A Phase Transition in U(1) Configuration Space: Vortex Annihilation and Oscillons

We show numerically that the low-momentum scattering of a vortex-antivortex pair leads to an oscillon for low scalar to vector mass ratios in the 2d Abelian Higgs model. The spherically symmetric oscillon lives $2-4$ orders of magnitude longer than the fundamental time scales and has an associated dipole gauge field strength and charge density. The annihilation also leaves a characteristic topological signature in the Chern-Simons density $n_{cs}$, and Higgs winding density $n_w$. The emergence of oscillons as remnants of the vortex-antivortex annihilation can be mapped onto a phase transition with control parameter given by $\beta=\frac{m^2_{scalar}}{m^2_{vector}}$ and critical value $\beta_c=0.073$.