A small cosmological constant due to non-perturbative quantum effects

We investigate the leading power corrections to the decay rates and distributions in the decay $B \rightarrow X_s \ell^+ \ell^- $ in the standard model (SM) using heavy quark expansion (HQE) in $(1/m_b)$ and a phenomenological model implementing the Fermi motion effects of the b quark bound in the B hadron. In the HQE method, we find that including the leading power corrections the decay width decreases by about 4% and the branching ratio by about 1.5% from their (respective) parton model values. The dilepton invariant mass spectrum is found to be stable against power corrections over a good part of this spectrum. However, near the high-mass end-point this distribution becomes negative with the current value of the non-perturbative parameter $\lambda_2$ (the $\lambda_1$-dependent corrections are found to be inoccouos), implying the breakdown of the HQE method in this region. Our results are at variance with the existing ones in the literature in both the decay rate and the invariant dilepton mass distribution calculated in the HQE approach. As an alternative, we implement the non-perturbative effects in the decay $B \rightarrow X_s \ell^+ \ell^- $ using a phenomenologically motivated Gaussian Fermi motion model. We find small corrections to the branching ratio, but the non-perturbative effects are perceptible in both the dilepton mass distribution and the Forward-Backward asymmetry in the high dilepton mass region. Using this model for estimating the non-perturbative effects, we present the decay rates and distributions for the inclusive process $B \rightarrow X_s \ell^+ \ell^- $ in the SM.

Inflation has presented solutions for a number of important cosmological problems while leaving some unanswered. In this paper, we present a new cosmological model based on the quantization of the zero-point field, which is consistent with empirical data, requires fewer assumptions, and presents answers to some of those unanswered questions. A comparison between standard cosmology and the theory presented in this paper is given herein. Vacuum energy density: The standard inflationary model needs both Hubble’s constant and matter density to estimate the vacuum energy density, but new cosmological model needs only Hubble’s constant. Non-vacuum energy density: The standard model cannot predict the non-vacuum energy density, but the new model can predict it using only Hubble’s constant. Ratio of vacuum energy to total energy: The standard model cannot predict the ratio of vacuum energy to total energy, but the new model can predict it, without using Hubble’s constant. Energy conservation: In the standard model, total energy is not conserved before inflation and at the time of the creation of the universe, but in the new model total energy is mathematically proved to be conserved from the beginning of the universe as net energy (including gravitational potential energy) is always zero. Flatness and homogeneity: The standard model requires an inflaton field with a specific potential energy distribution to explain it, but the new model does not need any such hypothetical field; the zero-point field is sufficient.

In this work we continue the investigation of the extrapolate dictionary for celestial holography recently proposed in [1], at both the perturbative and non-perturbative level. Focusing on scalar field theories, we give a complete set of Feynman rules for extrapolate celestial correlation functions and their radial reduction in the hyperbolic slicing of Minkowski space. We prove to all orders in perturbation theory that celestial correlators can be rewritten in terms of corresponding Witten diagrams in EAdS which, in the hyperbolic slicing of Minkowski space, follows from the fact that the same is true in dS space. We then initiate the study of non-perturbative properties of celestial correlators, deriving the radial reduction of the Källén-Lehmann spectral representation of the exact Minkowski two-point function. We discuss the analytic properties of the radially reduced spectral function, which is a meromorphic function of the spectral parameter, and highlight a connection with the Watson-Sommerfeld transform.

On non-perturbative effects at the high-temperature electroweak phase transition

We investigated how a magnetic topological defect affects the vacuum polarization of a charged massive scalar field in a flat (3+1)-dimensional space-time. The defect was modeled as an impenetrable-to-matter-field, finite-thickness tube with magnetic flux inside. We implemented the most general form of the Robin boundary condition on the surface of the magnetic tube, which enables a fully general analysis of the problem. We found that in flat space-time, the total vacuum energy generated by a magnetic topological defect depends on the curvature (ξ), except for special cases corresponding to the Dirichlet and Neumann boundary conditions. By contrast, when Robin’s general boundary conditions are imposed, the induced vacuum energy acquires an explicit dependence on the curvature coupling (ξ), which is significant even in flat space-time. A detailed study of the dependence of the effect on the boundary-condition parameter was carried out. The obtained results highlight the nontrivial role played by boundary conditions in vacuum polarization phenomena.

