Energy Independence of the Collins Asymmetry in $p^{\uparrow }p$ Collisions

The STAR experiment reports new, high-precision measurements of the transverse single-spin asymmetries for ${\pi }^{\pm }$ within jets, namely the Collins asymmetries, from transversely polarized $p^{\uparrow }p$ collisions at $\sqrt{s}$ = 510 GeV. The energy-scaled distribution of jet transverse momentum, $x_{\mathrm{T}}=2p_{\mathrm{T},\mathrm{j}\mathrm{e}\mathrm{t}}\mathrm{/}\sqrt{s}$, shows a remarkable consistency for Collins asymmetries of ${\pi }^{\pm }$ in jets between $\sqrt{s}$ = 200 GeV and 510 GeV. This indicates that the Collins asymmetries are nearly energy independent with, at most, a very weak scale dependence in $p^{\uparrow }p$ collisions. These results extend to high-momentum scales ($Q^2\le 3400$ GeV${}^2$) and enable unique tests of evolution and universality in the transverse-momentum-dependent formalism, thus providing important constraints for the Collins fragmentation functions.