Mass Divergences Research Articles

Geometric aspects of charged black holes in Palatini theories

Charged black holes in gravity theories in the Palatini formalism present a number of unique properties. Their innermost structure is topologically nontrivial, representing a wormhole supported by a sourceless electric flux. For certain values of their effective mass and charge curvature divergences may be absent, and their event horizon may also disappear yielding a remnant. We give an overview of the mathematical derivation of these solutions and discuss their geodesic structure and other geometric properties.

Scalar field theories on the world sheet: cutoff independent treatment

Following earlier work on the same topic, we consider once more scalar field theories on the world sheet parametrized by the light cone coordinates. For most of the way, we use the same approach as in the previous work, but there is an important new development. To avoid the light cone singularity at p^{+}=0, one world sheet coordinate had to be discretized, introducing a cutoff into the model.In the earlier work, this cutoff could not be removed, making the model unreliable. In the present article, we show that, by a careful choice of the mass counter term, both the infrared singularity at p^{+}=0 and the ultraviolet mass divergences can be simultaneously eliminated. We therefore finally have a cutoff independent model on a continuously parametrized world sheet. We study this model in the mean field approximation, and as before, we find solitonic solutions. Quantizing the solitonic collective coordinates gives rise to a string like model. However, in contrast to the standard string model, the trajectories here are not in general linear but curved.

Characterization of electromigration-induced mass divergences in multilayer interconnects by energy-dispersive x-ray spectroscopy

A nondestructive technique, based on energy-dispersive x-ray spectroscopy, was applied to characterize mass divergences in multilayer interconnects. The technique was used to reveal less than 0.5-μm-diam subsurface voids, precipitates, local changes in thickness of subsurface conducting layer, electromigration-induced mass divergences at conjugate mass source and sink in both the Al-Cu conducting layer and intermetallic compound overlayer, and a thin, hairline crack in the surface layer that is hardly visible in scanning electron microscopy.

Erratum: Factorization of soft and collinear divergences in QCD in the Feynman gauge via a background field gauge

We prove Ward-type identities which are needed in the proof of factorization of the Drell-Yan process. Previous treatments prove them only for an axial gauge, and the proofs are diagrammatic in nature. We, on the other hand, establish the identities for the Feynman gauge and through symmetry considerations at the Lagrangian level. Our strategy is to first derive exact results in a background field gauge and then to show that to leading order in the mass divergences the background-field-gauge results can be used in the Feynman gauge.

Factorization of soft and collinear divergences in QCD in the Feynman gauge via a background field gauge.

We prove Ward-type identities which are needed in the proof of factorization of the Drell-Yan process. Previous treatments prove them only for an axial gauge, and the proofs are diagrammatic in nature. We, on the other hand, establish the identities for the Feynman gauge and through symmetry considerations at the Lagrangian level. Our strategy is to first derive exact results in a background field gauge and then to show that to leading order in the mass divergences the background-field-gauge results can be used in the Feynman gauge.

Infrared and mass regularization in AF field theories (I). φ63

In the framework of asymptotically free (AF) field theories we determine the correction terms in the renormalization group (RG) approach to deep inelastic (DI) scattering and to the Drell-Yan (DY) process. This leads us to an order g 2 analysis of the DI/DY parton cross sections. Some of their contributions reveal ultraviolet (UV), infrared (IR) and mass (M) divergences which, after regularization, are removed by renormalization, IR and (partially) M cancellation. The initial-state M divergences, persisting in both processes, are removed by M factorization. Consistent IR and M regularization is constrained by the double-cut rule: its meaning and implications are explained. The calculations are performed in φ 6 3 theory which is AF, IR finite and technically simple. We use “on-shell”, “off-shell” and “massless” ( n-dimensional) mass assignments and demonstrate explicitly the regularization independence of the correction term.

Infrared and mass regularization in AF field theories (II). QCD

We determine the non-leading QCD corrections to deep inelastic (DI) scattering and to the Drell-Yan (DY) process by analysing the order g 2 parton cross sections. Using the insight and the techniques developed in the more simple environment of π 6 3, we regularize and subsequently remove the mass (M), infrared (IR), and ultraviolet (UV) divergences of the (double) cut graphs with the methods exposed in paper I. The QCD calculations are technically more involved. New M divergences are found, IR singularities occur, and overlapping M and IR singularities exist leading to double poles if n-dimensional regularization is used. Gluon gauge invariance must be satisfied. Although the off-shell method leads to gauge-dependent parton cross sections, the correction terms extracted via M factorization remain gauge invariant. The off-shell mass assignment was ill-defined in the past and did not satisfy the double cut rule; we explain the implications. The correction terms are explicitly shown to be independent of any regularization method. Defining the scale-dependent momentum distribution to consist of log Q 2 terms only, their influence in DI scattering is moderate, but considerable in DY massive μμ pair production for Q 2 ⩽ 100 GeV 2.

An operator approach to weighted cross sections

A formalism is developed for expressing annihilation cross sections directly in terms of the vacuum expectation values of certain time-ordered products. This necessitates the introduction of a class of operators defined as spatial of multilocal products of fields. The formalism is used to study qualitatively the effects of a dilute gas of instantons on weighted cross sections, and also to rederive results on the cancellation of mass divergences.

