Figure 2.1a shows the
gluon momentum fraction 
from our Monte Carlo studies of
the open charm production by photon-gluon fusion
(see par. 3.1.2 of the COMPASS proposal for a description of
Monte Carlo event generators)
integrated over the quasi-real
photon energy spectrum 
from 35 to 85 GeV.
The input unpolarized gluon distribution is the Duke-Owens set 1.1 and
GeV/c 
.
Other distributions, like the MRSA, give similar spectra.
The distribution is basically a convolution of the unpolarized gluon
distribution with the elementary photon-gluon fusion cross section and the
quasi-real photon spectrum.
In the range of 35-85 GeV this distribution is peaked at
, it starts at 
and
extends over 
, with a good coverage in the 
region.
According to recent parametrizations,
has a maximum in the range of our proposed measurement.
Figure: distribution of gluons in open charm production:
a) 
GeV;
b) dashed line 
GeV, solid line 
GeV.
With increasing , decreases; by splitting
the covered interval in smaller bins (or using a higher beam
energy as mentioned in the proposal)
we cover different regions.
Figure 2.1b shows the distributions for two different
bins of 30-45 GeV and 75-90 GeV, respectively.
It can be seen how the low bin covers the high region
and is peaked at 
while the high bin
covers the low region and is peaked at 
.
By splitting our interval, for instance into 4 bins, the
measurement error on the 
asymmetry for each single bin
will increase roughly by a factor of 2,
each bin having now a 
.
Such an analysis will also allow us to determine approximately
the shape in this range.
It has to be added that the error estimates reported in the proposal were based
on the 
decays only
(with and without 
tagging).
We can expect a considerable improvement on the
measurement including other D decay channels,
giving 
smaller than 4 %,
and hence a better sensitivity on 
.