Jet Topology Research Articles

A study of energy-energy correlations ine + e ? annihilations at $$\sqrt s = 34.6$$ GeV

We present high statistics measurements of the energy-energy correlation (EEC) and its related asymmetry (AEEC) ine+e− annihilation at a c.m. energy of 34.6 GeV. We find that the energy dependence as well as the large angle behaviour of the latter are well described by perturbative QCD calculations toOα(s2). Non-perturbative effects are estimated with the help of fragmentation models in which different jet topologies are separated using (ɛ, δ) cuts, and found to be small. The extracted values of\(\Lambda _{\overline {MS} }\) lie between 100 and 300 MeV.

The production of large transverse momentum jets in plarized photon-photon collisions

A comprehensive survey is presented of the polarization structure of the leading order QCD processes for the production of jets at largept in photon-photon collisions which are the result of colliding positrons. Results are given for asymmetries. It is shown that by separating events with various jet topologies it is possible to investigate different aspects of polarization and QCD. For instance the four anf three jet process asymmetries are found to be sensitive to the relative magnitudes of the perturbative anf non-perturbative components of the photon structure function. A discussion is given of the usefulness of polarization in separating the two gluon jet subprocess. It is concluded that such experiments could be very useful in understanding QCD and the strong interactions.

Normicity, a general jet measure

A general jet measure for identifying multi-jet final states ine+e− annihilations is introduced and discussed. It is a single valued quantity characterizing jet topologies and it is mostly free of nonperturbative effects. Using this test measure we present a new and simple algorithm to find multijet structures. Tests on simulated events show that this method forms a powerful tool to investigate hard gluon radiation.

Pattern recognition in layered track chambers using a tree algorithm

We present a new approach to the pattern recognition problem in multi-layer track chambers. Tracks are constructed from locally related hits using a tree algorithm. This approach has worked well in quite different track finding problems in the large cylindrical drift chamber in the TASSO detector at PETRA. Its success in analyzing complicated e+e− jet events indicates that it can be applied to other problems, including the complicated jet topologies expected at higher energy.

Variations, Characteristic Classes, and the Obstruction to Mapping Smooth to Continuous Cohomology

In a recent paper, the author gave an example of a singular foliation on ${{\mathbf {R}}^2}$ for which it is impossible to map the de Rham cohomology ${T_{{\text {DR}}}}$ to the continuous singular cohomology ${T_{\text {c}}}$ (in the sense of Bott and Haefliger’s continuous cohomology of spaces with two topologies) compatibly with evaluation of cohomology classes on homology classes. In this paper the obstruction to mapping ${T_{{\text {DR}}}}$ to ${T_{\text {c}}}$ is pinpointed by defining a whole family of cohomology theories ${T_{k,m,n}}$, based on cochains which vary in a ${C^k}$ manner, which mediate between the two. It is shown that the obstruction vanishes on nonsingularly foliated manifolds. The cohomology theories are extended to Haefliger’s classifying space $(B{\Gamma _q} \to B{J_q})$, with its germ and jet topologies, by using a notion of differentiable space similar to those of J. W. Smith and K. T. Chen. The author proposes that certain of the ${T_{kmn}}$ be used instead of ${T_{\text {c}}}$ to study Bott and Haefliger’s conjecture that the continuous cohomology of $(B{\Gamma _q} \to B{J_q})$ equals the relative Gel’fand-Fuks cohomology ${H^\ast }({\mathfrak {a}_q},{O_q})$. It is shown that ${T_{kmn}}(B{\Gamma _q} \to B{J_q})$ may contain new characteristic classes for foliations which vary only in a ${C^k}$ manner when a foliation is varied smoothly.

Variations, characteristic classes, and the obstruction to mapping smooth to continuous cohomology

In a recent paper, the author gave an example of a singular foliation on R 2 {{\mathbf {R}}^2} for which it is impossible to map the de Rham cohomology T DR {T_{{\text {DR}}}} to the continuous singular cohomology T c {T_{\text {c}}} (in the sense of Bott and Haefliger’s continuous cohomology of spaces with two topologies) compatibly with evaluation of cohomology classes on homology classes. In this paper the obstruction to mapping T DR {T_{{\text {DR}}}} to T c {T_{\text {c}}} is pinpointed by defining a whole family of cohomology theories T k , m , n {T_{k,m,n}} , based on cochains which vary in a C k {C^k} manner, which mediate between the two. It is shown that the obstruction vanishes on nonsingularly foliated manifolds. The cohomology theories are extended to Haefliger’s classifying space ( B Γ q → B J q ) (B{\Gamma _q} \to B{J_q}) , with its germ and jet topologies, by using a notion of differentiable space similar to those of J. W. Smith and K. T. Chen. The author proposes that certain of the T k m n {T_{kmn}} be used instead of T c {T_{\text {c}}} to study Bott and Haefliger’s conjecture that the continuous cohomology of ( B Γ q → B J q ) (B{\Gamma _q} \to B{J_q}) equals the relative Gel’fand-Fuks cohomology H ∗ ( a q , O q ) {H^\ast }({\mathfrak {a}_q},{O_q}) . It is shown that T k m n ( B Γ q → B J q ) {T_{kmn}}(B{\Gamma _q} \to B{J_q}) may contain new characteristic classes for foliations which vary only in a C k {C^k} manner when a foliation is varied smoothly.