collisions[^7].

The tunneling probability in [eq. (\[eq:schwinger2\])]{} will also give somewhat increased transverse momenta, but as the tunneling effect is a minor contribution to the $p_\perp$-distribution, this effect is rather small. A detailed description of the above modifications is presented in [appendix [\[sec:deta-descr-rope\]]{}]{}.

### Effects on multiplicity {#sec:eff-on-mult}

One could assume, that the factor $\kappa^2$ in the production rate in [eq. (\[eq:schwinger\])]{} should imply a change in the $b$-parameter in [eqs. (\[eq:Lund\])]{} and [(\[eq:split\])]{}, and thus significantly modify hadron multiplicities. The quantity $\mathcal{P}$ in [eq. (\[eq:schwinger\])]{} is the probability per unit volume and unit time. In a one-dimensional string, it should be interpreted as probability per unit length and unit time. Therefore the space-time distance between break-up points is expected to be proportional to $1/\kappa$. At the same time the “yo-yo” states representing mesons have extension and oscillation times proportional to $1/\kappa$. Thus the earlier production time is compensated by the smaller string length needed to form a meson. This is taken into account via the scaling factor $\kappa^2$ in [eq. (\[eq:stringarea\])]{}, with the effect that $b$ is essentially unchanged. (For $u$ and $d$ quarks, with masses of the order 10 MeV, and a single string with tension $\kappa
\approx\, 