Spin in Strong Interactions

Abstract

In this chapter, the basic theoretical relations underlying the design and analysis of polarization experiments involving strong interactions are reported on classical examples of pion–nucleon and nucleon–nucleon scattering. After the introduction of the density matrix and reaction matrix, we discuss such notions as the complete set of experiments and the equality of the polarization $\vec{P}$ in the direct reaction and the asymmetry $\vec{A}$ in the inverse reaction on the example of the simple pion–nucleon system. On the example of the nucleon–nucleon system, we present the method for explicitly constructing the reaction matrix, formulate the unitarity condition, and point to the possibilities of seeking the effects of parity and time reversal violation. The presentation is primarily based on the technique of nonrelativistic quantum mechanics. Relativistic pion–nucleon and nucleon–nucleon elastic scattering matrices are discussed in the concluding sections. The inclusion of the relativistic effects insignificantly changes the nonrelativistic results.