
doi: 10.1007/bf01566927
Mass splittings of mesons withL≧1 are discussed on the basis of a general spin-dependent potential consisting of a vector (V(r)) and a scalar (S(r)) part. For arbitraryV(r) andS(r), the four masses, for the three3 L J and the one1 L J=L levels, are given in terms of only three unknown expectation values 〈(1/r)(dV/dr)〉, 〈d 2 V/dr 2〉 and 〈(1/r)(dS/dr)〉. These expectations values are extracted for theP-wave $$u\bar s$$ (or $$d\bar s$$ ) mesons which are discussed in detail. It is argued that the 0++ mass should be around 1150 to 1230 MeV, rather than at 1350 MeV. On comparing the expectation values for the $$u\bar s$$ , $$c\bar c$$ , $$b\bar b$$ and the $$I = 1u\bar u$$ systems, we find that they all scale asa+bμ, wherea andb are constants and μ is the reduced mass. Remarkably enough, we also find that theP-wave meson masses for these systems satisfy mass formulae of the formA+B(m1+m2), with constantA andB. It is shown that similar linear mass formulae also work forS-wave mesons. These facts seem to reveal a rather general property of $$q\bar q$$ states.
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