  We present measurements of the differential cross sections of inclusive
$J/\psi$ meson production as a function of transverse momentum
($p_{T}^{J/\psi}$) using the $\mu^{+}\mu^{-}$ and $e^{+}e^{-}$ decay channels
in proton+proton collisions at center-of-mass energies of 510 and 500 GeV,
respectively, recorded by the STAR detector at the Relativistic Heavy Ion
Collider. The measurement from the $\mu^{+}\mu^{-}$ channel is for 0 $<
p_{T}^{J/\psi} <$ 9 GeV/$c$ and rapidity range $|y^{J/\psi}| < $ 0.4, and that
from the $e^{+}e^{-}$ channel is for 4 $< p_{T}^{J/\psi} <$ 20 GeV/$c$ and
$|y^{J/\psi}| < $ 1.0. The $\psi(2S)$ to $J/\psi$ ratio is also measured for 4
$< p_{T}^{\rm meson} <$ 12 GeV/$c$ through the $e^{+}e^{-}$ decay channel.
Model calculations, which incorporate different approaches toward the $J/\psi$
production mechanism, are compared with experimental results and show
reasonable agreement within uncertainties.

High Energy Physics - Experiment;Nuclear Experiment