Transverse phase space and its multipole decomposition

Relativistic phase space distributions are very interesting objects as they allow one to gather the information extracted from various types of experiments into a single coherent picture. Focusing on the four-dimensional transverse phase space, we identified all the possible angular correlations providing at the same time a clear physical interpretation of all the leading-twist generalized and transverse-momentum dependent parton distributions. We also developed a convenient representation of this four-dimensional space.