Validity Of Perturbation Theory Research Articles

Bounds on gauge bosons coupled to nonconserved currents

We discuss new bounds on vectors coupled to currents whose nonconservation is due to mass terms, such as $U(1{)}_{{L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}}$. Due to the emission of many final state longitudinally polarized gauge bosons, inclusive rates grow exponentially fast in energy, leading to constraints that are only logarithmically dependent on the symmetry breaking mass term. This exponential growth is unique to Stueckelberg theories and reverts back to polynomial growth at energies above the mass of the radial mode. We present bounds coming from the high transverse mass tail of $\mathrm{monolepton}+\mathrm{MET}$ events at the LHC, which beat out cosmological bounds to place the strongest limit on Stueckelberg $U(1{)}_{{L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}}$ models for most masses below a keV. We also discuss a stronger, but much more uncertain, bound coming from the validity of perturbation theory at the LHC.

Continuum model of the twisted graphene bilayer

The continuum model of the twisted graphene bilayer (Phys. Rev. Lett. 99, 256802, 2007) is extended to include all types of commensurate structures. The essential ingredient of the model, the Fourier components of the spatially modulated hopping amplitudes, can be calculated analytically, for any type of commensurate structures in the low twist angle limit. We show that the Fourier components that could give rise to a gap in the SE-even structures discussed by Mele (Phys. Rev. B 81, 161405 2010) vanish linearly with angle, whereas the amplitudes that saturate to finite values, as $\theta\to0$, ensure that all low angle structures share essentially the same physics. We extend our previous calculations beyond the validity of perturbation theory, to discuss the disappearance of Dirac cone structure at angles below 1^{\circ}.

Validity of first-order perturbation theory for scattering from one-dimensional and two-dimensional rough surfaces described by power-law spectra

First-order perturbation theory is a widely used model for estimating the backscatter of acoustic waves incident on a rough surface. The validity of perturbation theory for one-dimensional surfaces described by Gaussian spectra is well established. However, little has been done to confirm its range of validity when expanded to two-dimensional surfaces. Furthermore, the range of validity for surfaces described by power-law spectra has not been fully explored. This work seeks to benchmark first-order perturbation theory against a finite element method solution for scattering from one-dimensional and two-dimensional rough pressure-release surfaces described by power-law spectra. The relationship between ranges of validity of 1D and 2D surfaces will be considered. [Work sponsored by the Office of Naval Research, Ocean Acoustics.]

IR divergences in inflation and entropy perturbations

We study leading order perturbative corrections to the two pointcorrelation function of the scalar field describing the curvature perturbationin a slow-roll inflationary background, paying particularattention to the contribution of entropy mode loops. We find thatthe infrared divergences are worse than in pure de Sitter space:they are power law rather than logarithmic. The validity of perturbationtheory and thus of the effective field theory of cosmologicalperturbations leads to stringent constraints on the coupling constantsdescribing the interactions, in our model the quarticself-interaction coupling constant of the entropy field. If theself coupling constant is larger than some critical value whichdepends in particular on the duration of the inflationary phase,then perturbation theory breaks down. Our analysis may haveimplications for the stability of de Sitter space: thequantum effects which lead to an instability of de Sitter space willbe larger in magnitude in the presence of entropy fluctuations.

Quantum stress tensor fluctuations of a conformal field and inflationary cosmology

We discuss the additional perturbation introduced during inflation by quantum stress tensor fluctuations of a conformally invariant field such as the photon. We consider both a kinematical model, which deals only with the expansion fluctuations of geodesics, and a dynamical model which treats the coupling of the stress tensor fluctuations to a scalar inflaton. In neither model do we find any growth at late times, in accordance with a theorem due to Weinberg. What we find instead is a correction which becomes larger the earlier one starts inflation. This correction is non-Gaussian and highly scale dependent, so the absence of such effects from the observed power spectra may imply a constraint on the total duration of inflation. We discuss different views about the validity of perturbation theory at very early times during which currently observable modes are transplanckian.

