48 research outputs found
On multiplicities in length spectra of arithmetic hyperbolic three-orbifolds
Asymptotic laws for mean multiplicities of lengths of closed geodesics in
arithmetic hyperbolic three-orbifolds are derived. The sharpest results are
obtained for non-compact orbifolds associated with the Bianchi groups SL(2,o)
and some congruence subgroups. Similar results hold for cocompact arithmetic
quaternion groups, if a conjecture on the number of gaps in their length
spectra is true. The results related to the groups above give asymptotic lower
bounds for the mean multiplicities in length spectra of arbitrary arithmetic
hyperbolic three-orbifolds. The investigation of these multiplicities is
motivated by their sensitive effect on the eigenvalue spectrum of the
Laplace-Beltrami operator on a hyperbolic orbifold, which may be interpreted as
the Hamiltonian of a three-dimensional quantum system being strongly chaotic in
the classical limit.Comment: 29 pages, uuencoded ps. Revised version, to appear in NONLINEARIT
Supersymmetric QCD corrections to and the Bernstein-Tkachov method of loop integration
The discovery of charged Higgs bosons is of particular importance, since
their existence is predicted by supersymmetry and they are absent in the
Standard Model (SM). If the charged Higgs bosons are too heavy to be produced
in pairs at future linear colliders, single production associated with a top
and a bottom quark is enhanced in parts of the parameter space. We present the
next-to-leading-order calculation in supersymmetric QCD within the minimal
supersymmetric SM (MSSM), completing a previous calculation of the SM-QCD
corrections. In addition to the usual approach to perform the loop integration
analytically, we apply a numerical approach based on the Bernstein-Tkachov
theorem. In this framework, we avoid some of the generic problems connected
with the analytical method.Comment: 14 pages, 6 figures, accepted for publication in Phys. Rev.