Poissonian limit of soft gluon multiplicity

It is shown that the gluons produced with small transverse momenta $k_\perp$ inside a jet ($k_\perp <k_\perp^{cut}$, $k_\perp^{cut} \to 0$) are independently emitted from the primary parton, as QCD coherence suppresses their showering. Consequently, the low $k_{\perp}$ gluons follow a Poisson distribution, very much like the soft photons radiated by a charged particle in QED. On the contrary, the distribution of gluons with limited absolute momenta $|\vec{k} | <k^{cut}$ remains non-Poissonian even for small $k^{cut}$. It will be interesting to find out to what extent this perturbative prediction for partons survives the hadronization process.