UNIFICATION OF LINEAR REGGE TRAJECTORIES FOR ALL QQBAR FAMILIES

We report on a simple mass formula for the relativistic bound state QQ̄ system which describes remarkably well the family of mesons (ρ,ω,φ,Jψπ,K,K*,D,D*,F,F*): M2=(m1+m2)2+[2m1m2(m12+m22)](m1+m2)Ω(n+2)-c(m1+m2)2(m12+m22), where m1,m2 are the constituent quark masses, Ω is a universal constant (= 0.6624 GeV), n is the quantum number for the state, and c is an effective constant which measures how far off-shell the quarks are in their bound state, i.e., p12+m12+p22+m22 c•c depends weakly on the spin-triplet or singlet nature of the QQ̄ system. The parameters found in our fit are (in GeV units) mu=md=0.838 69, ms=0.879 88, mc=1.509 67, mb=4.393 12, c(triplet)=2.776 90, cπ(singlet)=2.508 40, cK(singlet)=2.492 76. A derivation based on a parton picture of a constituent-bound-state system of QQ̄ is given. Implications of this mass formula for higher-mass states are discussed. © 1979 The American Physical Society.