International Journal of Modern Physics A

We review methods and results for extracting the anomalous dimensions of operators from lattice field theory calculations. The most important application is the anomalous mass dimension in conformal or nearly conformal gauge field theories which might be related to dynamical electroweak symmetry breaking. Some discussion of the underlying theory of renormalization and mixing of operators is also included.

These are intended to be review notes on emergent symmetries, i.e. symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some background material and go through more recent problems in field theory, statistical mechanics and condensed matter. These problems illustrate how some important symmetries, such as Lorentz invariance and supersymmetry, usually believed to be fundamental, can arise naturally in low-energy regimes of systems involving a large number of degrees of freedom. The aim is to discuss how these examples could help us to face other complex and fundamental problems.

Gravity mediated supersymmetry breaking becomes comparable to gauge mediated supersymmetry breaking contributions when messenger masses are close to the GUT scale. By suitably arranging the gravity contributions, one can modify the soft supersymmetry breaking sector to generate a large stop mixing parameter and a light Higgs mass of 125 GeV. In this kind of hybrid models, however, the nice features of gauge mediation like flavor conservation, etc. are lost. To preserve the nice features, gravitational contributions should become important for lighter messenger masses and should be important only for certain fields. This is possible when the hidden sector contains multiple (at least two) spurions with hierarchical vacuum expectation values. In this case, the gravitational contributions can be organized to be “just right.” We present a complete model with two spurion hidden sector where the gravitational contribution is from a warped flavor model in a Randall–Sundrum setting. Along the way, we present simple expressions to handle renormalization group equations when supersymmetry is broken by two different sectors at two different scales.

Using elements of symmetry, as gauge invariance, several aspects of a Schrödinger equation represented in phase space are introduced and analyzed under physical basis. The hydrogen atom is explored in the same context. Then we add a Hénon–Heiles potential to the hydrogen atom in order to explore chaotic features.

We consider the nonminimally kinetic coupled version of DGP brane model, where the kinetic term of the scalar field is coupled to the metric and Einstein tensor on the brane by a coupling constant $\zeta$. We obtain the corresponding field equations, using the Friedmann–Robertson–Walker metric and the perfect fluid, and study the inflationary scenario to confront the numerical analysis of six typical scalar field potentials with the current observational results. We find that among the suggested potentials and coupling constants, subject to the e-folding $N=60$, the potentials $V(\varphi )=\sigma \varphi$, $V(\varphi )=\sigma {\varphi }^2$ and $V(\varphi )=\sigma {\varphi }^3$ provide the best fits with both Planck+WP+highL data and Planck+WP+highL+BICEP2 data.

We introduce the quantum holonomy-diffeomorphism ∗-algebra, which is generated by holonomy-diffeomorphisms on a three-dimensional manifold and translations on a space of SU(2)-connections. We show that this algebra encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Furthermore, we show that semiclassical states exist on the holonomy-diffeomorphism part of the algebra but that these states cannot be extended to the full algebra. Via a Dirac-type operator we derive a certain class of unbounded operators that act in the GNS construction of the semiclassical states. These unbounded operators are the type of operators, which we have previously shown to entail the spatial three-dimensional Dirac operator and Dirac–Hamiltonian in a semiclassical limit. Finally, we show that the structure of the Hamilton constraint emerges from a Yang–Mills-type operator over the space of SU(2)-connections.

Diffractive dissociation processes are analyzed in the framework of covariant reggeization. We have considered the general form of hadronic tensor and its asymptotic behavior for $t\to 0$ in the case of conserved tensor currents before reggeization. Resulting expressions for differential cross-sections of single dissociation (SD) process $(pp\to pM)$, double dissociation (DD) $(pp\to M_1{M}_2)$ and for the proton–Pomeron cross-section are given in detail, and corresponding problems of the approach are discussed.

We consider first-order transition amplitudes in external fields in QED in the expanding de Sitter space and point out that they are gauge dependent quantities. We examine the gauge variations of the amplitudes assuming a decoupling of the interaction at large times, which allows to conclude that the source of the problem lies in the fact that the frequencies of the modes in the infinite future become independent of the comoving momenta. We show that a possibility to assure the gauge invariance of the external field amplitudes is to restrict to potentials which vanish sufficiently fast at infinite times, and briefly discuss a number of options in the face of the possible gauge invariance violation in the full interacting theory.

The process of radiation of 120 GeV positrons moving in a channeling regime in (011) plane of a single crystal was considered. At the beginning on the basis of the theory of nonlinear oscillations, the trajectory of moving positrons at different initial conditions was derived. Then taking into account the nonlinearity of motion, the distribution function over oscillation amplitudes of channeling particles was found. After this, the intensity of radiation at different initial conditions was calculated with the help of two various methods. These results may be useful for comparison with experimental data at positron energies from 100 and more GeV.

In this paper, we propose a new version for the noncommutative superspace in 3D. This version is shown to be convenient for performing quantum calculations. In the paper, we use the theory of the chiral superfield as a prototype for possible generalizations, calculating the one-loop two-point function of a chiral superfield and the one-loop low-energy effective action in this theory.

The Higgs triplet model predicts the existence of the doubly and singly charged Higgs bosons ($H^{\pm \pm }$ and $H^{\pm }$), whose decay modes are relevant to the vacuum expectation value of the triplet $v_{\mathrm{\Delta }}$ and the mass spectrum of these scalars. In this paper, we study the pair production of $H^{++}{H}^{-}$ via the processes in $e^{+}{e}^{-}$ collisions: $e^{+}{e}^{-}\to H^{++}{H}^{-}{W}^{-}$ and $e^{+}{e}^{-}\to V{V}^{\ast }\to e^{-}{\bar{\nu }}_e{H}^{++}{H}^{-}$. The numerical results show that the production rates can reach the level of several fb with a center of energy at the TeV scale. The characteristic signals and relevant SM backgrounds are also discussed in both the degenerate and nondegenerate cases. In most of the parameter spaces, their possible signals might be detected via these processes in the future high-energy linear collider experiments with $\sqrt{s}=3.0\mathrm{\text{TeV}}$ and ${\pounds }_{\mathrm{\text{int}}}=1000{\mathrm{\text{fb}}}^{-1}$.