Together with the singularities, the integration over the phase space of
particle 5 produces in particular the appearence of ln(p_{Tm}) and

ln^{2}(p_{Tm}) terms in Part I, as well as
ln(p_{Tm}) ln(R_{th}) and ln(R_{th}) terms in
Parts II a and II b,

plus terms which vanish as p_{Tm} --> 0.
These logarithmic terms are extracted analytically.

Furthermore, the subtraction method used in C_{3} and C_{4}
allows to keep the full R_{th} dependence, in particular the terms

O(R_{th}^{2n}) ln(p_{Tm})) to all orders n in
R_{th} in C_{3} and C_{4}.

On the other hand, terms vanishing with
p_{Tm}, of order O(p_{Tm} ln(p_{Tm})) or smaller, are
dropped.

Besides, when the inelastic configurations generated on Part II c are
projected onto any inclusive observable, dependences of the corresponding

contribution on p_{Tm} and R_{th} are numerically generated.

The default choice for p_{Tm} in the input file
is 0.05 p_{Tinf}, p_{Tinf} being the lowest of the
p_{T} of the two hard particles produced.

The parameters p_{Tm} and R_{th} are unphysical, i.e. they need
not be matched to any definition of any observable. On the contrary, the result
for any observable has to be independent of the actual choice made for the
unphysical parameters R_{th} and p_{Tm} when all contributions
from 2 --> 2, quasi 2 --> 2, and inelastic (genuine 2 --> 3) are added,
although each of them separately does have a strong dependence. The
cancellation of the R_{th} dependence is exact as a matter of principle
of the subtraction method; yet it proceeds through numerical compensations. The
dependence on p_{Tm} of the sum is very small at least when small
enough values are used. The user should check these
cancellations in her or his calculations, separately for each of the three
mechanisms.

Typically for example, for **DIPHOX**, in the Tevatron and LHC energy
ranges, with p_{Tinf} of the order of a couple of tens of GeV,
when p_{Tm} is varied from 0.01 to 0.5 GeV,
the NLO contributions to "one-" and "two fragmentation" vary by less than
1% and 5% respectively (the precise calculation of the "two fragmentation"
contribution takes a lot of time. In this case the 5% accuracy indicated here
actually
reflects essentially statistical uncertainties, rather than a slow convergence
as p_{Tm} is reduced. A better test of stability
would be obtained at the expense of a more extensive computation). Similarly,
the q qbar and gg initiated processes contributing to the
"two direct" mechanism at NLO vary by less than a few percent when considered
separately.

An explicit example of these cancellations is given in the appendix B
of Eur. Phys. J. C16, 311 (2000)
[hep-ph/9911340]