The invariant mass resolution for the decay in the
muon program is mainly affected by the multiple scattering in the target
region (the total thickness of the target itself is 60 g/cm ).
Table 3.14 summarizes the main contributions to multiple scattering
of the K and the in the proposed apparatus.
As stated in the proposal, multiple scattering alone gives a contribution
of almost 10 MeV/c , essentially independent of the D energy,
to the invariant mass resolution.
The requirements on the tracker system are the following:
Table 3.14: Material encountered by outgoing hadrons (average values).
As explained in section 5.2.5 of the proposal, a simplified layout was used to investigate the invariant mass resolution for the decay. Also, to avoid complications with tracking in the magnetic field, the fields of the two spectrometer magnets were taken as box fields, and all the chambers were placed outside the field regions. More specifically:
It is apparent therefore, that the present simulations provide only upper limits to the obtainable resolution and that the use of a complete reconstruction program will result in a mass resolution better than the values we presently quote.
In Table 3.15 we give overall values for the invariant mass resolution for D's entering the geometrical acceptance of the apparatus. Several situations are considered :
(a) multiple scattering errors + location errors
(b) multiple scattering errors only
(c) location errors only
(d) location errors + a systematic shift of 100 microns in both horizontal and vertical coordinate of every tracker, while the direction of the shift is given randomly at the initialisation of the program.
Table 3.15: Resolution of the reconstructed mass for conditions (a) - (d), explained in the text, and different energies of the D meson.
We can conclude that the proposed layout meets the stated requirements and an alignment accuracy of 100 microns, well within reach and already obtained with trackers of similar dimensions at SMC, is sufficient.