First measurement of the gluon polarisation in the nucleon using D mesons at COMPASS

The complicated structure of the nucleon has been studied with great success in deep-inelastic lepton-nucleon scattering (DIS) experiments at CERN, SLAC and DESY. As a result the unpolarised structure functions have been measured accurately over a wide kinematic range. From these measurements it is possible to determine the gluon density in the nucleon with good accuracy via a so-called QCD fit. In the case of the spin structure of the nucleon the situation is different. Even after decades of experimental and theoretical efforts it remains to be understood how the spin of the nucleon of 1/2 in units of h-bar is to be accounted for in terms of contributions from the quarks and gluons inside the nucleon. Of particular interest is the question whether the polarised gluon density can explain the unexpected smallness of the quark contribution to the nucleon spin. The QCD fit, which worked well in the unpolarised case, yields a polarised gluon density Delta G which is only badly constrained. This is due to the fact that the information on the polarised structure functions is only available in a rather small kinematic range, since the corresponding measurements are so far exclusively performed by fixed-target experiments. The limited knowledge of the structure functions aggravates the difficulty that the gluon distribution enters only in next-to-leading order and is thus suppressed by the strong coupling constant. A direct measurem ent of Delta G is therefore needed to get a clearer picture. This direct measurement is the major aim of the COMPASS experiment at CERN, where polarised muons are scattered off a polarised fixed target. The process on which this measurement is based is the photon-gluon fusion (PGF). It can result in the production of a charm-anti-charm-quark pair and is then tagged by detecting the charmed mesons in the final state. This approach is used in this thesis and results in a theoretically very clean sample of PGF events, assuming that the intrinsic charm content in the nucleon is negligible. Since the charm tagging of the PGF process is very much statistically limited, it profits directly from improvements of the reconstruction efficiency. A major contribution was made in the course of this work concerning the reconstruction of the momentum of the beam muons. The efficiency of this reconstruction was initially limited by the fact that information from the contributing detectors, installed about 100\,m apart along the beam line, could only be associated by using the time stamp of the corresponding measurements. The main improvement is that now also space information is taken into account, based on the knowledge of the transfer matrix of the beam line. In total the fraction of non-reconstructable events could be decreased from 19% to 6%. The polarised target used in the COMPASS experiment is a large solid-state target which does no t allow the use of dedicated vertex detectors. The identification of the charmed mesons thus has to proceed via the reconstruction of their invariant mass. In order to control the combinatorial background, the reconstruction relies heavily on the RICH detector. This work contributed to the understanding of how this detector and the spectrometer in general can be used best in order to extract the cleanest possible signal of charmed mesons. Especially the tagging of D-star decays results in a very clear signal and thus makes COMPASS the first polarised fixed-target experiment which is able to extract the gluon polarisation via the open charm approach. The analysing power needed for the extraction is given by the ratio of spin dependent and spin averaged muon-nucleon cross sections, which have been calculated to first order in the strong coupling constant. These cross sections cannot be computed exactly in the analysis, since they depend on parton kinematics, which are poorly known due to the fact that typically only one of the two charmed mesons produced in the PGF process is detected. Thus a parametrisation based on Monte Carlo simulations was prepared, which maps the parton kinematics onto measurable quantities. This makes the analysing power available on an event-by-event basis with sufficient accuracy and thus allows a statistically optimal analysis. The final result for the gluon polarisation is extracted at a mean momentu m fraction carried by the gluon of eta=0.15 and at a scale mu^2=13(GeV/c)^2 and was found to be Delta G / G =-0.31+/-0.44(stat.)+/-0.07(syst.). The systematic error is mostly due to the uncertainty on the mass of the charm quark, possible false asymmetries and the background contribution to the asymmetry. This result for Delta G/G is consistent with parametrisations obtained from QCD fits to polarised DIS data.