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

EW one-loop corrections to the longitudinally polarized Drell--Yan scattering. (I). The Neutral current case

Complete one-loop electroweak corrections to neutral current Drell-Yan process $p p \to \ell^+\ell^- X$ are presented for the case of longitudinal polarization of initial particles. Cross sections for longitudinally polarized protons allow us to estimate different combinations of polarized quark distributions from single- and double-spin asymmetries. Numerical impact of electroweak next-order corrections to asymmetries as function of the vector boson rapidity and lepton pseudorapidities in the hadron-hadron centre-of-mass frame using the MC generator ReneSANCe is thoroughly studied.Comment: 7 pages, 9 figure

Stereospecificity in the proton magnetic relaxation rate of enantiotopic methyls and the methyl rotation barrier

It is proposed that a distinction should be made between stereospecificity of the first kind, which provides spectral (line assignments in the NMR spectrum) and structural (molecular conformations) information, and stereospecificity of the second kind, which only provides spectral information, on the basis of the relaxation times T1. The nature of the stereospecificity was revealed in detail during analysis of the reasons for the differences in the proton relaxation times of enantiotopic gem-dimethyl groups in the conformationally rigid molecule of 2-oxo-5,5-dimethyl-1,3,2-dioxathiane. It is suggested that the barrier to rotation of the methyl in the geminal CH3-C-H fragment can be assessed from the temperature dependence of the t1 time of the methine proton. The experiment was carried out with the stereoisomeric r-2-tert-butyl-4-methyl-trans-7-methyl[2]1,3-dioxepane. © 1987 Plenum Publishing Corporation