On the Spontaneous and Simultaneous Breaking of Internal and Scale symmetry in Effective Field Theories of extra dimensional origin enhanced with Higher Dimensional Operators: A New Approach to the Hierarchy Problem

Abstract: Way before the very recent discovery of the Higgs boson the associated mechanism was under speculation due to a theoretical inconsistency, the well known Higgs hierarchy problem. The inconsistency refers to the sensitivity of the Higgs mass to the ultra violet contributions which results in the need of a very strong fine tuning of the physical parameters in order to leave the mass almost unaffected by the quantum corrections. Many solutions have been proposed regarding the Higgs mass fine tuning problem during the past years, however, none of them has given a confirmation signal. In this dissertation we propose a novel solution to the Higgs hierarchy problem based on a specific extra dimensional model with very special boundary conditions and higher that four dimensional operators. This is the so called Non-perturbative gauge Higgs unification model, an SU(2) 5-d orbifold lattice model with obifold boundary conditions leading to a 4d boundary. On the latter lives a kind of an Abelian Higgs model, an ideal case for our purpose since it possesses a non-trivial effective potential sensitive to the UV corrections at first glance and yet relieved of the complexity of the Standard Model’s higher gauge group contributions. Therefore, our first step is to deal with the usual Abelian Higgs model in four spacetime dimensions where we examine its physicality and consistency under different gauge choices proving that the associated effective potential is gauge invariant. Then we introduce the Non-perturbative gauge Higgs unification model under the assumption that bulk and boundary are completely disconnected. Even though this hypothesis gives consistent results does not solve the fine tuning problem and the need to consider a connection between bulk and boundary becomes urgent. A consequence of this is that the insertion of higher dimensional operators is unavoidable. Therefore, before going back to our original model we examine the effective potential of a real scalar field enhanced with dimension six and eight operators. What we show is the various cases under which such a potential is both stable and exhibits spontaneous and simultaneous breaking of internal and scale symmetry as it reaches an interacting or a Gaussian fixed point. Finally, with these in our hands we turn back to the 5-d orbifold model and take into account the bulk-boundary connection which produces an effective action enhanced with higher that four dimensional operators, at the 4-d boundary, whose nature includes non-perturbative information related to a first order quantum phase transition. Under these circumstances the effective action acquires a finite cut-off that is low and the fine tuning of the scalar mass is rather mild.

general relativity and quantum cosmologyHEP - latticeHEP - phenomenologyHEP - theorymathematical physics

Audience: researchers in the topic

High Energy Theory, Gravity and Cosmology Seminars @ NTUA