Improving constraints on gluon spin-momentum correlations in transversely polarized protons via midrapidity open-heavy-flavor electrons in $p^{\uparrow }+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$

Polarized proton-proton collisions provide leading-order access to gluons, presenting an opportunity to constrain gluon spin-momentum correlations within transversely polarized protons and enhance our understanding of the three-dimensional structure of the proton. Midrapidity open-heavy-flavor production at $\sqrt{s}=200\mathrm{GeV}$ is dominated by gluon-gluon fusion, providing heightened sensitivity to gluon dynamics relative to other production channels. Transverse single-spin asymmetries of positrons and electrons from heavy-flavor hadron decays are measured at midrapidity using the PHENIX detector at the Relativistic Heavy Ion Collider. These charge-separated measurements are sensitive to gluon correlators that can in principle be related to gluon orbital angular momentum via model calculations. Explicit constraints on gluon correlators are extracted for two separate models, one of which had not been constrained previously.

Figure 1

Fraction of measured electron candidates attributed to each background source ($f_i$), charge combined ($+/-$).

Figure 2

Fractions of measured positron candidates attributed to each background source ($f_i$); results are shown in Table 1 and used as inputs to the background correction procedure, charge ($+$).

Figure 3

Fractions of measured electron candidates attributed to each background source ($f_i)$; results are shown in Table 1 and used as inputs to the background correction procedure, charge ($-$).

Figure 4

$A_N(\mathrm{OHF}\to e^{\pm })$ (red) circles and (blue) squares for positrons and electrons, respectively. Also plotted are predictions of $A_N(D^0/\overline{D^0}\to e^{\pm })$ from Ref. [38], and $A_N((D^0/{\overline{D}}^0+D^{+/-})\to e^{\pm })$ from Ref. [39] for best-fit trigluon-correlator-normalization parameters, with the red/blue solid, dashed, and dotted lines corresponding to central values of the $1\sigma$ confidence intervals shown in the legend.

Figure 5

Results of the statistical analysis performed to extract best-fit parameters ${\lambda }_f$ and ${\lambda }_d$ by comparing data to theory [38]. ${\chi }^2({\lambda }_f,{\lambda }_d)-{\chi }_{\min }^2$ is shown for (a) $e^{+}$ and (b) $e^{-}$. Panel (c) shows the 1, 2, and $3\sigma$ confidence level regions, ${\chi }^2({\lambda }_f,{\lambda }_d)-{\chi }_{\min }^2<n^2$ ($n=1$, 2, 3).