We discuss other contributions to the vacuum energy of quantum field theories and quantum gravity, which have not been considered in the literature. As is well known, the presence of virtual particles in vacuum provides the so famous and puzzling contributions to the vacuum energy. In fact, these mainly come from loop integrations over the four-momenta space. However, we argue that these also imply the presence of a mass density of virtual particles in every volume cell of space-time. The most important contribution comes from quantum gravity bubbles, corresponding to virtual black hole pairs. The presence of virtual masses could lead to another paradox: the space-time itself would have an intrinsic virtual mass density contribution leading to a disastrous contraction —as is known, no negative masses exist in general relativity. We dub this effect the cosmological problem of second type: if not other counter-terms existed, the vacuum energy would be inevitably destabilized by virtual-mass contributions. It would be conceivable that the cosmological problem of second type could solve the first one. Virtual masses renormalize the vacuum energy to an unpredicted parameter, as in the renormalization procedure of the Standard Model charges. In the limit of (Pauli-Villars limit), virtual black holes have a mass density providing an infinite counter-term to the vacuum energy divergent contribution (assuming ). Therefore, in the same Schwinger-Feynman-Tomonaga attitude, the problem of a divergent vacuum energy could be analogous to the put-by-hand procedure used for Standard Model parameters.

The QCD corrections to the decay rate for $Z\ensuremath{\rightarrow}W+\mathrm{hadrons}$ are analyzed. The decay rate is shown to be insensitive to nonperturbative QCD effects and calculable using perturbation theory in ${\ensuremath{\alpha}}_{s}({M}_{Z}\ensuremath{-}{M}_{W})$. The logarithms of $\frac{s}{{M}_{Z}^{2}}$, where $s$ is the invariant mass of the hadrons, are summed to all orders in the leading-logarithm approximation. Making a naive order-of-magnitude estimate for the remaining QCD corrections, the branching fraction for this decay mode in the standard model is estimated to be (1.1 \ifmmode\pm\else\textpm\fi{} 0.3) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}7}$.

Large-order behavior and nonperturbative effects

We minimally extend the Standard Model field content by adding new vectorlike fermions at the TeV scale to allow gauge coupling unification at a realistic scale. We embed the model into an SU(5) grand unified theory that is asymptotically safe and features an interacting fixed point for the gauge coupling. There are no Landau poles of the U(1) gauge and Higgs couplings in this new setting. Gauge, Yukawa, and Higgs couplings are retraced from the fixed point and matched at the grand unification scale to those of the Standard Model rescaled up to the same energy. All couplings, their fixed point values, and critical exponents always remain in the perturbative regime.

A bstract The discovery of an axion-like particle above the QCD line would rule out Grand Unified Theories, including the perturbative heterotic string with the Standard Model embedded in a single E 8 factor or SO(32). In this work we study a possible loophole to this observation, given by compactifications of the E 8 × E 8 heterotic string with a non-standard embedding of the Standard Model into the 10-dimensional gauge group. If electromagnetism is embedded into both E 8 factors, axions can couple to photons via the anomaly without coupling to QCD. We obtain upper bounds to the coupling-to-mass ratio g aγ / m a for these axion-like particles as a function of the supersymmetry breaking scale and the unified gauge coupling. To be compatible with the measured gauge couplings and the weak mixing angle sin 2 θ w at low-energies, phenomenologically viable models with non-standard U(1) Y embedding require sizeable one-loop threshold corrections from string states and/or charged matter at intermediate energy scales. We study how these effects modify the tree-level upper bounds to g aγ / m a and show that, in the perturbative regime, they reduce the leading order estimates. Axion-like particles far above the QCD line are only possible in certain models where perturbation theory is lost. The main conclusion is that the discovery of an axion violating the bounds found in this work would be incompatible with large classes of otherwise phenomenologically viable string models, including the perturbative heterotic SO(32) and E 8 × E 8 string, the type-I string, and certain heterotic M-theories. The role of small gauge instantons and worldsheet instantons in making some of the axion-like particles heavy and cosmologically relevant is briefly discussed.

