An invertible map between 3D Breit-frame mechanical distributions and 2D infinite-momentum-frame mechanical densities in spin-1 hadrons

Abstract

We construct an invertible map between the complete set of 3D Breit-frame pressure and shear force distributions and the constrained space of 2D infinite-momentum-frame pressure and shear force densities in coordinate space for spin-1 hadrons. The correspondence between the two sets of distributions in different frames is established by combining the geometric forward and inverse Abel transformations with recoil operators after separating the Wigner rotation induced mixing effects on the infinite-momentum-frame side. Unlike in the spin-1/2 case, these mixings complicate the coordinate space relations for spin-1 hadrons by introducing additional multipole structures, but the constraints among the form factors propagate into constraints on mechanical densities, so that these additional multipoles do not introduce new mechanical information.