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The analytical perturbative approach allows one to predict the
limit of
the one-particle invariant density in QCD jets 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 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.
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