Practical tools for third order cosmological perturbations

We discuss cosmological perturbation theory at third order, deriving the gauge transformation rules for metric and matter perturbations, and constructing third order gauge invariant quantities. We present the Einstein tensor components, the evolution equations for a perfect fluid, and the Klein-Gordon equation at third order, including scalar, vector and tensor perturbations. In doing so, we also give all second order tensor components and evolution equations in full, exhilarating generality.Comment: 17 pages, revtex4; v2: corresponds to version published in JCA

(B-L) Symmetry vs. Neutrino Seesaw

We compute the effective coupling of the Majoron to W bosons at \cO(\hbar) by evaluating the matrix element of the (B-L) current between the vacuum and a $W^+W^-$ state. The (B-L) anomaly vanishes, but the amplitude does not vanish as a result of a UV finite and non-local contribution which is entirely due to the mixing between left-chiral and right-chiral neutrinos. The result shows how anomaly-like couplings may arise in spite of the fact that the (B-L) current remains exactly conserved to all orders in $\hbar$, lending additional support to our previous proposal to identify the Majoron with the axion.Comment: 13 pages, 1 figure, with additional explanations and clarification

Modelling non-dust fluids in cosmology

Currently, most of the numerical simulations of structure formation use Newtonian gravity. When modelling pressureless dark matter, or `dust', this approach gives the correct results for scales much smaller than the cosmological horizon, but for scenarios in which the fluid has pressure this is no longer the case. In this article, we present the correspondence of perturbations in Newtonian and cosmological perturbation theory, showing exact mathematical equivalence for pressureless matter, and giving the relativistic corrections for matter with pressure. As an example, we study the case of scalar field dark matter which features non-zero pressure perturbations. We discuss some problems which may arise when evolving the perturbations in this model with Newtonian numerical simulations and with CMB Boltzmann codes.Comment: 5 pages; v2: typos corrected and refs added, submitted version; v3: version to appear in JCA

The check of QCD based on the tau-decay data analysis in the complex q^2-plane

The thorough analysis of the ALEPH data on hadronic tau-decay is performed in the framework of QCD. The perturbative calculations are performed in 3 and 4-loop approximations. The terms of the operator product expansion (OPE) are accounted up to dimension D=8. The value of the QCD coupling constant alpha_s(m_tau^2)=0.355 pm 0.025 was found from hadronic branching ratio R_tau. The V+A and V spectral function are analyzed using analytical properties of polarization operators in the whole complex q^2-plane. Borel sum rules in the complex q^2 plane along the rays, starting from the origin, are used. It was demonstrated that QCD with OPE terms is in agreement with the data for the coupling constant close to the lower error edge alpha_s(m_tau^2)=0.330. The restriction on the value of the gluonic condensate was found =0.006 pm 0.012 GeV^2. The analytical perturbative QCD was compared with the data. It is demonstrated to be in strong contradiction with experiment. The restrictions on the renormalon contribution were found. The instanton contributions to the polarization operator are analyzed in various sum rules. In Borel transformation they appear to be small, but not in spectral moments sum rules.Comment: 24 pages; 1 latex + 13 figure files. V2: misprints are corrected, uncertainty in alpha_s is explained in more transparent way, acknowledgement is adde

Enhanced mesoscopic fluctuations in the crossover between random matrix ensembles

In random-matrix ensembles that interpolate between the three basic ensembles (orthogonal, unitary, and symplectic), there exist correlations between elements of the same eigenvector and between different eigenvectors. We study such correlations, using a remarkable correspondence between the interpolating ensembles late in the crossover and a basic ensemble of finite size. In small metal grains or semiconductor quantum dots, the correlations between different eigenvectors lead to enhanced fluctuations of the electron-electron interaction matrix elements which become parametrically larger than the non-universal fluctuations.Comment: 4 pages, RevTeX; 3 figure

Orbital and spin contributions to the gg-tensors in metal nanoparticles

We present a theoretical study of the mesoscopic fluctuations of $g$-tensors in a metal nanoparticle. The calculations were performed using a semi-realistic tight-binding model, which contains both spin and orbital contributions to the $g$-tensors. The results depend on the product of the spin-orbit scattering time $\tau_{\textrm{\small so}}$ and the mean-level spacing $\delta$, but are otherwise weakly affected by the specific shape of a {\it generic} nanoparticle. We find that the spin contribution to the $g$-tensors agrees with Random Matrix Theory (RMT) predictions. On the other hand, in the strong spin-orbit coupling limit $\delta \tau_{\textrm{\small so}}/\hbar \to 0$, the orbital contribution depends crucially on the space character of the quasi-particle wavefunctions: it levels off at a small value for states of $d$ character but is strongly enhanced for states of $sp$ character. Our numerical results demonstrate that when orbital coupling to the field is included, RMT predictions overestimate the typical $g$-factor of orbitals that have dominant $d$-character. This finding points to a possible source of the puzzling discrepancy between theory and experiment.Comment: 21 pages, 6 figures; accepted for publication in Physical Review

Localized D-dimensional global k-defects

We explicitly demonstrate the existence of static global defect solutions of arbitrary dimensionality whose energy does not diverge at spatial infinity, by considering maximally symmetric solutions described by an action with non-standard kinetic terms in a D+1 dimensional Minkowski space-time. We analytically determine the defect profile both at small and large distances from the defect centre. We verify the stability of such solutions and discuss possible implications of our findings, in particular for dark matter and charge fractionalization in graphene.Comment: 6 pages, published versio

Supersymmetry with a Chargino NLSP and Gravitino LSP

We demonstrate that the lightest chargino can be lighter than the lightest neutralino in supersymmetric models with Dirac gaugino masses as well as within a curious parameter region of the MSSM. Given also a light gravitino, such as from low scale supersymmetry breaking, this mass hierarchy leads to an unusual signal where every superpartner cascades down to a chargino that decays into an on-shell W and a gravitino, possibly with a macroscopic chargino track. We clearly identify the region of parameters where this signal can occur. We find it is generic in the context of the R-symmetric supersymmetric standard model, whereas it essentially only occurs in the MSSM when sign(M1) is not equal to sign(M2) = sign(\mu) and tan(beta) is small. We briefly comment on the search strategies for this signal at the LHC.Comment: 27 pages and 16 figure