Two-scalar Theory Research Articles

Hierarchy problem and fine-tuning in a decoupling approach to multiscale effective potentials

In many realizations of beyond the Standard Model theories, new massive particles are introduced, leading to a multiscale system with widely separated energy scales. In this setting the Coleman-Weinberg effective potential, which describes the vacuum of the theory at the quantum level, has to be supplemented with a prescription to handle the hierarchy in mass scales. In any quantum field theory involving scalar fields and multiple, highly differing mass scales, it is, in general, not possible to choose a single renormalization scale that will remove all the large logarithms in the effective potential. In this paper, we focus on the so-called decoupling method, which freezes the effects of heavy particles on the renormalization group running of the light degrees of freedom at low energies. We study this for a simple two-scalar theory and find that, while the decoupling method leads to an acceptable and convergent effective potential, the method does not solve the fine-tuning problem that is inherent to the hierarchy problem of multiscale theories. We also consider an alternative implementation of the decoupling approach, which gives different results for the shape of the potential, but still leads to similar conclusions on the amount of fine-tuning in the model. We suggest a way to avoid running into this fine-tuning problem by adopting a prescription on how to fix parameters in such decoupling approaches.

Lessons fromTμμon inflation models: Two-scalar theory and Yukawa theory

We demonstrate two properties of the trace of the energy-momentum tensor $T^{\mu}_{~ \mu}$ in the flat spacetime. One is the decoupling of heavy degrees of freedom; i.e., heavy degrees of freedom leave no effect for low-energy $T^{\mu}_{~ \mu}$-inserted amplitudes. This is intuitively apparent from the effective field theory point of view, but one has to take into account the so-called trace anomaly to explicitly demonstrate the decoupling. As a result, for example, in the $R^{2}$ inflation model, scalaron decay is insensitive to heavy degrees of freedom when a matter sector ${\it minimally}$ couples to gravity (up to a non-minimal coupling of a matter scalar field other than the scalaron). The other property is a quantum contribution to a non-minimal coupling of a scalar field. The non-minimal coupling disappears from the action in the flat spacetime, but leaves the so-called improvement term in $T^{\mu}_{~ \mu}$. We study the renormalization group equation of the non-minimal coupling to discuss its quantum-induced value and implications for inflation dynamics. We work it out in the two-scalar theory and Yukawa theory.

Unification of late- and early-time acceleration, with that of the intermediate eras, by scalar fields

In this work we shall investigate how to realize a cosmological evolution which describes all the evolution eras of our Universe, by using scalar-tensor theories. Particularly, we shall use single scalar and two-scalar theories, and by employing several well known reconstruction schemes, we shall investigate which scalar-tensor theories can realize the unification cosmology. For both the single and two-scalar theories, we find the kinetic terms and the potential of the theory and we also address the issue of the stability of the solutions towards linear perturbations. As we show, in the two-scalar description no instabilities occur, but in the single scalar description, certain solutions are unstable. Also we demonstrate that in the single scalar case, the power spectrum corresponding to early times is nearly scale invariant and compatible with the latest observational data. Finally, we perform an analysis of the effective equation of state, and we show that the EoS describes in a unified way early and late-time acceleration, and in addition it also describes the radiation and matter domination era between the acceleration eras.

Reconstructing the universe history, from inflation to acceleration, with phantom and canonical scalar fields

We consider the reconstruction technique in theories with a single or multiple (phantom and/or canonical) scalar fields. With the help of several examples, it is demonstrated explicitly that the universe expansion history, unifying early-time inflation and late-time acceleration, can be realized in scalar-tensor gravity. This is generalized to the theory of a scalar field coupled nonminimally to the curvature and to a Brans-Dicke-like theory. Different examples of unification of inflation with cosmic acceleration, in which de Sitter, phantom, and quintessence type fields play the fundamental role---in different combinations---are worked out. Specifically, the frame dependence and stability properties of de Sitter space scalar field theory are studied. Finally, for two-scalar theories, the late-time acceleration and early-time inflation epochs are successfully reconstructed, in realistic situations in which the more and more stringent observational bounds are satisfied, using the freedom of choice of the scalar field potential, and of the kinetic factor.

The mechanism of confinement and chiral symmetry breaking in quark nuclear physics

We discuss the question of inverse symmetry breaking at non-zero temperature using the exact renormalization group. We study a two-scalar theory and concentrate on the nature of the phase transition during which the symmetry is broken. We also examine the persistence of symmetry breaking at temperatures higher than the critical one.

Inverse symmetry breaking and the exact renormalization group

We discuss the question of inverse symmetry breaking at non-zero temperature using the exact renormalization group. We study a two-scalar theory and concentrate on the nature of the phase transition during which the symmetry is broken. We also examine the persistence of symmetry breaking at temperatures higher than the critical one.

High temperature phase transition in two-scalar theories.

Two-scalar theories at high temperature exhibit a rich spectrum of possible critical behaviour, with a second or first order phase transition. In the vicinity of the critical temperature one can observe critical exponents, tricritical points and crossover behaviour. None of these phenomena are visible to high temperature perturbation theory.

High temperature phase transitions in two-scalar theories with large N techniques

We consider a theory of a scalar one-component field f coupled to a scalar N-component field χ. Using large N techniques we calculate the effective potential in the leading order in 1 N . We show that this is equivalent to a resummation of an infinite subclass of graphs in perturbation theory, which involve fluctuations of the χ field only. We study the temperature dependence of the expectation value of the f field and the resulting first and second order phase transitions.