Sum Rules for Magnetic Moments and Polarizabilities in QED and Chiral Effective-Field Theory

We elaborate on a recently proposed extension of the Gerasimov-Drell-Hearn (GDH) sum rule which is achieved by taking derivatives with respect to the anomalous magnetic moment. The new sum rule features a {\it linear} relation between the anomalous magnetic moment and the dispersion integral over a cross-section quantity. We find some analogy of the linearized form of the GDH sum rule with the `sideways dispersion relations'. As an example, we apply the linear sum rule to reproduce the famous Schwinger's correction to the magnetic moment in QED from a tree-level cross-section calculation and outline the procedure for computing the two-loop correction from a one-loop cross-section calculation. The polarizabilities of the electron in QED are considered as well by using the other forward-Compton-scattering sum rules. We also employ the sum rules to study the magnetic moment and polarizabilities of the nucleon in a relativistic chiral EFT framework. In particular we investigate the chiral extrapolation of these quantities.Comment: 24 pages, 7 figures; several additions, published versio

Comment on ``Evidence for Narrow Baryon Resonances in Inelastic pp Scattering''

Compton scattering data are sensitive to the existence of low-mass resonances reported by Tatischeff et al. We show that such states, with their reported properties, are excluded by previous Compton scattering experiments.Comment: One page, submitted to PR

Cosmic Rays From Cosmic Strings

It has been speculated that cosmic string networks could produce ultra-high energy cosmic rays as a by-product of their evolution. By making use of recent work on the evolution of such networks, it will be shown that the flux of cosmic rays from cosmologically useful, that is GUT scale strings, is too small to be used as a test for strings with any foreseeable technology.Comment: 11, Imperial/TP/93-94/2

High Temperature Matter and Gamma Ray Spectra from Microscopic Black Holes

The relativistic viscous fluid equations describing the outflow of high temperature matter created via Hawking radiation from microscopic black holes are solved numerically for a realistic equation of state. We focus on black holes with initial temperatures greater than 100 GeV and lifetimes less than 6 days. The spectra of direct photons and photons from $\pi^0$ decay are calculated for energies greater than 1 GeV. We calculate the diffuse gamma ray spectrum from black holes distributed in our galactic halo. However, the most promising route for their observation is to search for point sources emitting gamma rays of ever-increasing energy.Comment: 33 pages, 13 figures, to be submitted to PR

Do Evaporating Black Holes Form Photospheres?

Several authors, most notably Heckler, have claimed that the observable Hawking emission from a microscopic black hole is significantly modified by the formation of a photosphere around the black hole due to QED or QCD interactions between the emitted particles. In this paper we analyze these claims and identify a number of physical and geometrical effects which invalidate these scenarios. We point out two key problems. First, the interacting particles must be causally connected to interact, and this condition is satisfied by only a small fraction of the emitted particles close to the black hole. Second, a scattered particle requires a distance ~ E/m_e^2 for completing each bremsstrahlung interaction, with the consequence that it is improbable for there to be more than one complete bremsstrahlung interaction per particle near the black hole. These two effects have not been included in previous analyses. We conclude that the emitted particles do not interact sufficiently to form a QED photosphere. Similar arguments apply in the QCD case and prevent a QCD photosphere (chromosphere) from developing when the black hole temperature is much greater than Lambda_QCD, the threshold for QCD particle emission. Additional QCD phenomenological arguments rule out the development of a chromosphere around black hole temperatures of order Lambda_QCD. In all cases, the observational signatures of a cosmic or Galactic halo background of primordial black holes or an individual black hole remain essentially those of the standard Hawking model, with little change to the detection probability. We also consider the possibility, as proposed by Belyanin et al. and D. Cline et al., that plasma interactions between the emitted particles form a photosphere, and we conclude that this scenario too is not supported.Comment: version published in Phys Rev D 78, 064043; 25 pages, 3 figures; includes discussion on extending our analysis to TeV-scale, higher-dimensional black hole

