We review the present status of QCD corrections to weak decays beyond the leading-logarithmic approximation, including particle-antiparticle mixing and rare and $\mathrm{CP}$-violating decays. After presenting the basic formalism for these calculations we discuss in detail the effective Hamiltonians of all decays for which the next-to-leading-order corrections are known. Subsequently, we present the phenomenological implications of these calculations. The values of various parameters are updated, in particular the mass of the newly discovered top quark. One of the central issues in this review are the theoretical uncertainties related to renormalization-scale ambiguities, which are substantially reduced by including next-to-leading-order corrections. The impact of this theoretical improvement on the determination of the Cabibbo-Kobayashi-Maskawa matrix is then illustrated. [S0034-6861(96)00304-2]

Weak decays beyond leading logarithms

The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the postNewtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many nonlinear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail eects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary’s orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.

/pdf/gravitational-radiation-from-post-newtonian-sources-and-g96j1cyq78.pdf

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries.

Superstring theoryをめぐって(放談室)

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

Automated one-loop calculations in four and D dimensions

Dimensional renormalization is defined in such a way that the renormalized action principle holds. It is shown that this leads to a minimal, additive renormalization. The derivation of Ward-Takahashi indentities and Callan-Symanzik equations from the action principle is exemplified.

/pdf/dimensional-renormalization-and-the-action-principle-4htcoqloh4.pdf

Dimensional Renormalization and the Action Principle

In this paper we consider generalizations in 4 dimensions of the Einstein-Maxwell equations which typically arise from Kaluza-Klein theories. We specify conditions such that stationary solutions lead to non-linearσ-models for symmetric spaces. Using both this group theoretic structure and some properties of harmonic maps we are able to generalize many of the known existence and uniqueness theorems for black holes in Einstein-Maxwell theory to this more general setting.

/pdf/4-dimensional-black-holes-from-kaluza-klein-theories-3s6kw6kcvt.pdf

$4$-dimensional black holes from Kaluza-Klein theories

In the framework of dimensional renormalization the existence of Green's functions to all orders of perturbation theory is proved for theories with massless particles, provided all terms in the interaction Lagrangian have infrared degree Ω≧4. If the vanishing of masses is enforced by some symmetry and this symmetry is respected by dimensional regularization, Schwinger's action principle holds for these Green's functions as in the massive case.

https://projecteuclid.org/download/pdf_1/euclid.cmp/1103900441

Dimensionally renormalized Green's functions for theories with massless particles. II

Gravitating monopole solutions

We study the global behaviour of static, spherically symmetric solutions of the Einstein-Yang-Mills equations with gauge groupSU(2). Our analysis results in three disjoint classes of solutions with a regular origin or a horizon. The 3-spaces (t=const.) of the first, generic class are compact and singular. The second class consists of an infinite family of globally regular, resp. black hole solutions. The third type is an oscillating solution, which although regular is not asymptotically flat.

/pdf/static-spherically-symmetric-solutions-of-the-einstein-yang-zq0ksnobmx.pdf

Peter Breitenlohner

Papers

Dimensional Renormalization and the Action Principle

$4$-dimensional black holes from Kaluza-Klein theories

Dimensionally renormalized Green's functions for theories with massless particles. II

Gravitating monopole solutions

Static spherically symmetric solutions of the Einstein-Yang-Mills equations