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

Long multiplets in supersymmetric mechanics

The "long" indecomposable N=2, d=1 multiplet (2, 4, 2) defined in arXiv:1503.05537 [hep-th] as a deformation of the pair of chiral multiplets (2, 2, 0) and (0, 2, 2) by a number of the mass-dimension parameters is described in the superfield approach. We present its most general superfield and component actions, as well as a generalization to the case with the superfields of the opposite Grassmann parities and dimensionless deformation parameter. We show that the long N=2, d=1 multiplets are naturally embedded into the chiral SU(2|1), d=1 superfields having nonzero external spins with respect to SU(2) \subset SU(2|1). A superfield with spin s contains 2s long multiplets and two short multiplets (2, 2, 0) and (0, 2, 2). Two possible N=4, d=1 generalizations of the N=2 long multiplet in the superfield approach are also proposed.Comment: 1 + 19 pages, new comments added, typos corrected, published versio

Super K\"ahler oscillator from SU(2|1) superspace

We construct a new version of the worldline SU(2|1) superspace as a deformation of the standard N =4, d=1 superspace and show that it naturally provides off- and on-shell description of general supersymmetric K\"ahler oscillator model considered earlier at the classical level within the Hamiltonian approach. The basic object is a generalized chiral SU(2|1), d=1 superfield with the off-shell field content (2, 4, 2). The frequency of the oscillator and the strength of external magnetic field are defined by two parameters: the contraction parameter $m$ and the new parameter $\lambda$ which reflects the freedom in defining the chiral SU(2|1), d=1 superspace. We treat both classical and quantum cases.Comment: 0 + 13 pages, typos corrected, reference adde

A new N = 8 nonlinear supermultiplet

We construct a new off-shell $\mathcal{N}{=}8$, $d{=}1$ nonlinear supermultiplet $(\mathbf{4,8,4})$ proceeding from the nonlinear realization of the $\mathcal{N}{=}8$, $d{=}1$ superconformal group $OSp(4^{\star}|4)$ in its supercoset $\frac{OSp(4^{\star}|4)}{SU(2)_{\mathcal{R}}\otimes \left\{D,K\right\} \otimes SO(4)}$. The irreducibility constraints for the superfields automatically follow from appropriate covariant conditions on the $osp(4^{\star}|4)$-valued Cartan superforms. We present the most general sigma-model type action for $(\mathbf{4,8,4})$ supermultiplet. The relations between linear and nonlinear $(\mathbf{4,8,4})$ supermultiplets and linear $\mathcal{N}{=}8$ $(\mathbf{5,8,3})$ vector supermultiplet are discussed.Comment: 15 pages, LaTeX file, PACS numbers: 11.30.Pb, 03.65.-

Allowed charge transfers between coherent conductors driven by a time-dependent scatterer

We derive constraints on the statistics of the charge transfer between two conductors in the model of arbitrary time-dependent instant scattering of non-interacting fermions at zero temperature. The constraints are formulated in terms of analytic properties of the generating function: its zeroes must lie on the negative real axis. This result generalizes existing studies for scattering by a time-independent scatterer under time-dependent bias voltage.Comment: 5 pages, no figures, corrected misprints and minor changes in version