Tunneling potentials for the tunneling action: gauge invariance

We formulate a procedure to obtain a gauge-invariant tunneling rate at zero temperature using the recently developed tunneling potential approach. This procedure relies on a consistent power counting in gauge coupling and a derivative expansion. The tunneling potential approach, while numerically more efficient than the standard bounce solution method, inherits the gauge-dependence of the latter when naïvely implemented. Using the Abelian Higgs model, we show how to obtain a tunneling rate whose residual gauge-dependence arises solely from the polynomial approximations adopted in the tunneling potential computation.