Measurement of charged pion double spin asymmetries at midrapidity in longitudinally polarized $p+p$ collisions at $\sqrt{s}=510\mathrm{GeV}$

The PHENIX experiment at the Relativistic Heavy Ion Collider has measured the longitudinal double spin asymmetries, $A_{LL}$, for charged pions at midrapidity ($|\eta |<0.35$) in longitudinally polarized $p+p$ collisions at $\sqrt{s}=510\mathrm{GeV}$. These measurements are sensitive to the gluon spin contribution to the total spin of the proton in the parton momentum fraction $x$ range between 0.04 and 0.09. One can infer the sign of the gluon polarization from the ordering of pion asymmetries with charge alone. The asymmetries are found to be consistent with global quantum-chromodynamics fits of deep-inelastic scattering and data at $\sqrt{s}=200\mathrm{GeV}$, which show a nonzero positive contribution of gluon spin to the proton spin.

Figure 1

Trigger efficiency curves of the EMCal-RICH trigger for positively charged (open [blue] squares) and negatively charged (closed [red] circles) pion candidates in the PbSc as a function of the transverse momentum of the track. The energy threshold of the trigger was at 3.7 GeV. Note that a cut on the ratio between cluster energy to reconstructed momentum ($E/p$) was applied in preselection of the ${\pi }^{\pm }$ sample. The charge difference seen at higher $p_T$ originates from the momentum reconstruction which could not be perfectly calibrated in the high rate conditions of the 2013 data taking period.

Figure 2

Pion candidate transverse momentum distributions after successively applying raw track criteria (closed [black] circles), RICH hit requirement (closed [red] squares) and electron rejection via $E/p$, matching and shower shape (closed [blue] triangles).

Figure 3

Comparison of reconstructed particle momentum distributions as a function of the transverse momentum in the data and MC simulations. The pion candidates of the data (closed [black] circles) are corrected for the trigger efficiency. The pion (closed [blue] triangles), electron (closed [green] squares), kaon (closed [yellow] inverted triangles), proton (closed [purple] crosses), and all (histogram [red] lines) contributions of the MC simulation are scaled by the luminosity for apple-to-apple comparison.

Figure 4

Energy over momentum ratio for pion candidates in bins of transverse momentum. Reconstructed data (closed [black] circles) are compared to luminosity scaled MC contributions by pions (closed [blue] triangles) and electrons (closed [green] squares) as well as their sum (histogram [red] lines). Due to the minimum energy requirement in the trigger, the data drops at very low values to zero. Note that there are huge tails from true electrons in lower $E/p$ regions. This is because electrons from photon conversion and/or decay in flight are reconstructed with higher transverse momentum and then the measured $E/p$ are lowered. These off-vertex electron backgrounds are eliminated using the $E/p$ cuts.

Figure 5

Double-spin asymmetries $A_{LL}$ as a function of transverse momentum for positive (closed [blue] squares) and negative pions (closed [red] circles), as well as the previously published [7] neutral pions (open [black] squares). The statistical uncertainties of asymmetries and the point-to-point systematic uncertainties from background are represented by the continuous lines and the gray bands, respectively. The expected asymmetries based on the DSSV [5] fit (only from the 200 GeV data but none of the 510 GeV data) are displayed in the indicated line types. The uncertainty bands on the fits are not shown as they affect all charges in similar ways.

Figure 6

Double spin asymmetries $A_{LL}$ as a function of $x_T=2p_T/\sqrt{s}$ for positive (closed [blue] squares) and negative pions (closed [red] circles) at $\sqrt{s}=510\mathrm{GeV}$ as well as charged pions at 200 GeV (closed [purple] triangles and closed [black] inverted triangles). The data shown here are tabulated in Table 1.