Abstract :
I consider the quantity δ(m1m2m3) ≡ Mq1q2q3 − (Mq1q2 + Mq2q3 + Mq1q3)2, where the Mʹs represent the ground state spin-averaged hadron masses with the indicated quark content and the mʹs the corresponding constituent quark masses. I assume a logarithmic interquark potential, the validity of a nonrelativistic approach, and various standard potential model inputs. Simple scaling arguments then imply that the quantity R(x) ≡ δ(mmm3)δ(m0m0m0) depends only on the ratio x = mm3, and is independent of m0 as well as any parameters appearing in the potential. A simple and accurate analytic determination of δ(mmm3), and hence R(x), is given using the 1D expansion where D is the number of spatial dimensions. When applicable, this estimate of R(x) compares very well to experiment — even for hadrons containing light quarks. A prediction of the above result which is likely to be tested in the near future is MΣb∗2+(MΛb + MΣb)4 = 5774±4 MeV/c2.
