55,327 research outputs found
Measures of Intermediate Entropies for Skew Product Diffeomorphisms
In this paper we study a skew product map with a measure of
positive entropy. We show that if on the fibers the map are
diffeomorphisms with nonzero Lyapunov exponents, then has ergodic measures
of intermediate entropies. To construct these measures we find a set on which
the return map is a skew product with horseshoes along fibers. We can control
the average return time and show the maximum entropy of these measures can be
arbitrarily close to .Comment: 12 pages, a few mistakes corrected, some sections seriously rewritte
TMD Evolution: Matching SIDIS to Drell-Yan and W/Z Boson Production
We examine the QCD evolution for the transverse momentum dependent
observables in hard processes of semi-inclusive hadron production in deep
inelastic scattering and Drell-Yan lepton pair production in collisions,
including the spin-average cross sections and Sivers single transverse spin
asymmetries. We show that the evolution equations derived by a direct integral
of the Collins-Soper-Sterman evolution kernel from low to high Q can describe
well the transverse momentum distribution of the unpolarized cross sections in
the Q^2 range from 2 to 100 GeV^2. In addition, the matching is established
between our evolution and the Collins-Soper-Sterman resummation with
b*-prescription and Konychev-Nodalsky parameterization of the non-perturbative
form factors, which are formulated to describe the Drell-Yan lepton pair and
W/Z boson production in hadronic collisions. With these results, we present the
predictions for the Sivers single transverse spin asymmetries in Drell-Yan
lepton pair production and boson production in polarized pp and collisions for several proposed experiments. We emphasize that these
experiments will not only provide crucial test of the sign change of the Sivers
asymmetry, but also provide important opportunities to study the QCD evolution
effects.Comment: 46 pages, 15 figure
- …