  Measurement by the STAR experiment at RHIC of the cold nuclear matter (CNM)
effects experienced by inclusive $J/\psi$ at mid-rapidity in 0-100\% $p$+Au
collisions at $\sqrt{s_{_{\mathrm{NN}}}}$ = 200 GeV is presented. Such effects
are quantified utilizing the nuclear modification factor, $R_{p\mathrm{Au}}$,
obtained by taking a ratio of $J/\psi$ yield in $p$+Au collisions to that in
$p$+$p$ collisions scaled by the number of binary nucleon-nucleon collisions.
The differential $J/\psi$ yield in both $p$+$p$ and $p$+Au collisions is
measured through the dimuon decay channel, taking advantage of the trigger
capability provided by the Muon Telescope Detector in the RHIC 2015 run.
Consequently, the $J/\psi$ $R_{p\mathrm{Au}}$ is derived within the transverse
momentum ($p_{\mathrm{T}}$) range of 0 to 10 GeV/$c$. A suppression of
approximately 30% is observed for $p_{\mathrm{T}}<2$ GeV/$c$, while $J/\psi$
$R_{p\mathrm{Au}}$ becomes compatible with unity for $p_{\mathrm{T}}$ greater
than 3 GeV/$c$, indicating the $J/\psi$ yield is minimally affected by the CNM
effects at high $p_{\mathrm{T}}$. Comparison to a similar measurement from
0-20% central Au+Au collisions reveals that the observed strong $J/\psi$
suppression above 3 Gev/$c$ is mostly due to the hot medium effects, providing
strong evidence for the formation of the quark-gluon plasma in these
collisions. Several model calculations show qualitative agreement with the
measured $J/\psi$ $R_{p\mathrm{Au}}$, while their agreement with the $J/\psi$
yields in $p$+$p$ and $p$+Au collisions is worse.
