Limiting behaviour at low momenta

The analytical perturbative approach allows one to predict the limit of the one-particle invariant density in QCD jets $E dn/{d^3p}\equiv dn/dy\,d^2p_T$ at very small momenta p or, equivalently, in the limit of vanishing rapidity and transverse momentum [17]. If the dual description of hadronic and partonic states is adequate down to very small momenta, a finite, energy-independent limit of the invariant hadronic density, I₀, is expected. This is a direct consequence of the colour coherence in soft gluon branching. A possible rise of I₀ with centre-of-mass energy would indicate that either coherence or the local duality (or both) break down. Since colour coherence is a general property of QCD as a gauge theory, it is the LPHD concept that is tested in measurements of the soft hadrons.

The e⁺e^- annihilation data on charged and identified particle inclusive spectra have been found to follow the MLLA prediction surprisingly well, also at low centre-of-mass energies. The invariant spectra at low momentum scale approximately (within 10%) between 1.6 and 140 GeV and agree with perturbative calculations which become very sensitive to the strong running of $\alpha_S$ at small scales [18].

At this workshop, H1 presented the first Breit frame measurements of the invariant energy spectra in DIS as a function of Q, (see Fig. 3 in [14]). For sufficiently high Q, the data show that the low-momentum limit in that region of phase space is essentially independent of Q and indeed similar to that in e⁺e^- annihilation.