Massive Yang-Mills model and diffractive scattering

We argue that the massive Yang-Mills model of Kunimasa and Goto, Slavnov, and Cornwall, in which massive gauge vector bosons are introduced in a gauge-invariant way without resorting to the Higgs mechanism, may be useful for studying diffractive scattering of strongly interacting particles. With this motivation, we perform in this model explicit calculations of S-matrix elements between quark states, at the tree level, one loop, and two loops, and discuss issues of renormalizability and unitarity. In particular, it is shown that the S-matrix element for quark scattering is renormalizable at one-loop order, and is only logarithmically non-renormalizable at two loops. The discrepancies in the ultraviolet regime between the one-loop predictions of this model and those of massless QCD are discussed in detail. In addition, some of the similarities and differences between the massive Yang-Mills model and theories with a Higgs mechanism are analyzed at the level of the S matrix. Finally, we briefly discuss the high-energy behavior of the leading order amplitude for quark-quark elastic scattering in the diffractive region. The above analysis sets up the stage for carrying out a systematic computation of the higher order corrections to the two-gluon exchange model of the Pomeron using massive gluons inside quantum loops.