Mass divergences of wide-angle scattering amplitudes

The mass divergences of wide-angle scattering amplitudes are examined in a class of field theories including those with elementary vector fields. Power-counting arguments are used to show that, apart from renormalization effects, the wide-angle gauge-singlet scattering amplitude has a well-defined zero-mass limit and hence satisfies the renormalization-group equations. The same techniques also reproduce the earlier results for Yukawa and ${\ensuremath{\varphi}}^{4}$ theories.

Mass divergences in two-particle inelastic scattering

Feynman integrals for two-particle inelastic scattering are studied in the limit that the ratio of particle masses to all relevant invariants vanishes. The discussion applies to renormalizable field theories including quantum chromodynamics. Dominant contributions arise from momentum configurations which recall the parton model. The results can be applied to cross sections for single-particle or multiparticle inclusive reactions and to cross sections averaged over small regions of phase space.

Mass divergences in annihilation processes. I. Origin and nature of divergences in cut vacuum polarization diagrams

The origin of mass divergences in internal loop momentum integrals of cut vacuum polarization diagrams is investigated. It is found that loop momentum configurations which can give rise to mass divergences are of a severely limited form and have a direct interpretation in terms of physically realizable processes. A power-counting procedure suitable for estimating the nature of mass divergences is developed, and it is found that in a large class of field theories, cross sections smeared over a small region of phase space are at worst logarithmically divergent.

Mass divergences in annihilation processes. II. Cancellation of divergences in cut vacuum polarization diagrams

The cancellation of mass divergences in cut vacuum polarization diagrams is investigated. Ensembles of states are identified, the summation over which produces transition probabilities which are free of mass divergences. States included in these ensembles can be characterized as having a "jetlike" structure. The reasoning is extended to a large class of renormalizable field theories, including non-Abelian gauge theories.

Zero-mass limit for gauge-singlet production amplitudes

A power-counting argument is given that one-particle irreducible amplitudes for wide-angle production of on-shell gauge-singlet particles are free of mass divergences, even in totally massless field theories.

Deviations from Electron-Muon Universality in the Leptonic Decays of the Intermediate Bosons

The deviations from electron-muon Universality induced by the higher-order corrections in the leptonic decays of the intermediate bosons are analyzed in the framework of the renormalizable theories of weak and electromagnetic interactions. Some general theorems are derived for the second-order weak and electromagnetic corrections which are valid for all renormalizable theories which incorporate electron-muon universality as a zeroth-order relation. The connection of our results with the theorem of cancellation of mass divergences is briefly discussed.

Mass Divergences and Callan-Symanzik Equations in Quantum Electrodynamics

We discuss the connection between the theorems on mass divergences of unrenormalized (but regularized) vertex functions and the asymptotic Callan-Symanzik equations in quantum electrodynamics. To illustrate the point, we first use these theorems to give a rather simple derivation of the asymptotic Callan-Symanzik equation for the renormalized photon propagator and later generalize the analysis to the $2n+l$ vertex function. By a natural extension of the argument, one obtains nonasymptotic equations in which the inhomogeneous terms involve mass derivatives of the unrenormalized vertex functions multiplied by suitable products of the renormalization constants ${Z}_{2}$ and ${Z}_{3}$. As a by-product, one obtains partial differential equations for ${Z}_{2}$ and ${Z}_{3}$ regarded as functions of the masses. The method can be used when several internal masses are present in the problem, in either the conventional or the intermediate renormalization schemes.

Energy-Momentum Structure Form Factors of Particles

By emphasizing the analogy between mass and charge as sources of fields, we are led to examine the mechanical structure of a particle in terms of the matrix elements $〈{\mathrm{p}}^{\ensuremath{'}}|{\ensuremath{\theta}}_{\ensuremath{\alpha}\ensuremath{\beta}}(0)|\mathrm{p}〉$, where ${\ensuremath{\theta}}_{\ensuremath{\alpha}\ensuremath{\beta}}(x)$ is the total energy-momentum tensor, just as the matrix elements $〈{\mathrm{p}}^{\ensuremath{'}}|{j}_{\ensuremath{\alpha}}(0)|\mathrm{p}〉$ of the current operator ${j}_{\ensuremath{\alpha}}(x)$ define its electromagnetic structure. Although the off-diagonal matrix elements $〈{\mathrm{p}}^{\ensuremath{'}}|{\ensuremath{\theta}}_{\ensuremath{\alpha}\ensuremath{\beta}}(0)|\mathrm{p}〉$ are not accessible to direct experimental observation, the diagonal element $〈\mathrm{p}|{\ensuremath{\theta}}_{\ensuremath{\alpha}\ensuremath{\beta}}(0)|\mathrm{p}〉$ is just proportional to the total mass. Consequently, we can study the contributions to the total mass in terms of vertex functions instead of propagators and, using the techniques of dispersion theory, relate the contribution to the total mass to integrals over physical scattering processes. We examine electrodynamics and the pion-nucleon interaction in perturbation theory and show how the mass divergences emerge as a consequence of the high-energy behavior of the Coulomb amplitude and the nucleon-nucleon scattering amplitude. Finally, using elastic unitarity, we can relate mass splittings in a multiplet to integrals over the differences in $S$-wave phase shifts.