We obtain analytic expressions for the third-order corrections due to the strong interaction Coulomb potential to the S-wave Green function, energy levels and wave functions at the origin for arbitrary principal quantum number n. Together with the known non-Coulomb correction this results in the complete spectrum of S-states up to order α 5 s . The numerical impact of these corrections on the Upsilon spectrum and the top quark pair production cross section near threshold is estimated.

Results are reported from the HERMES experiment at HERA on a measurement of the neutron spin structure function ~(x, Q2) in deep inelastic scattering using 27.5 GeV longitudinally polarized positrons incident on a polarized 3He internal gas target. The data cover the kinematic range 0.023 < x < 0.6 and 1 (GeV/c) 2 < Q2 < 15 (GeV/c) 2. The integral fo~i0623 ~(x) dx evaluated at a fixed Qz of 2.5 (GeV/c) 2 is-0.0344-0.013(stat.)+0.005(syst.). Assuming Regge behavior at low x, the first moment F'~ = fl ~(x)dx is-0.037 ± 0.013(stat.)±0.005(syst.)±0.006(extrapol.

We compute the third-order correction to the S-wave quarkonium wave functions |ψ n (0)| 2 at the origin from non-Coulomb potentials in the effective non-relativistic Lagrangian. Together with previous results on the Coulomb correction and the ultrasoft correction computed in a companion paper, this completes the thirdorder calculation up to a few unknown matching coefficients. Numerical estimates of the new correction for bottomonium and toponium are given.

We present new results on the NNNLO top-antitop production cross section near threshold from potential and ultrasoft gluon corrections. The new non-logarithmic third-order terms are in the 10% range and lead to a significant reduction in the theoretical error.

14 The names of the seventh and eighth quarks are from Greek seven (hepta) and eight (okto). The fourth lepton / has been named to balance two Greek letters M, T with Roman e ,f'. 15 To obtain the desired pattern of the symmetry breaking, one needs a cubic term in the potential. See Li, Ref. 8. 16 M. S. Chanowitz, J. Ellis, and M. K. Gaillard, Nucl. Phys. B128, 506 (1977); H. Georgi and D. V. Nanopoulos, Nucl. Phys. B155, 52 (1979).