Spin alignment of the high p_T 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 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 there exist significant spin alignment in both cases, and they can be measured in experiments such as those at RHIC.