21,047 research outputs found
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 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
Impurity center in a semiconductor quantum ring in the presence of a radial electric field
The problem of an impurity electron in a quantum ring (QR) in the presence of
a radially directed strong external electric field is investigated in detail.
Both an analytical and a numerical approach to the problem are developed. The
analytical investigation focuses on the regime of a strong wire-electric field
compared to the electric field due to the impurity. An adiabatic and
quasiclassical approximation is employed. The explicit dependencies of the
binding energy of the impurity electron on the electric field strength,
parameters of the QR and position of the impurity within the QR are obtained.
Numerical calculations of the binding energy based on a finite-difference
method in two and three dimensions are performed for arbitrary strengths of the
electric field. It is shown that the binding energy of the impurity electron
exhibits a maximum as a function of the radial position of the impurity that
can be shifted arbitrarily by applying a corresponding wire-electric field. The
maximal binding energy monotonically increases with increasing electric field
strength. The inversion effect of the electric field is found to occur. An
increase of the longitudinal displacement of the impurity typically leads to a
decrease of the binding energy. Results for both low- and high-quantum rings
are derived and discussed. Suggestions for an experimentally accessible set-up
associated with the GaAs/GaAlAs QR are provided.Comment: 16 pages, 8 figure
- …