Constraints on Cosmic Strings due to Black Holes Formed from Collapsed Cosmic String Loops

The cosmological features of primordial black holes formed from collapsed cosmic string loops are studied. Observational restrictions on a population of primordial black holes are used to restrict $f$, the fraction of cosmic string loops which collapse to form black holes, and $\mu$, the cosmic string mass-per-unit-length. Using a realistic model of cosmic strings, we find the strongest restriction on the parameters $f$ and $\mu$ is due to the energy density in $100 MeV$ photons radiated by the black holes. We also find that inert black hole remnants cannot serve as the dark matter. If earlier, crude estimates of $f$ are reliable, our results severely restrict $\mu$, and therefore limit the viability of the cosmic string large-scale structure scenario.Comment: (Plain Tex, uses tables.tex -- wrapped lines corrected), 11 pages, FERMILAB-Pub-93/137-

Blue spectra and induced formation of primordial black holes

We investigate the statistical properties of primordial black hole (PBH) formation in the very early Universe. We show that the high level of inhomogeneity of the early Universe leads to the formation of the first generation PBHs. %The existence of these PBHs This causes later the appearance of a dust-like phase of the cosmological expansion. We discuss here a new mechanism for the second generation of PBH formation during the dust-like phase. This mechanism is based on the coagulation process. We demonstrate that the blue power spectrum of initial adiabatic perturbations after inflation leads to overproduction of primordial black holes with $10^9$g$\le M\le10^{15}$g if the power index is $n\ge1.2$.Comment: 16 pages, 2 figure

Cosmological constraints on primordial black holes produced in the near-critical gravitational collapse

The mass function of primordial black holes created through the near-critical gravitational collapse is calculated in a manner fairly independent of the statistical distribution of underlying density fluctuation, assuming that it has a sharp peak on a specific scale. Comparing it with various cosmological constraints on their mass spectrum, some newly excluded range is found in the volume fraction of the region collapsing into black holes as a function of the horizon mass.Comment: 9 pages. Typos corrected. To appear in Physical Review

Supersymmetry and primordial black hole abundance constraints

We study the consequences of supersymmetry for primordial black hole (PBH) abundance constraints. PBHs with mass less than about 10^{11}g will emit supersymmetric particles when they evaporate. In most models of supersymmetry the lightest of these particles, the lightest supersymmetric particle (LSP), is stable and will hence survive to the present day. We calculate the limit on the initial abundance of PBHs from the requirement that the present day LSP density is less than the critical density. We apply this limit, along with those previously obtained from the effects of PBH evaporation on nucleosynthesis and the present day density of PBHs, to PBHs formed from the collpase of inflationary density perturbations, in the context of supersymmetric inflation models. If the reheat temperature after inflation is low, so as to avoid the overproduction of gravitinos and moduli, then the lightest PBHs which are produced in significant numbers will be evaporating around the present day and there are therefore no constraints from the effects of the evaporation products on nucleosynthesis or from the production of LSPs. We then examine models with a high reheat temperature and a subsequent period of thermal inflation. In these models avoiding the overproduction of LSPs limits the abundance of low mass PBHs which were previously unconstrained. Throughout we incorporate the production, at fixed time, of PBHs with a range of masses, which occurs when critical collapse is taken into account.Comment: 8 pages RevTeX file with 3 figures incorporated (uses RevTeX and epsf). Version to appear in Phys. Rev. D: minor change to calculation and added discussio

Generalized polarizabilities and the chiral structure of the nucleon

We discuss the virtual Compton scattering reaction $e^-p\to e^-p\gamma$ at low energies. We present results for the generalized polarizabilities of the nucleon obtained in heavy baryon chiral perturbation theory at $O(p^3)$.Comment: 5 pages, LaTex file, 1 postscript figure, uses ``espcrc1.sty'', talk given by S. Scherer at the 15th International Conference on Few Body Problems in Physics, Groningen, The Netherlands, 22-26 July 1997, to appear in the proceedings (Nucl. Phys. A