Transverse single spin asymmetry in the Drell-Yan process

We revisit the transverse single spin asymmetry in the angular distribution of a Drell-Yan dilepton pair. We study this asymmetry by using twist-3 collinear factorization, and we obtain the same result both in covariant gauge and in the light-cone gauge. Moreover, we have checked the electromagnetic gauge invariance of our calculation. Our final expression for the asymmetry differs from all the previous results given in the literature. The overall sign of this asymmetry is as important as the sign of the Sivers asymmetry in Drell-Yan.Comment: 9 page

Reviewing model calculations of the Collins fragmentation function

The Collins fragmentation function describes a left/right asymmetry in the fragmentation of a transversely polarized quark into a hadron in a jet. Four different model calculations of the Collins function have been presented in the literature. While based on the same concepts, they lead to different results and in particular to different signs for the Collins function. The purpose of the present work is to review the features of these models and correct some errors made in previous calculations. A full study of the parameter dependence and the possible modifications to these models is beyond the scope of the paper. However, some general conclusions are drawn

Dihadron fragmentation functions for large invariant mass

Using perturbative Quantum Chromodynamics, we compute dihadron fragmentation functions for a large invariant mass of the dihadron pair. The main focus is on the interference fragmentation function H_1^{\open}, which plays an important role in spin physics of the nucleon. Our calculation also reveals that H_1^{\open} and the Collins fragmentation function have a closely related underlying dynamics. By considering semi-inclusive deep-inelastic scattering, we further show that collinear factorization in terms of dihadron fragmentation functions, and collinear factorization in terms of single hadron fragmentation functions provide the same result in the region of intermediate invariant mass.Comment: 4 pages; issue with layout fixe

Partonic Pole Matrix Elements for Fragmentation

A model-independent analysis of collinear three-parton correlation functions for fragmentation is performed. By investigating their support properties it is shown, in particular, that the so-called partonic pole matrix elements vanish. This sheds new light on the understanding of transverse single spin asymmetries in various hard semi-inclusive reactions. Moreover, it gives additional strong evidence for the universality of transverse-momentum-dependent fragmentation functions.Comment: 4 pages, 2 figures; minor changes, matches journal versio

The Enigma of Frequency-Dependent Selection [Revised and updated 16 June 1998]

Frequency-dependent selection is so fundamental to modern evolutionary thinking that everyone interested in evolutionary biology 'knows' the concept. It is even so fundamental that many authors of textbooks do not bother to define it. Yet it turns out that different authors (and sometimes even one and the same author) use the term to refer to different types of selection. In this paper we try to uncover the sources of this confusion. The concept is fairly well defined in the original concept of population genetical theory, which focuses on short-term evolutionary change, and basically ignores density-dependence. The problems start when the original concept is used in the context of long-term evolution, in which density-dependence is essential: without density dependence, lines of descent either die out or explode on the relevant time scales. With density-dependence, the definition of frequency-dependent selection, in the form in which it is usually given, becomes ambiguous. The concept of weak and strong frequency-dependence distinguish between two very different forms of frequency-dependent selection occurring in populations which experience density-dependent population regulation

Evolution of Mixed Maturation Strategies in Semelparous Life-histories: the Crucial Role of Dimensionality of Feedback Environment [Updated 18 August 1998]

We study the evolution of age-at-maturity in a semelparous life history with two age-classes. An individual may breed in the first year of its life and die, or delay breeding to the second year. In this setting a mixed strategy means that a fraction of the individual's offspring breed in the first possible breeding event, while the remaining fraction delay breeding. Current theory seems to imply that mixed strategies are not evolutionarily stable strategies (ESS) under a steady state population dynamical regime. We show that a two-dimensional feedback environment may allow the evolution of mixed age-at-maturity. Furthermore, different phenotypes need to perceive the environment differently. The biological reasoning behind these conditions is different resource usage or predation pressure between two age-classes. Thus, the conventional explanations for the occurrence of mixed strategies in natural populations, environmental stochasticity or complex dynamics, are not needed

Lorentz invariance relations and Wandzura-Wilczek approximation

A complete list of the so-called Lorentz invariance relations between parton distribution functions is given and some of their consequences are discussed, such as the Burkhardt-Cottingham sum rule. The violation of these relations is considered in a model independent way. It is shown that several Lorentz invariance relations are not violated in a generalized Wandzura-Wilczek approximation, indicating that numerically their violation may be small.Comment: 10 pages; Proceedings of the workshop "Recent Advances in Perturbative QCD and Hadronic Physics", July 20-24, 2009, at ECT*, Trento (Italy), in honor of Anatoli V. Efremov on the occasion of his 75th birthday; to appear in Mod. Phys. Lett.

Evolutionary branching in a stochastic population model with discrete mutational steps

Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a trait, and also by population sizes, and that mutations lead to small changes in trait value. Then, traditionally, the evolutionary dynamics is studied in the limit of vanishing mutational step sizes. In the present approach, small but non-negligible mutational steps are considered. By means of theoretical analysis in the limit of infinitely large populations, as well as computer simulations, we demonstrate how discrete mutational steps affect the patterns of evolutionary branching. We also argue that the average time to the first branching depends in a sensitive way on both mutational step size and population size.Comment: 12 pages, 8 figures. Revised versio