Two-loop soft anomalous dimensions and NNLL resummation for heavy quark production

I present results for two-loop soft anomalous dimensions for heavy quark production which control soft-gluon resummation at next-to-next-to-leading-logarithm (NNLL) accuracy. I derive an explicit expression for the exact result and study it numerically for top quark production via e+ e- -> t tbar, and I construct a surprisingly simple but very accurate approximation. I show that the two-loop soft anomalous dimensions with massive quarks display a simple proportionality relation to the one-loop result only in the limit of vanishing quark mass. I also discuss the extension of the calculation to single top and top pair production in hadron colliders.Comment: 10 pages, 6 figures; improved form of the analytical result; equation adde

On zero-divisors in group rings of groups with torsion

Nontrivial pairs of zero-divisors in group rings are introduced and discussed. A problem on the existence of nontrivial pairs of zero-divisors in group rings of free Burnside groups of odd exponent $n \gg 1$ is solved in the affirmative. Nontrivial pairs of zero-divisors are also found in group rings of free products of groups with torsion.Comment: 8 pages, to appear in Canadian Math. Bul

Beyond Sperner's lemma

The present paper is devoted to a recent beautiful and ingenious proof of Brouwer's fixed point theorem due to mathematical economists H. Petri and M. Voorneveld. The heart of this proof is an analogue of Sperner's lemma motivated by Shapley-Scarf model of markets of agents with preferences over indivisible goods. The goal of the paper is to present a relatively abstract version of Petri-Voorneveld proof which makes transparent both its similarities and its differences with the classical proof based on Sperner's lemma and a well known Knaster-Kuratowski-Mazurkiewich argument.Comment: 9 page

Analytical study of anisotropic compact star models

A simple classification is given of the anisotropic relativistic star models, resembling the one of charged isotropic solutions. On the ground of this database, and taking into account the conditions for physically realistic star models, a method is proposed for generating all such solutions. It is based on the energy density and the radial pressure as seeding functions. Numerous relations between the realistic conditions are found and the need for a graphic proof is reduced just to one pair of inequalities. This general formalism is illustrated with an example of a class of solutions with linear equation of state and simple energy density. It is found that the solutions depend on three free constants and concrete examples are given. Some other popular models are studied with the same method.Comment: 19 pages, 2 figures, revised, to appear in Eur. Phys. J. C, one column journal styl