How to probe the spin – dependent gluon distributions †

Two–spin asymmetries A π 0 LL are calculated for various types of spin–dependent gluon distributions. It is concluded that the E581/704 data on A π 0 LL do not necessarily rule out the large gluon polarization but restrict severely the x dependence of its distribution. Moreover, A J/ψ LL are calculated for the forthcoming test of spin–dependent gluon distributions. The advent of so–called " the proton spin crisis " which has emerged from the measurement of g p 1 (x) by the EMC Collaboration, has stimulated a great theoretical and experimental activity in paricle physics [1]. So far various theoretical approaches have been provided to get rid of the crisis [2]. Although some of them are very successful, a lot of problems remain to be solved. One of the remaining problems is on the polarized gluon distributions (δG(x)) in a proton. In this Talk, we are concentrated on several physical processes such as inclusive π 0 – [3], high p T direct photon– [4] and inclusive J/ψ–productions [5] in polarized hadron–polarized hadron reactions, which possess important informations on the polarized gluons. Here we discuss only π 0 – and J/ψ–productions. The interesting physical parameter to be discussed is the two–spin † Talk presented at meeting on " Dynamics of Quarks · Hadrons " (Yukawa Inst.