Theory and phenomenology of an exceptional supersymmetric standard model

We make a comprehensive study of the theory and phenomenology of a low-energy supersymmetric standard model originating from a string-inspired ${E}_{6}$ grand unified gauge group. The exceptional supersymmetric standard model (ESSM) considered here is based on the low-energy standard model gauge group together with an extra ${Z}^{\ensuremath{'}}$ corresponding to an extra $U(1{)}_{N}$ gauge symmetry under which right-handed neutrinos have zero charge. The low-energy matter content of the ESSM corresponds to three 27 representations of the ${E}_{6}$ symmetry group, to ensure anomaly cancellation, plus an additional pair of Higgs-like doublets as required for high-energy gauge coupling unification. The ESSM is therefore a low-energy alternative to the minimal supersymmetric standard model (MSSM) or next-to-minimal supersymmetric standard model (NMSSM). The ESSM involves extra matter beyond the MSSM contained in three $5+{5}^{*}$ representations of $SU(5)$, plus three $SU(5)$ singlets which carry $U(1{)}_{N}$ charges, one of which develops a vacuum expectation value, providing the effective $\ensuremath{\mu}$ term for the Higgs doublets, as well as the necessary exotic fermion masses. We explore the renormalization group flow of the ESSM and examine theoretical restrictions on the values of new Yukawa couplings caused by the validity of perturbation theory up to the grand unification scale. We then discuss electroweak symmetry breaking and Higgs phenomenology and establish an upper limit on the mass of the lightest Higgs particle which can be significantly heavier than in the MSSM and NMSSM, in leading two-loop approximation. We also discuss the phenomenology of the ${Z}^{\ensuremath{'}}$ and the extra matter, whose discovery will provide a smoking gun signal of the model.

High-Z Projectile Ionization: Studies on the Validity of First-Order Perturbation Theory

First-order perturbation theory is a widely used method when studying the excitation and ionization of high-Z, hydrogen-like ions. In many applications, this theory has been found helpful explaining the ionization of projectile electrons in collisions with different target materials. It has recently been questioned by several experiments, though. Here, we comment on the validity of perturbation theory at intermediate and high energies and show that an improved screening model, which is based on the (many-electron) density distribution in the target atoms, helps understand most of the experimental findings for light and medium-Z elements up to energies of several (ten) GeV/u

Thermal effects on the low energyN=2SUSY Yang-Mills theory

Using the low energy effective action of the $N=2$ supersymmetric SU(2) Yang-Mills theory we calculate the free energy, $\ensuremath{\Omega},$ at finite temperature, both in the semiclassical region and in the dual monopole-dyon theory. In all regions $\ensuremath{\Omega}$ depends on both the temperature T and the appropriate moduli parameter, and is thus minimized only for specific values of the moduli parameter, in contrast with the $T=0$ case where the energy vanishes all over moduli space. Within the validity of perturbation theory, we find that the finite temperature Yang-Mills theory is stable only at definite points in moduli space, i.e. for a specific value of the monopole-dyon mass or when the scalar field expectation value goes to infinity.

Vacuum stability bounds in the two-Higgs doublet model

In the standard model, the requirements of vacuum stability and the validity of perturbation theory up to the unification scale force the mass of the Higgs boson to be approximately between 130 GeV and 180 GeV. We re-examine these requirements in the (non-supersymmetric) two-Higgs doublet model, in the light of the large top quark mass, and constrain the masses of the Higgs bosons in this model. It is found that the mass of the charged Higgs boson must be lighter than 150 GeV. This bound is below the lower bound in the popular model-II two-Higgs doublet model, and thus we conclude that this model cannot be valid up to the unification scale. The bounds on the neutral Higgs scalars are also discussed.

Calculation of RHEED Intensities for Imperfect Surfaces

RHEED calculation techniques for imperfect surfaces are reviewed and some applications of the calculational methods are described. Systems of interest typically consist of a perfectly ordered substrate which is periodic in three dimensions together with a surface which has imperfections in the form of disorder or steps. Calculational techniques for this type of system include: supercell methods in which the disorder is modeled by considering a large periodic system; perturbation theory in the distorted wave Born approximation where the scattering by the imperfections is taken to be a perturbation but the scattering by the periodic part of the system is treated exactly; the multislice method as used in transmission electron diffraction theory; and a promising new approach based on Green's functions. The validity of perturbation theory is investigated in detail and it is shown to give good agreement with supercell calculations in the case where the potential of the imperfections is weak or where their correlation length is small. This makes perturbation theory very suitable for treating disordered over-layers, but stepped surfaces with a large correlation length require the other methods. These methods are more expensive computationally and some possible ways of reducing the CPU time are considered. Finally, illustrative results are presented to show how the various calculational techniques can be applied to real systems. Particular cases include RHEED intensity oscillations and reflection electron microscope images.

Coleman-Weinberg phase transition in two-scalar models

We explore the Coleman-Weinberg phase transition in regions outside the validity of perturbation theory. For this purpose we study a Euclidean field theory with two scalars and discrete symmetry in four dimensions. The phase diagram is established by a numerical solution of a suitable truncation of exact non-perturbative flow equations. We find regions in parameter space where the phase transition (in its dependence on the mass term) is of the second or the first order, separated by a triple point. Our quantitative results for the first order phase transition compare well to the standard perturbative Coleman-Weinberg calculation of the effective potential.

Higgs boson masses in the model with two Higgs doublets and spontaneous CP-violation

The renormalization group equations are investigated for two Higgs doublet extension of a standard model with spontaneous CP violation. Assuming the validity of perturbation theory up to unification energies, the restrictions for the Higgs boson masses are found.

