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 .