2,914 research outputs found
Virtual Legendrian Isotopy
An elementary stabilization of a Legendrian link in the spherical
cotangent bundle of a surface is a surgery that results in
attaching a handle to along two discs away from the image in of the
projection of the link . A virtual Legendrian isotopy is a composition of
stabilizations, destabilizations and Legendrian isotopies.
In contrast to Legendrian knots, virtual Legendrian knots enjoy the property
that there is a bijective correspondence between the virtual Legendrian knots
and the equivalence classes of Gauss diagrams.
We study virtual Legendrian isotopy classes of Legendrian links and show that
every such class contains a unique irreducible representative. In particular we
get a solution to the following conjecture of Cahn, Levi and the first author:
two Legendrian knots in that are isotopic as virtual Legendrian knots
must be Legendrian isotopic in Comment: 10 pages, 4 figur
Simple singularities of multigerms of curves
We classify stably simple reducible curve singularities in complex spaces of
any dimension. This extends the same classification of of irreducible curve
singularities obtained by V.I.Arnold. The proof is essentially based on the
method of complete transversals by J.W.Bruce et al.Comment: 18 page
QED Bremsstrahlung in decays of electroweak bosons
Isolated lepton momenta, in particular their directions are the most
precisely measured quantities in pp collisions at LHC. This offers
opportunities for multitude of precision measurements. It is of practical
importance to verify if precision measurements with lep- tons in the final
state require all theoretical effects evaluated simultaneously or if QED
bremsstrahlung in the final state can be separated without unwanted precision
loss. Results for final state bremsstrahlung in the decays of narrow resonances
are obtained from the Feynman rules of QED in an unambiguous way and can be
controlled with a very high precision. Also for resonances of non-negligible
width, if calculations are appropriately performed, such separation from the
remaining electroweak effects can be expected. Our paper is devoted to
validation that final state QED bremsstrahlung can indeed be separated from the
rest of QCD and electroweak effects, in the production and decay of Z and W
bosons, and to estimation of the resulting systematic error. The quantitative
discussion is based on Monte Carlo programs PHOTOS and SANC, as well as on KKMC
which is used for benchmark results. We show, that for a large classes of W and
Z boson observables as used at LHC, theoretical error on photonic
bremsstrahlung is 0.1 or 0.2%, depending on the program options used. An
overall theoretical error on QED final state radiation, i.e. taking into
account missing corrections due to pair emission and interference with initial
state radiation is estimated respectively at 0.2% or 0.3% again depending on
the program option used.Comment: 1+28 pages, 20 figure
Extra lepton pair emission corrections to Drell-Yan processes in PHOTOS and SANC
In the paper we present results for final state emissions of lepton pairs in
decays of heavy intermediate states such as Z boson. Short presentations of
PHOTOS and SANC algorithms and physics assumptions are given. Numerical
distributions of relevance for LHC observables are shown. They are used in
discussions of systematic errors in the predictions of pair emissions as
implemented in the two programs. Suggestions for the future works are given.
Present results confirm, that for the precision of 0.3% level, in simulation of
final state the pair emissions can be avoided. For the precision of 0.1-0.2%,
the results obtained with the presented programs should be enough. To cross
precision tag of 0.1%, the further work is however required.Comment: 21 pages, 12 figure
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