Weakly-coupled heterotic string is known to have problems of dilaton/moduli stabilization, supersymmetry breaking (by hidden-sector gaugino condensation), gauge coupling unification, QCD axion, as well as cosmological problems involving dilaton/moduli and axion. The author studies these problems by adopting the point of view that they arise mostly due to limited calculational power, little knowledge of the full vacuum structure, and an inappropriate treatment of gaugino condensation. It turns out that these problems can be solved or are much less severe after a more consistent and complete treatment. There are two kinds of non-perturbative effects in the construction of string effective field theory: the field-theoretical non-perturbative effects of gaugino condensation (with an important constraint ignored in the past) and the stringy nonperturbative effects conjectured by S. Shenker, which are best described using the linear multiplet formalism. Stringy non-perturbative corrections to the Kaehler potential are invoked to stabilize the dilaton at a value compatible with a weak coupling regime. Modular invariance is ensured through the Green-Schwarz counterterm and string threshold corrections which, together with hidden matter condensation, lead to moduli stabilization at the self-dual point where the vev's of moduli's F components vanish. In the vacuum, supersymmetry is broken at a realistic scale with vanishing cosmological constant. As for soft supersymmetry breaking, this model always leads to a dilaton-dominated scenario. For the strong CP problem, the model-independent axion has the right properties to be the QCD axion. Furthermore, there is a natural hierarchy between the dilaton/moduli mass and the gravitino mass, which could solve both the cosmological moduli problem and the cosmological problem of the model-independent axion.

We search for self tuning solutions to the Einstein-scalar field equations for the simplest class of `Fab-Four' models with constant potentials. We first review the conditions under which self tuning occurs in a cosmological spacetime, and by introducing a small modification to the original theory—introducing the second and third Galileon terms—show how one can obtain de Sitter states where the expansion rate is independent of the vacuum energy. We then consider whether the same self tuning mechanism can persist in a spherically symmetric inhomogeneous spacetime. We show that there are no asymptotically flat solutions to the field equations in which the vacuum energy is screened, other than the trivial one (Minkowski space). We then consider the possibility of constructing Schwarzschild de Sitter spacetimes for the modified Fab Four plus Galileon theory. We argue that the only model that can successfully screen the vacuum energy in both an FLRW and Schwarzschild de Sitter spacetime is one containing `John' ∼ Gμν ∂μϕ∂νϕ and a canonical kinetic term ∼ ∂αϕ ∂αϕ. This behaviour was first observed in [1]. The screening mechanism, which requires redundancy of the scalar field equation in the `vacuum', fails for the `Paul' term in an inhomogeneous spacetime.

It has been observed more than 25 years ago that sigma model perturbation theory suffers from strongly RG-relevant high-gradient operators. The phenomenon was first seen in 1-loop calculations for the O(N) vector model and it is known to persist at least to two loops. More recently, Ryu et al. suggested that a certain deformation of the psl(N|N) WZNW-model at level k=1, or equivalently the psl(N|N) Gross–Neveu model, could be free of RG-relevant high-gradient operators and they tested their suggestion to leading order in perturbation theory. In this note we establish the absence of strongly RG-relevant high-gradient operators in the psl(2|2) Gross–Neveu model to all loops. In addition, we determine the spectrum for a large subsector of the model at infinite coupling and observe that all scaling weights become half-integer. Evidence for a conjectured relation with the CP1|2 sigma model is not found.

The Gross–Neveu model at finite temperature at next-to-leading order in the 1/ N expansion

The problem of description of the strong interaction of a quantum dot (QD) with an acoustic phonon reservoir is discussed. It is shown that the generalized dynamical equation of motion derived in [Gainutdinov R. Kh. 1989 J. Phys. A: Math. Gen. 22 269] as the most general equation of motion consistent with the current concepts of quantum physics and provides an effective way to solve the problem of the QD in the excitonic regime with the phonon reservoir beyond the perturbation theory. A nonperturbative solution for the exciton self-energy function was found. At temperatures, more than 10 K these self-energy functions differ profoundly from that obtained in the second-Born approximation.