Mass hierarchy, mass gap and corrections to Newton's law on thick branes with Poincare symmetry

We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schroedinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with m^2>0, in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza-Klein (KK) excitations and to compute the corrections to Newton's law in the thin brane limit. In the first case we consider a solution with a mass gap in the spectrum of KK fluctuations with two bound states - the massless 4D graviton free of tachyonic instabilities and a massive KK excitation - as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the (thin) Randall-Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved as in the Lykken-Randall model and the model is completely free of naked singularities.Comment: 25 pages in latex, no figures, content changed, corrections to Newton's law included for smooth version of RS model and an author adde

The O(N)-model within the Phi-derivable expansion to order lambda^2: on the existence, UV and IR sensitivity of the solutions to self-consistent equations

We discuss various aspects of the O(N)-model in the vacuum and at finite temperature within the Phi-derivable expansion scheme to order lambda^2. In continuation to an earlier work, we look for a physical parametrization in the N=4 case that allows to accommodate the lightest mesons. Using zero-momentum curvature masses to approximate the physical masses, we find that, in the parameter range where a relatively large sigma mass is obtained, the scale of the Landau pole is lower compared to that obtained in the two-loop truncation. This jeopardizes the insensitivity of the observables to the ultraviolet regulator and could hinder the predictivity of the model. Both in the N=1 and N=4 cases, we also find that, when approaching the chiral limit, the (iterative) solution to the Phi-derivable equations is lost in an interval around the would-be transition temperature. In particular, it is not possible to conclude at this order of truncation on the order of the transition in the chiral limit. Because the same issue could be present in other approaches, we investigate it thoroughly by considering a localized version of the Phi-derivable equations, whose solution displays the same qualitative features, but allows for a more analytical understanding of the problem. In particular, our analysis reveals the existence of unphysical branches of solutions which can coalesce with the physical one at some temperatures, with the effect of opening up a gap in the admissible values for the condensate. Depending on its rate of growth with the temperature, this gap can eventually engulf the physical solution.Comment: 26 pages, 15 figures, uses RevTeX4-1, published versio

Scalar field theory in the strong self-interaction limit

Standard Model with a classical conformal invariance holds the promise to give a better understanding of the hierarchy problem and could pave the way for beyond the standard model physics. So, we give here a mathematical treatment of a massless quartic scalar field theory with a strong self-coupling both classically and for quantum field theory. We use a set of classical solutions recently found and show that there exists an infinite set of infrared trivial scalar theories with a mass gap. Free particles have superimposed a harmonic oscillator set of states. The classical solution is displayed through a current expansion and the next-to-leading order quantum correction is provided. Application to the Standard Model would entail the existence of higher excited states of the Higgs particle and reduced decay rates to WW and ZZ that could be already measured.Comment: 33 pages, 2 figures. Version accepted for publication in the European Physical Journal

Random matrix theory of unquenched two-colour QCD with nonzero chemical potential

We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential mu. In this symmetry class the determinant of the Dirac operator is real but not necessarily positive. Despite this sign problem the unquenched matrix model remains completely solvable and provides detailed predictions for the Dirac operator spectrum in two different physical scenarios/limits: (i) the epsilon-regime of chiral perturbation theory at small mu, where mu^2 multiplied by the volume remains fixed in the infinite-volume limit and (ii) the high-density regime where a BCS gap is formed and mu is unscaled. We give explicit examples for the complex, real, and imaginary eigenvalue densities including Nf=2 non-degenerate flavours. Whilst the limit of two degenerate masses has no sign problem and can be tested with standard lattice techniques, we analyse the severity of the sign problem for non-degenerate masses as a function of the mass split and of mu. On the mathematical side our new results include an analytical formula for the spectral density of real Wishart eigenvalues in the limit (i) of weak non-Hermiticity, thus completing the previous solution of the corresponding quenched model of two real asymmetric Wishart matrices.Comment: 45 pages, 31 figures; references added, as published in JHE

The Effect of Particle Drag and Wall Absorption on Mass Transfer in Concentric Annulus Flows

The effects of the irreversible boundary reaction and the particle drag on mass transfer are studied analytically in concentric annulus flows. The solution of mathematical model, based on the generalized dispersion model brings out the mass transport following by the insertion of catheter on an artery in terms of the three effective transport coefficients, viz., the exchange, convection and diffusion coefficient. A general expression is derived which shows clearly the time dependent nature of the coefficients in the dispersive model. The complete time dependent expression for the exchange coefficient is obtained explicitly and independent of velocity distribution in the flow; however it does depend on the initial solute distribution. Because of the complexity of the problem only asymptotic large time evaluations are made for the convective and diffusion coefficients, but these are sufficient to give the physical insight into the nature of the problem of the effects of drag and absorption parameters. It is found that as absorption parameter increases exchange and convection coefficients will be enhanced, but diffusion coefficient will be reduced. After certain period of time exchange coefficient will be constant for different values annular gap. As the drag parameter increases convection and diffusion coefficients will be reduced. With the enhancement of catheter radius i.e., the annular gap will be reduced then the convection and diffusion coefficients will be decreased

Renormalization of the mass gap

The full gluon propagator relevant for the description of the truly non-perturbative QCD dynamics, the so-called intrinsically non-perturbative gluon propagator has been derived in our previous work. It explicitly depends on the regularized mass gap, which dominates its structure at small gluon momentum. It is automatically transversal in a gauge invariant way. It is characterized by the presence of severe infrared singularities at small gluon momentum, so the gluons remain massless, and this does not depend on the gauge choice. In this paper we have shown how precisely the renormalization program for the regularized mass gap should be performed. We have also shown how precisely severe infrared singularities should be correctly treated. This allowed to analytically formulate the exact and gauge-invariant criteria of gluon and quark confinement. After the renormalization program is completed, one can derive the gluon propagator applicable for the calculation of physical observables processes, etc., in low-energy QCD from first principles.Comment: 16 pages, no figures, no tables, some minor changes are introduce

Gauge Fields, Fermions and Mass Gaps in 6D Brane Worlds

We study fluctuations about axisymmetric warped brane solutions in 6D minimal gauged supergravity. Much of our analysis is general and could be applied to other scenarios. We focus on bulk sectors that could give rise to Standard Model gauge fields and charged matter. We reduce the dynamics to Schroedinger type equations plus physical boundary conditions, and obtain exact solutions for the Kaluza-Klein wave functions and discrete mass spectra. The power-law warping, as opposed to exponential in 5D, means that zero mode wave functions can be peaked on negative tension branes, but only at the price of localizing the whole Kaluza-Klein tower there. However, remarkably, the codimension two defects allow the Kaluza-Klein mass gap to remain finite even in the infinite volume limit. In principle, not only gravity, but Standard Model fields could `feel' the extent of large extra dimensions, and still be described by an effective 4D theory.Comment: 33 pages, 2 figures; typesetting problem fixed ({\o}replaced by \omega