New Quadratic Mass Relations for Heavy Mesons

By assuming the existence of (quasi)-linear Regge trajectories for heavy mesons, we derive new quadratic mass relations of non-Gell-Mann–Okubo type, 6M(qq̄) + 3M(cc̄) = 8M(cq̄), 20M(qq̄) + 5M(bb̄) = 16M(bq̄), q = n(= u, d), s which show excellent agreement with experiment. We also establish the sum rule M(īi) +M(jj̄)− 2M(jī) ≈ const for any pair of flavors, (i, j). E-mail: [email protected]. Present address: Theoretical Division, MS B285, Los Alamos National Laboratory, Los Alamos, NM 87545, USA E-mail: [email protected]. Permanent address: School of Physics and Astronomy, Tel-Aviv University, Ramat-Aviv, Israel. Also at Department of Physics, Bar-Ilan University, Ramat-Gan, Israel E-mail: [email protected]