Bottomonium hyperfine splittings from lattice NRQCD including radiative and relativistic corrections

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We present a calculation of the hyperfine splittings in bottomonium using lattice Nonrelativistic QCD. The calculation includes spin-dependent relativistic corrections through O(v⁶), radiative corrections to the leading spin-magnetic coupling and, for the first time, non-perturbative 4-quark interactions which enter at alphaₛ² v³. We also include the effect of u,d,s and c quark vacuum polarisation. Our result for the 1S hyperfine splitting is M(Upsilon,1S) - M(etab,1S)= 60.0(6.4) MeV. We find the ratio of 2S to 1S hyperfine splittings (M(Upsilon,2S) - M(etab,2S))/ (M(Upsilon,1S) - M(etab,1S)) = 0.445(28).