Die Messung der Gluonpolarisation durch die Produktion von Hadronpaaren mit großen Transversalimpulsen in tiefinelastischer Myonstreuung am Nukleon

The spin structure of the nucleon is investigated at the COMPASS experiment at the CERN-SPS using polarized muons scattering off polarized nucleons. The contribution of the quarks to nucleon spin, as measured in the inclusive deep-inelastic scattering, is not sufficient to explain the spin of the nucleon. Thus it has to be clarified how the gluon polarization and the angular momenta of quarks and gluons contribute to the spin of the nucleon. Since the gluon polarization can only be estimated from the $Q^{2}$-dependence of inclusive deep inelastic asymmetries, a direct measurement of the gluon polarization is mandatory. The COMPASS collaboration determines the gluon polarization from cross section asymmetries in photon-gluon fusion processes using open charm production or the production of hadron pairs with large transverse momenta. This thesis presents a measurement of the gluon polarization using the COMPASS data of the years 2003 and 2004. The events with large virtuality, $Q^{2}>1$ $GeV^{2}/c^{2}$ and hadron pairs with large transverse momenta, $p_{\perp}>0.7$ $GeV/c$ have been used in the analysis. The photon-nucleon asymmetry was determined by using a weighted double ratio method of the selected events. The cut on $p_{\perp}>0.7$ $GeV/c$ suppresses leading order processes, so that the obtained asymmetry can be directly linked to the gluon polarization, if the analyzing power and the photon-gluon fusion fraction is known. The measured value is very small and compatible with a vanishing gluon polarization. To avoid false asymmetries, which could be caused by a change of the detector acceptances double ratios were analyzed, where the cross section cancels, and only detector asymmetries remain. It is shown that the COMPASS spectrometer was stable during the time of data taking. For the computation of the analyzing power Monte Carlo events were generated using the LEPTO and the COMGeant software packages. In this context a good MC description of the data is important. For this the JETSET parameters were optimized in order to improve the MC description. A value of rn$\frac{\Delta G}{G}=0.054\pm0.145_{(stat)}\pm0.131_{(sys)}\pm0.04_{(MC)}$ is obtained for the gluon polarization with a momentum fraction of $\langle x_{gluon} \rangle=0.1$ and $\langle Q^{2}\rangle=1.9$ $GeV^{2}/c^{2}$. This result points to a very small gluon polarization and agrees well with the results of other methods, like open charm production and the results, which were obtained at the doubly polarized RHIC Collider at the BNL.