Higher quarkonia

In this paper we survey all radial and orbital excitations of the I=0 and I=1 n (n) over bar system anticipated up to 2.1 GeV. We give detailed predictions of their quasi-two-body branching fractions and identify characteristic decay modes that can isolate quarkonia; this should be useful in distinguishing quarkonia from glueballs and hybrids. Several of the ''missing mesons'' with L-q (q over bar)=2 and L-q (q over bar)=3 are predicted to decay dominantly into certain S+P and S+D modes, and should appear in experimental searches for hybrids in the same mass region. We also consider the topical issues of whether some of the recently discovered or controversial meson resonances, including glueball and hybrid candidates, can be accommodated as quarkonia.