We present the first measurements of the forward and midrapidity $η$-meson cross sections from $p$$+$$p$ collisions at $\sqrt{s}=500$ and $510$~GeV, respectively. We also report the midrapidity $η/π^0$ ratio at 510 GeV. The forward cross section is measured differentially in $η$-meson transverse momentum ($p_T$) from 1.0 to 6.5~GeV/$c$ for pseudorapidity $3.0<|η|<3.8$. The midrapidity cross section is measured from 3.5 to 44 GeV/$c$ for pseudorapidity $|η|<0.35$. Both cross sections serve as critical inputs to an updated global analysis of the $η$-meson fragmentation functions.
The invariant differential cross section of $\eta$ mesons at forward rapidity in pp collisions at center-of-mass energy 500 GeV.
The invariant differential cross section of $\eta$ mesons at central rapidity in pp collisions at center-of-mass energy 510 GeV.
The ratio of $\eta$ to $\pi^0$ cross sections at central rapidity in pp collisions at center-of-mass energy 510 GeV.
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