for the decay and finite lifetime of the string. $A$ is a measure of the space-time area covered by the string before the breakup, and $b$ is a constant. Conventionally the area $A$ is scaled by the square of the string tension $\kappa$: $$A\equiv\mathcal{A}\, \kappa^2,
\label{eq:stringarea}$$ where $\mathcal{A}$ is the area in space and time. Consequently the dimension of $b$ is $(energy)^{-2}$.

The result in [eq. (\[eq:Lund\])]{} can be generated in a Monte Carlo simulation by producing the mesons in an iterative way starting from one of the string ends, where each meson takes a fraction $z$ of the remaining energy. In each step the relevant $z$-value is given by the probability distribution or splitting function: $$f(z)=N\frac{(1-z)^a}{z}e^{-b m^2/z}.
\label{eq:split}$$ Here the constant $a$ is related to $N$ and $b$ through the normalization constraint $\int f(z)\ dz = 1$. The production points for the pairs will be located around a hyperbola in space-time, with a typical proper time determined by $$\langle \tau^2\rangle = \frac{1+a}{b\,\kappa^2}.
\label{eq:averagetau}$$ This timescale is also related to the particle multiplicity via the relation $$d\,N/d\,y \sim \sqrt{\langle \tau^2\rangle}\,\kappa/m = \sqrt{\frac{1+a}{b\,m^2}}.
\label{eq:particledensity}$$ We note that absorbing the string tension in the definition of $b$, via the scaling in [eq. 