Recently conjectured three- (and more-) body mass inequalities are investigated for the quark models of baryons in which it is assumed that baryon masses are the ground-state energies of Schrödinger-type operators with pair potentials V. It is proved that these inequalities hold (even with a “relativistic” form for the kinetic energy) if V belongs to a certain class (which includes many potentials commonly used), but that they do not hold for all V (even in the nonrelativistic case). One example of our results is 2M(cqs)≥ M(cqq) + M(css).
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- 13.R. Askey, in Harmonic Analysis on Homogeneous Spaces: Proceedings of the Symposia in Pure Mathematics, Vol. 26 (American Mathematics Society, Providence, 1973), pp. 335–338. In this paper Askey proves the sufficiency of (9) if a conjecture about Bessel functions holds. This he proves for d odd in R. Askey, Trans. Am. Math. Soc. 179, 71 (1973). The even-d case was proved in J. Fields and M. Ismail, J. Math. Anal. 6, 551 (1975).CrossRefGoogle Scholar