Bottomonium hyperfine splittings from lattice NRQCD including radiative and relativistic corrections

Abstract

We present a calculation of the hyperfine splittings in bottomonium using lattice Nonrelativistic QCD. The calculation includes spin-dependent relativistic corrections through O(v^6), radiative corrections to the leading spin-magnetic coupling and, for the first time, non-perturbative 4-quark interactions which enter at alpha_s^2 v^3. 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(eta_b,1S)= 60.0(6.4) MeV. We find the ratio of 2S to 1S hyperfine splittings (M(Upsilon,2S) - M(eta_b,2S))/ (M(Upsilon,1S) - M(eta_b,1S)) = 0.445(28).

6 pages, 3 figures. An error was recently found in the coefficients of the 4-quark operators in the lattice NRQCD action that we use here. We have therefore redone this calculation with the corrected coefficients and give the full updated version of the paper here