Massive Yang-Mills model and diffractive scattering

We argue that the massive Yang-Mills model of Kunimasa and Goto, Slavnov, andCornwall, in which massive gauge vector bosons are introduced in agauge-invariant way without resorting to the Higgs mechanism, may be useful forstudying diffractive scattering of strongly interacting particles. We performin this model explicit calculations of S-matrix elements between quark states,at tree level, one loop, and two loops, and discuss issues of renormalisabilityand unitarity. In particular, it is shown that the S-matrix element for quarkscattering is renormalisable at one-loop order and is only logarithmicallynon-renormalisable at two loops. The discrepancies in the ultraviolet regimebetween the one-loop predictions of this model and those of massless QCD arediscussed in detail. Also, some of the similarities and differences between themassive Yang-Mills model and theories with a Higgs mechanism are analysed atthe level of the S-matrix. Finally, we briefly discuss the high-energybehaviour of the leading-order amplitude for quark-quark elastic scattering inthe diffractive region. The above analysis sets up the stage for carrying out asystematic computation of the higher order corrections to the two-gluonexchange model of the Pomeron using massive gluons inside quantum loops.Comment: 38 pages, Latex, with 7 PostScript pictures. Introduction and Section 6 further enlarged, minor typos correcte