Helicity Density Matrix Formalism and Polarized Processes in QCD

In this thesis, we shall first present helicity density matrix formalism to deal with the polarized processes in quantum chromodynamics(QCD), in which the calculations of the desired cross sections (or asymmetries in many cases) are simplified to take traces of products of helicity density matrices in the underlying particles' (partons, hadrons, etc.) helicity spaces. The parton distribution and fragmentation functions turn out to be the helicity density matrix elements which survive the QCD symmetries. The main advantages of this formalism are that it has very clear physical pictures, simplifies the calculation, and, most importantly, can be easily used to deal with interference effects between different partial waves in multiparticle production in semi-inclusive processes. Then this formalism will be used to propose new ways to measure nucleon's transversity, the least known quark distribution function inside the nucleon at leading twist (twist-two). The processes of interest are the two pion semi-inclusive productions in the transversely polarized deep inelastic scattering (only the target is polarized) and nucleon nucleon collisions (only one beam is polarized). A set of novel quark interference fragmentation functions are introduced in the framework of the helicity density matrix formalism and are used to probe the nucleon's transversity distribution function. The advantages of this method are that the effect is leading twist, meson pairs are abundantly produced in quark fragmentation, and the essential final state interaction phase is well studied. Thesis Supervisor: Robert L. Jaffe Title: Professor Dedicated to My Family for Their Love and Supports