Relativistic versus gluon mass effects: the role of 1/Q corrections in quarkonia decays

We present a detailed discussion of the relativistic corrections to quarkonia decay widths making use of a new, rigorous, QCD formalism. The results confirm our previous conclusion that relativistic corrections alone are unable to explain the discrepancy existing until now between perturbative QCD and experiments. We re-analyse the experimental data by using simple phase-space corrections parametrized in terms of two phenomenological parameters Mg (the 'effective gluon mass' at each quarkonium scale) determined by fitting the inclusive photon spectra in radiative decays of the Υ and J/ψ. In this case, all cc-bar and bb-bar decay widths provide values of αs which are consistent and in good agreement with the relative perturbative running from the c-quark to the b-quark mass scale and with the extrapolation from deep inelastic scattering. For the Υ, the value Mg≅1.2 GeV is in good agreement with the theoretical expectation that, asymptotically, the effective gluon mass should tend to its theoretical value mg≅1.5±0.3 GeV as derived from the experimental value of the gluon condensate (αsG2) in a recent calculation of dynamical mass generation in QCD. The smaller value Mg≅0.66 GeV found for the J/ψ can also be understood since a gluon mass mg≅1.5 GeV forces the primary gluons of J/ψ decays to fuse into light-quark pairs thus leading to an effective reduction of the measured gluon mass. Taking into account gluon mass corrections and small relativistic corrections derived from recent estimates of the pole masses of the c- and b-quarks, we obtain the following values of the strong coupling constant: αs(mb)=0.200±0.002-0.006+0.010 αs(mc)=0.302±0.008-0.050+0.038 where the first errors are experimental and the second are estimates of the theoretical systematic error. Finally, the possible impact of effective gluon mass effects for estimates of the non-perturbative 1/Q power corrections in various processes is discussed. (author)