Spin alignment of the high pT vector mesons in polarized pp collisions at high energies

Using the same method as that used in e+e- annihilation and lepton-nucleon deep inelastic scattering, we calculate the spin alignment of vector mesons with high transverse momenta in high energy pp collisions with one longitudinally polarized beam. We present the results obtained at BNL RHIC energies. We also study the spin alignment of such vector mesons in the case of a transversely polarized proton beam and present its relation to the transversity distribution in the nucleon. Numerical results obtained using simple models for the transversity distributions are also given. These results show that significant spin alignment exists in both cases and can be measured in experiments such as those at the RHIC