Evolution of Magnetic Fields in Freely Decaying Magnetohydrodynamic Turbulence

We study the evolution of magnetic fields in freely decaying magnetohydrodynamic turbulence. By quasi-linearizing the Navier-Stokes equation, we solve analytically the induction equation in quasi-normal approximation. We find that, if the magnetic field is not helical, the magnetic energy and correlation length evolve in time respectively as E_B \propto t^{-2(1+p)/(3+p)} and \xi_B \propto t^{2/(3+p)}, where p is the index of initial power-law spectrum. In the helical case, the magnetic helicity is an almost conserved quantity and forces the magnetic energy and correlation length to scale as E_B \propto (log t)^{1/3} t^{-2/3} and \xi_B \propto (log t)^{-1/3} t^{2/3}.Comment: 4 pages, 2 figures; accepted for publication in PR

O(N)O(N) model in Euclidean de Sitter space: beyond the leading infrared approximation

We consider an $O(N)$ scalar field model with quartic interaction in $d$-dimensional Euclidean de Sitter space. In order to avoid the problems of the standard perturbative calculations for light and massless fields, we generalize to the $O(N)$ theory a systematic method introduced previously for a single field, which treats the zero modes exactly and the nonzero modes perturbatively. We compute the two-point functions taking into account not only the leading infrared contribution, coming from the self-interaction of the zero modes, but also corrections due to the interaction of the ultraviolet modes. For the model defined in the corresponding Lorentzian de Sitter spacetime, we obtain the two-point functions by analytical continuation. We point out that a partial resummation of the leading secular terms (which necessarily involves nonzero modes) is required to obtain a decay at large distances for massless fields. We implement this resummation along with a systematic double expansion in an effective coupling constant $\sqrt\lambda$ and in 1/N. We explicitly perform the calculation up to the next-to-next-to-leading order in $\sqrt\lambda$ and up to next-to-leading order in 1/N. The results reduce to those known in the leading infrared approximation. We also show that they coincide with the ones obtained directly in Lorentzian de Sitter spacetime in the large N limit, provided the same renormalization scheme is used.Comment: 31 pages, 5 figures. Minor changes. Published versio

Lifshitz scalar fields: one loop renormalization in curved backgrounds

We consider an interacting Lifshitz field with z=3 in a curved spacetime. We analyze the renormalizability of the theory for interactions of the form lambda phi^n, with arbitrary even n. We compute the running of the coupling constants both in the ultraviolet and infrared regimes. We show that the Lorentz violating terms generate couplings to the spacetime metric that are not invariant under general coordinate transformations. These couplings are not suppressed by the scale of Lorentz violation and therefore survive at low energies. We point out that in these theories, unless the effective mass of the field is many orders of magnitude below the scale of Lorentz violation, the coupling to the four dimensional Ricci scalar xi (4)R phi^2 does not receive large quantum corrections xi >> 1.Comment: 17 pages. Minor changes. Published versio

Controlling the Range of Interactions in the Classical Inertial Ferromagnetic Heisenberg Model: Analysis of Metastable States

A numerical analysis of a one-dimensional Hamiltonian system, composed by $N$ classical localized Heisenberg rotators on a ring, is presented. A distance $r_{ij}$ between rotators at sites $i$ and $j$ is introduced, such that the corresponding two-body interaction decays with $r_{ij}$ as a power-law, $1/r_{ij}^{\alpha}$ ($\alpha \ge 0$). The index $\alpha$ controls the range of the interactions, in such a way that one recovers both the fully-coupled (i.e., mean-field limit) and nearest-neighbour-interaction models in the particular limits $\alpha=0$ and $\alpha\to\infty$, respectively. The dynamics of the model is investigated for energies $U$ below its critical value ($U<U_{c}$), with initial conditions corresponding to zero magnetization. The presence of quasi-stationary states (QSSs), whose durations $t_{\rm QSS}$ increase for increasing values of $N$, is verified for values of $\alpha$ in the range $0 \leq \alpha <1$, like the ones found for the similar model of XY rotators. Moreover, for a given energy $U$, our numerical analysis indicates that $t_{\rm QSS} \sim N^{\gamma}$, where the exponent $\gamma$ decreases for increasing $\alpha$ in the range $0 \leq \alpha <1$, and particularly, our results suggest that $\gamma \to 0$ as $\alpha \to 1$. The growth of $t_{\rm QSS}$ with $N$ could be interpreted as a breakdown of ergodicity, which is shown herein to occur for any value of $\alpha$ in this interval.Comment: 16 pages, 7 figure

Hierarchy from Baryogenesis

We study a recently proposed mechanism to solve the hierarchy problem in the context of the landscape, where the solution of the hierarchy problem is connected to the requirement of having baryons in our universe via Electroweak Baryogenesis. The phase transition is triggered by the fermion condensation of a new gauge sector which becomes strong at a scale Lambda determined by dimensional transmutation, and it is mediated to the standard model by a new singlet field. In a ``friendly'' neighborhood of the landscape, where only the relevant operators are ``scanned'' among the vacua, baryogenesis is effective only if the higgs mass m_h is comparable to this low scale Lambda, forcing m_h to be of order Lambda, and solving the hierarchy problem. A new CP violating phase is needed coupling the new singlet and the higgs field to new matter fields. We study the constraints on this model given by baryogenesis and by the electron electric dipole moment (EDM), and we briefly comment on gauge coupling unification and on dark matter relic abundance. We find that next generation experiments on the EDM will be sensitive to essentially the entire viable region of the parameter space, so that absence of a signal would effectively rule out the model.Comment: 28 pages, 4 figures. v2: Added comments and references. Corrected one typo in eq.(81). Conclusions unaltere

N-Relaxion: Large Field Excursions from a Few Site Relaxion Model

Relaxion models are an interesting new avenue to explain the radiative stability of the Standard Model scalar sector. They require very large field excursions, which are difficult to generate in a consistent UV completion and to reconcile with the compact field space of the relaxion. We propose an N-site model which naturally generates the large decay constant needed to address these issues. Our model offers distinct advantages with respect to previous proposals: the construction involves non-abelian fields, allowing for controlled high energy behaviour and more model building possibilities, both in particle physics and inflationary models, and also admits a continuum limit when the number of sites is large, which may be interpreted as a warped extra dimension.Comment: 7 pages, 2 figures; v2: version to appear in PR