higgs mass at zero temperature. Two stage phase transition is found for a particular matter content, which is the strong first order at each stage. We further study supersymmetric gauge models with the Scherk-Schwarz supersymmetry breaking. We again observe the first order electroweak phase transition and multi stage phase transition.Comment: 18 pages, 7 figures, references corrected, minor correctio

Development of a Chisel Digger for Harvesting Groundnut

A chisel digger was designed and developed at ICRlSAT Asia Center for harvesting virginia bunch type groundnut crops. It consists of a digger-bottom and a standard. The digger-bottom has two shares that are inclined at 120" to each other and contain chisel points for inc~eased penetration into the soil. A single digger-bottom attached to a draw pole can be pulled by a pair of oxen and two or more digger-bottoms attached to a tool bar can be pulled by a tractor. The bullock-drawn chisel digger can harvest a 60-cm wide strip or two rows of the crop sown at a 30-cm row spacing. It can harvest about 0.7 ha per day (8 h) with less than 5% losses. It undercuts the tap roots of groundnut plants and leaves the plants upright without any dragging. The chisel digger performed satisfactorily even under soil conditions where blade type diggers could not penetrate up-to the desired depth