No abstract

Nonperturbative studies of field theory require the Schwinger-Dyson equations to be truncated to make them tractable. Thus, when investigating the behavior of the fermion propagator, for example, an Ansatz for the three-point vertex has to be made. While the well-known Ward identity determines the longitudinal part of this vertex in terms of the fermion propagator as shown by Ball and Chiu, it leaves the transverse part unconstrained. However, Brown and Dorey have recently emphasized that the requirement of multiplicative renormalizability is not satisfied by arbitrary Ansatze for the vertex. We show how this requirement restricts the form of the transverse part. By considering the example of QED in the quenched approximation, we present a form for the vertex that not only satisfies the Ward identity but is multiplicatively renormalizable to all orders in leading and next-to-leading logarithms in perturbation theory and so provides a suitable Ansatz for the full three-point vertex.

No abstract

A scalar glueball is predicted in the 1-GeV mass region. The present analysis is concerned with experimental evidence for such a state. It has been proposed that glueballs should be preferentially produced in supposedly glue-rich processes such as I ) decay and double-Pomeron exchange. However, any meson of such a mass and quantum number has very restricted decay channels availableessentially only nn and, if the mass allows, Ki?. In this case, any production process is very tightly correlated to elastic reactions, na-an and TI--KK, by unitarity. Novel processes cannot then reveal effects that could not be seen in these elastic reactions. Nevertheless, they can valuably supplement this standard information where it lacks precision. Recent high-statistics results on central dimeson production at the CERN ISR enable us to perform an extensive new coupled-channel analysis of Z=0 S-wave nn and KE final states. This unambiguously reveals three resonances in the 1-GeV region, S1(991), S2(988), and ~(900), where the naive quark model expects just two. We discuss in detail these new features and how they may be confirmed experimentally, and give their present interpretation. The S1(991) is a plausible candidate for the scalar glueball. We examine other production reactions (heavy-flavor decays and y y reactions) leading to the same final states, and discuss how, with future precision, these can probe fine details.