$e^+e^-$ pairs with a rate per unit time and unit volume given by: $$\mathcal{P} \propto (e\,\mathcal{E})^2 \exp\left(-\,
  \frac{\pi\,\mu^2}{e\,\mathcal{E}}\right). 
\label{eq:schwinger}$$ Here $\mu$ is the electron mass and $\mathcal{E}$ the electric field strength. Thus $e\mathcal{E}$ is the force acting on the produced electron or positron. As pointed out in ref. [@Brezin:1970xf], this result can be interpreted as the effect of a tunneling process. Classically the electron and the positron cannot be produced in a point, but only separated by a distance $2\mu/e\mathcal{E}$, such that the reduction in the electric field energy can be transferred into the mass of the pair. In quantum theory the particles are produced locally by an interaction Lagrangian $\sim e \bar{\psi}(x)
\gamma_\mu \psi(x) A_\mu(x)$, and have to tunnel through the classically forbidden region, where the wavefunctions can be estimated by the WKB method.

When generalizing this result to $q\bar{q}$ pair production [@Casher:1978wy; @Andersson:1980vj; @Gurvich:1979nq; @Glendenning:1983qq] in a linear confined colour field, the tunneling mechanism implies that $e\mathcal{E}$ has to be replaced by the force acting on a quark,  by the string tension[^4] $\kappa\sim
1$ GeV/fm. For the production of a pair with opposite transverse momenta $p_\perp$ in this process, the mass $\mu$ in [eq. (\[eq:schwinger\])]{} will be replaced 