  The differential cross section for $Z^{0}$ production, measured as a function
of the boson's transverse momentum ($p_{\mathrm{T}}$), provides important
constraints on the evolution of the transverse momentum dependent parton
distribution functions (TMDs). The transverse single spin asymmetry (TSSA) of
the $Z^{0}$ is sensitive to one of the polarized TMDs, the Sivers function,
which is predicted to have the opposite sign in $p+p$ $\rightarrow W/Z+ X$ from
that which enters in semi-inclusive deep inelastic scattering. In this Letter,
the STAR Collaboration reports the first measurement of the $Z^{0}/\gamma^{*}$
differential cross section as a function of its $p_{\mathrm{T}}$ in $p$$+$$p$
collisions at a center-of-mass energy of 510 GeV, together with the
$Z^{0}/\gamma^{*}$ total cross section. We also report the measurement of
$Z^{0}/\gamma^{*}$ TSSA in transversely polarized $p$$+$$p$ collisions at 510
GeV.