The region of validity of perturbation theory

Abstract We present a study of the region of validity of perturbation theory applied to rough surface scattering. We solve numerically the case of a periodic surface or grating varying in one dimension. For a statistical ensemble of gratings with a sufficiently long period one may obtain a good approximation of rough surface scattering. We use this to test the validity of perturbation theory. Only the perfect conductor case was considered. We find that as the grazing angle becomes small the perturbation result for the TE (E horizontal) polarization remains valid, while for the TM (E vertical) polarization it breaks down. The results show that the perturbation results should be used carefully when being compared with experimental data at grazing angles.

SPONTANEOUS CP-VIOLATION WITHIN THE FRAMEWORK OF SU(2)L×SU(2)R×U(1) MODELS WITH MANIFEST CP INVARIANCE REVISITED

The case of spontaneous CP violation for large mt is reanalyzed and the validity of perturbation theory is checked by calculating the second order corrections to the CKM matrix. For a very large right-handed mass scale, the perturbation theory breaks down in some cases. While in other cases consistent with perturbation theory, the model predicts too large ε′/ε. Two possible alternatives are: (a) models with low right-handed mass scales with three generations and (b) models with heavy right-handed mass scales with four generations, avoid the above problems and values of ε′/ε and electric dipole moment of the neutron consistent with present data are obtained.

Resonant and nonresonant effects in the multiphoton detachment of a one-dimensional model ion with a short-range potential

We study multiphoton detachment for a one-dimensional ion model with a Dirac δ-function potential, numerically solving the Schrödinger equation. We analyze the influence of a multiphoton resonance just at the ionization threshold. The intensity dependence of the cross section of the process is related to various ponderomotive thresholds. For low-intensity fields and short times non-energy-conserving terms are dominant. The validity of perturbation theory is tested also.

Perturbative corrections to acoustic Doppler backscattering I.: Ocean surface gravity waves

Perturbative corrections to the Doppler backscattering spectrum using Rayleigh–Rice perturbation theory are examined. For comparison with recent results regarding the validity of perturbation theory in the static limit, calculations using Pierson–Moskowitz and modified Toba spectra to describe the wave height distribution are performed. The order [kh]4 interference term acts to lower the weight associated with the lowest-order delta function peaks at the ‘‘Bragg frequencies’’ for backscattering. Another term of the same order spreads the spectrum away from these delta peaks.

Short-time multiphoton detachment in a one-dimensional model with very-short-range potential.

We study multiphoton ionization for a one-dimensional atom model (with only one bound state) solving numerically the Schr\odinger equation. The intensity dependence of the cross section of the process is related to different ponderomotive thresholds. For very-low-intensity fields and very short times ``non-energy-conserving'' terms are dominant. The validity of perturbation theory has also been tested.

Above-threshold ionization of atomic hydrogen

Within the framework of perturbation theory, the method of analytical continuation of transition matrix elements is proposed. The method is based on the Sturmian expansion of the transition matrix elements and the analytical continuation of the divergent part of the Sturmian transition matrix elements in the case of above-threshold ionization with one excess photon. Investigation of the ratio Q(N+1)/Q(N) with λ and comparison with experimental data proves the validity of perturbation theory up to I = 1013 W cm−2 for multiphoton ionization of atomic hydrogen in the ground state.

A topological study of the dynamical effects of entanglements

The constraint that extended molecules such as polymers cannot pass through each other is formulated in terms of a topological invariant. A simple model of the motion of a labelled loop entangled in a uniform background of amorphous loops is studied. A dynamical weighting factor is found which effectively removes configurational changes that would lead to the labelled loop passing through the strands of the background material. A perturbation treatment of this weighting factor is presented which describes the effects of the entanglements in terms of random environmental forces possessing considerable space and time correlations. A detailed analytic calculation is presented for the case of a labelled molecule with a rigid-ring configuration. This calculation illustrates the limited validity of perturbation theory in dealing with entanglements and suggests the existence of a transition in time to a random 'tube'-like behaviour, where the centre-of-mass motion of the ring depends on the time as t1/4 instead of the usual diffusive t1/2. The origin of this behaviour can be located in the long-time persistence of the bond vector correlation function of the labelled ring.

Application of tridiagonalization to the many-body problem. II. FiniteT

In a previous paper of the same title, we obtained the ground-state energy of a magnetic (Wolff-model) impurity in a nonmagnetic metal. In the present Brief Report, we calculate the impurity's contribution to the density of states and heat capacity of the metal at low temperatures. Here, the Lancz\"os reduction ("tridiagonalization") converges less rapidly, so that our results are of qualitative merit only. Nevertheless, we confirm the validity of perturbation theory in the weak-coupling regime, and find, at strong coupling, that the interaction introduces an extra fraction $\frac{2}{N}$ of states at the Fermi level.