Next-to-leading order numerical calculations in the Coulomb gauge

Calculations of observables in quantum chromodynamics can be performed using a method in which all of the integrations, including integrations over virtual loop momenta, are performed numerically. We use the flexibility inherent in this method in order to perform next-to-leading order calculations for event shape variables in electron-positron annihilation in the Coulomb gauge. The use of the Coulomb gauge provides the potential to go beyond a purely order ${\alpha }_s^2$ calculation by including, for instance, renormalon or parton showering effects. We expect that the approximations needed to include such effects at all orders in ${\alpha }_s$ will be simplest in a gauge in which unphysically polarized gluons do not propagate over long distances.