Working group report: Collider Physics

This is summary of the activities of the working group on collider physics in the IXth Workshop on High Energy Physics Phenomenology (WHEPP-9) held at the Institute of Physics, Bhubaneswar, India in January 2006. Some of the work subsequently done on these problems by the subgroups formed during the workshop is included in this report.     

A vinyl substitution reaction in fluoroalkenes

Based on the results of CNDO and INDO quantum-chemical calculations, the possibility of a vinyl substitution (along with an addition) upon reaction of perfluoropropylene, perfluoroisobutylene, and trifluorochloroethylene with alcohols, thiols, and amines, and the absence of a similar reaction in the case of tetrafluoroethylene is explained. The calculations allow the prediction that a vinyl substitution should take place in similar reactions of 1,1-di- and trifluoroethylenes, but not with mono- and 1,2-difluoroethylenes.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 12, pp. 2802–2805, December, 1991.     

Exchange Relation Planar Algebras

An inclusion of II ₁ factors NM of finite index has as an invariant, a double sequence of finite-dimensional algebras known as the standard invariant. Planar algebras were introduced by V. Jones as a geometric tool for computing standard invariants of existing subfactors as well as generating standard invariants for new subfactors. In this paper we define a class of planar algebras, termed exchange relation planar algebras, that provides a general framework for understanding several classes of known subfactor inclusions: the Fuss–Catalan algebras (i.e. those coming from the presence of intermediate subfactors) and all depth 2 subfactors. In addition, we present a new class of planar algebras (and thus a new class of subfactors) coming from automorphism subgroups of finite groups.