Power counting and effective field theory for charmonium

Abstract

We hypothesize that the correct power counting for charmonia is in the parameter ${\ensuremath{\Lambda}}_{\mathrm{QCD}}{/m}_{c},$ but is not based purely on dimensional analysis (as is heavy quark effective theory). This power counting leads to predictions which differ from those resulting from the usual velocity power counting rules of non-relativistic QCD (NRQCD). In particular, we show that while ${\ensuremath{\Lambda}}_{\mathrm{QCD}}{/m}_{c}$ power counting preserves the empirically verified predictions of spin symmetry in decays, it also leads to new predictions which include a hierarchy between spin singlet and triplet octet matrix elements in the $J/\ensuremath{\psi}$ system, a quenching of the net polarization in production at large transverse momentum, and no end point enhancement in radiative decays. We discuss explicit tests which can differentiate between the traditional and new theories of NRQCD.