How the small hyperfine splitting of P-wave mesons evades large loop corrections

The recent discoveries of the bottomonia states h_b(1P) and h_b(2P) confirm the quark model prediction, already verified in the charmonia sector, that the hyperfine splitting of P-wave mesons is very small. The striking agreement is somewhat surprising because the non-relativistic result, for which the splitting is zero, may be modified due to large mass shifts from coupling to open flavour meson pairs. This paper is based on the observation that in most models hyperfine splitting remains small despite what are in many cases large mass shifts. This effect is shown to be a generic feature of models in which the coupling is driven by the creation of a spin-one pair.