Hadron-pair production on transversely polarized targets in semi-inclusive deep inelastic scattering

Nucleons such as protons and neutrons are composite objects made of quarks, which are bound together by the strong force via the exchange of gluons. The probability of finding a quark of flavor q carrying the momentum fraction x of the fast moving parent nucleon is described by a parton distribution function (PDF) f q 1 ( x ) , the number density. The spin, an intrinsic angular momentum of elementary particles such as quarks but also of composite objects like nucleons, couples with magnetic fields, which allows one to align it. Taking into account this additional parameter, the spin, the scheme of PDFs in leading twist is expanded by the helicity distribution g q 1 ( x ) and the transversity distribution h q 1 ( x ) . The first distribution covers the case where the nucleon and the quark are longitudinally polarized, while a transverse polarization is taken into account by the latter. A tool for the investigation of the PDFs is inclusive deep inelastic scattering (DIS) of electro- magnetic probes off (un)polarized nucleons at fixed-target experiments. This only gives access to f q 1 ( x ) and g q 1 ( x ) , while the chiral-odd nature of the transversity distribution prevents a measurement without detecting the final hadronic states. However, h q 1 ( x ) can be observed in semi-inclusive DIS (SIDIS) in combination with another chiral-odd function like the dihadron fragmentation function H ^ q 1 in the production of a hadron-pair. The resulting experimental challenge is the reason why f q 1 ( x ) and g q 1 ( x ) have been investigated for almost four decades, while h q 1 ( x ) is still subject to recent measurements and analyses. The 160 GeV =c polarized muon beam of CERN's M2 beamline allows the COMPASS ex- periment to investigate spin effects using polarized solid-state targets. Since the year 2002 COMPASS has collected unique data sets on transversely polarized targets of lithium deuteride and ammonia, serving as deuteron and proton targets, respectively. The work of this thesis started with the analysis of asymmetries of h + h