Exact bounds and estimates on the masses of “beautiful” hadrons

Abstract

Using the QCD inspired postulate that forces between quarks are flavour-independent together with general concavity properties of the eigenvalues of a hamiltonian as a function of a parameter, we derive upper bounds on the masses of B, B∗ (b u , b d ) ⩞ b and Λ b from the experimental information on strange and charmed hadrons. The bound on M B + M B ∗ is so close to the experimental lower limit that we investigate the question whether our bounds are not in fact relatively accurate estimates and conclude affirmatively. We discuss the crucial experiment problem of the B ∗ − B and ⩞ b − Λ b mass differences and conclude in particular that the decay ⩞ b → Λ b + τ is certainly allowed. We find 5208 ≲ M B < 5288 MeV, 5285 ≲ M B ∗ < 5365 MeV , 5574 ≲ M Λb < 5654 MeV, 5771 ≲ M ⩞ b < 5851 MeV 52 ≲ M B ∗ − M B ≲ 57 MeV , 187 ≲ M ⩞ b − M Λ b ≲ 207 MeV .