1,579 research outputs found
Toponogov comparison theorem for open triangles
Dedicated to Professor Gromoll: The aim of our article is to generalize the
Toponogov comparison theorem to a complete Riemannian manifold with smooth
convex boundary. A geodesic triangle will be replaced by an open (geodesic)
triangle standing on the boundary of the manifold, and a model surface will be
replaced by the universal covering surface of a cylinder of revolution with
totally geodesic boundary. Applications of our theorem are found in our article
"Applications of Toponogov's comparison theorems for open triangles"
(arXiv:1102.4156).Comment: This version 4 (36 pages, no figures) is a version to appear in
Tohoku Mathematical Journa
Probing new intra-atomic force with isotope shifts
In the development of atomic clocks, some atomic transition frequencies are
measured with remarkable precision. These measured spectra may include effects
of a new force mediated by a weakly interacting boson. Such effects might be
distilled out from possible violation of a linear relation in isotope shifts
between two transitions, as known as King's linearity, with relatively
suppressed theoretical uncertainties. We discuss the experimental sensitivity
to a new force in the test of the linearity as well as the linearity violation
owing to higher order effects within the Standard Model. The sensitivity to new
physics is limited by such effects. We have found that for Yb, the higher
order effect is in the reach of future experiments. The sensitivity to a heavy
mediator is also discussed. It is analytically clarified that the sensitivity
becomes weaker than that in the literature. Our numerical results of the
sensitivity are compared with other weak force search experiments.Comment: 16 pages, 3 figures; published versio
Collider signatures of the SO(5) x U(1) gauge-Higgs unification
Collider signatures of the gauge-Higgs unification model
in the Randall-Sundrum warped space are explored. Gauge couplings of quarks and
leptons receive small corrections from the fifth dimension whose effects are
tested by the precision data. It is found that the forward-backward asymmetries
in collisions on the pole are well explained in a wide range of
the warp factor , but the model is consistent with the branching fractions
of decay only for large z_L \simg 10^{15}. Kaluza-Klein (KK) spectra of
gauge bosons, quarks, and leptons as well as gauge and Higgs couplings of
low-lying KK excited states are determined. Right-handed quarks and leptons
have larger couplings to the KK gauge bosons than left-handed ones. Production
rates of Higgs bosons and KK states at Tevatron, LHC and ILC are evaluated. The
first KK has a mass 1130 GeV with a width 422 GeV for . The
current limit on the production at Tevatron and LHC indicates . A large effect of parity violation appears in the difference between
the rapidity distributions of and in the decay of the first KK .
The first KK gauge bosons decay into light and heavy quarks evenly.Comment: 45 pages, 6 figures. Contributions from the first KK photon are taken
into accoun
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