Massive Vector Mesons and Gauge Theory

We show that the requirements of renormalizability and physical consistency imposed on perturbative interactions of massive vector mesons fix the theory essentially uniquely. In particular physical consistency demands the presence of at least one additional physical degree of freedom which was not part of the originally required physical particle content. In its simplest realization (probably the only one) these are scalar fields as envisaged by Higgs but in the present formulation without the ``symmetry-breaking Higgs condensate''. The final result agrees precisely with the usual quantization of a classical gauge theory by means of the Higgs mechanism. Our method proves an old conjecture of Cornwall, Levin and Tiktopoulos stating that the renormalization and consistency requirements of spin=1 particles lead to the gauge theory structure (i.e. a kind of inverse of 't Hooft's famous renormalizability proof in quantized gauge theories) which was based on the on-shell unitarity of the $S$-matrix. We also speculate on a possible future ghostfree formulation which avoids ''field coordinates'' altogether and is expected to reconcile the on-shell S-matrix point of view with the off-shell field theory structure.Comment: 53 pages, version to appear in J. Phys.

A Phenomenological Analysis of Gluon Mass Effects in Inclusive Radiative Decays of the J/ψ\rm{J/\psi} and $\Upsilon

The shapes of the inclusive photon spectra in the processes \Jp \to \gamma X and \Up \to \gamma X have been analysed using all available experimental data. Relativistic, higher order QCD and gluon mass corrections were taken into account in the fitted functions. Only on including the gluon mass corrections, were consistent and acceptable fits obtained. Values of $0.721^{+0.016}_{-0.068}$ GeV and $1.18^{+0.09}_{-0.29}$ GeV were found for the effective gluon masses (corresponding to Born level diagrams) for the \Jp and \Up respectively. The width ratios \Gamma(V \to {\rm hadrons})/\Gamma(V \to \gamma+ {\rm hadrons}) V=\Jp, \Up were used to determine $\alpha_s(1.5 {\rm GeV})$ and $\alpha_s(4.9 {\rm GeV})$. Values consistent with the current world average $\alpha_s$ were obtained only when gluon mass correction factors, calculated using the fitted values of the effective gluon mass, were applied. A gluon mass $\simeq 1$ GeV, as suggested with these results, is consistent with previous analytical theoretical calculations and independent phenomenological estimates, as well as with a recent, more accurate, lattice calculation of the gluon propagator in the infra-red region.Comment: 50 pages, 11 figures, 15 table