A particle of mass \(m\) moves along the positive radial direction under the influence of a conservative central force. The potential energy of the particle as a function of separation distance \(r\) is given by

\[ U(r) = 4\varepsilon \left[ \left(\dfrac{\sigma}{r}\right)^{12} - \left(\dfrac{\sigma}{r}\right)^6 \right] \]

where \(\varepsilon\) and \(\sigma\) are positive constants. The particle is initially located at its stable equilibrium separation \(r_{\text{eq}}\). In terms of \(\varepsilon\), \(m\), and given constants, what is the minimum initial speed \(v_{\text{esc}}\) that must be given to the particle so that it can escape to an infinitely large separation (\(r \to \infty\))?