Deep inelastic vortex scattering: A third outcome for head-on collisions

Results are presented from numerical simulations of the flat-space nonlinear Maxwell-Klein-Gordon equations demonstrating deep inelastic scattering of $m=1$ vortices for a range of Ginzburg-Landau (or Abelian-Higgs) parameters ($\kappa$), impact parameters ($b$), and initial velocities ($v_0$). The threshold ($v_0^*$) of right-angle scattering is explored for head-on ($b=0$) collisions by varying $v_0$. Solutions obey time-scaling laws, $T\propto \alpha\ln(v_0-v_0^*)$, with $\kappa$-dependent scaling exponents, $\alpha$, and have $v_0^*$ that appear not to have the previously reported upper bound. The arbitrarily long-lived static intermediate attractor at criticality ($v_0=v_0^*$) is observed to be the $\kappa$-specific $m=2$ vortex solution. Scattering angles are observed for off-axis ($b\neq 0$) collisions for a wide range of $b$, $v_0$, and $\kappa$. It is shown that for arbitrarily small impact parameters ($b\rightarrow 0$), the unstable %but arbitrarily long-lived $\kappa$-dependent $m=2$ "critical" vortex is an intermediate attractor and decays with a $\kappa$-\emph{independent} scattering angle of $135^{\circ}$, as opposed to either of the well-known values of $180^{\circ}$ or $90^{\circ}$ for $b=0$.