Abstract
Heavy-quarkonium states such as the $J/\ensuremath{\psi}$ meson can be approximately treated as a nonrelativistic system. This paper presents the first relativistic corrections to the $J/\ensuremath{\psi}$ polarization in photoproduction and hadroproduction processes. The corrections were found to be appreciable, which might shed light on the $J/\ensuremath{\psi}$ polarization puzzle.
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