Results on Elastic Cross Sections in Proton-Proton Collisions at $\sqrt{s}=510$ GeV with the STAR Detector at RHIC

We report results on an elastic cross section measurement in proton-proton collisions at a center-of-mass energy $\sqrt{s}=510$ GeV, obtained with the Roman Pot setup of the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The elastic differential cross section is measured in the four-momentum transfer squared range $0.23\le -t\le 0.67$ GeV${}^2$. We find that a constant slope $B$ does not fit the data in the aforementioned $t$ range, and we obtain a much better fit using a second-order polynomial for $B(t)$. The $t$ dependence of $B$ is determined using six subintervals of $t$ in the STAR measured $t$ range, and is in good agreement with the phenomenological models. The measured elastic differential cross section $\mathrm{d}\sigma \mathrm{/}\mathrm{d}\mathrm{t}$ agrees well with the results obtained at $\sqrt{s}=546$ GeV for proton–antiproton collisions by the UA4 experiment. We also determine that the integrated elastic cross section within the STAR $t$-range is ${\sigma }_{\mathrm{e}\mathrm{l}}^{\mathrm{f}\mathrm{i}\mathrm{d}}=462.1\pm 0.9(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})\pm 1.1(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})\pm 11.6(\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e})$~$\mu \mathrm{b}$.