Measurement of charged pion double spin asymmetries at midrapidity in longitudinally polarized $p$$+$$p$ collisions at $\sqrt{s}=510$ 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 $\sqrt{s}=510$ 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 $\sqrt{s}=200$ GeV, which show a nonzero positive contribution of gluon spin to the proton spin.

The PHENIX experiment at the Relativistic Heavy Ion Collider has measured the longitudinal double spin asymmetries, ALL, for charged pions at midrapidity (|η| < 0.35) in longitudinally polarized p+p collisions at √ s = 510 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 √ s = 200 GeV, which show a nonzero positive contribution of gluon spin to the proton spin.

I. INTRODUCTION
The spin of the proton is known to beh/2, yet its decomposition in terms of its constituents, quarks and gluons, is not very well known. Initially, the fixed-target deep-inelastic scattering (DIS) experiments measured the polarized structure function, g 1 (x, Q 2 ), where x is the parton momentum fraction of the proton and Q 2 is the momentum transfer squared, enabling the reconstruction of the quark spin contributions, ∆Σ(x, Q 2 ), with the help of weak and hyperon decay constants. Early measurements found this contribution to be substantially smaller than expected [1], leading to the so-called spin crisis. In addition to the quark spins, gluon spins as well as the constituents' orbital angular momenta can contribute to the spin sum rule [2]. Because DIS at low to moderate energies essentially couples through the electromagnetic interaction, it is most sensitive to the quark spin contributions and the gluon spin only enters via scaling violations.
In contrast, in polarized p+p collisions, for example at the Relativistic Heavy Ion Collider (RHIC), the dominant hard interaction happens via the strong interaction. Therefore, for midrapidity (|η| < 0.35) hadronic or jet final states with small to intermediate energies, quark-gluon and gluon-gluon interactions are the dominant processes. Consequently, longitudinal-double-spin asymmetries, A LL , are sensitive to the gluon-spin contribution to the proton, ∆g(x, Q 2 ). The RHIC jet [3] and pion asymmetry measurements [4,5] at a centerof-mass energy, √ s, of 200 GeV found the first indication of a nonzero gluon-spin contribution to the nucleon spin when the data was analyzed together with the DIS and semi-inclusive DIS results in a global analysis [6,7]. Subsequently, various measurements at higher collision energy of 510 GeV have confirmed this nonzero gluon * Deceased † PHENIX Spokesperson: akiba@rcf.rhic.bnl.gov polarization [8][9][10] and those combined with results at √ s = 200 GeV [11] have extended the parton momentum fraction x coverage to lower values of approximately 10 −3 .
While the global fits clearly prefer a positive gluon polarization in the probed x range, another direct experimental confirmation would be helpful. The addition of charged pion asymmetries with the help of different fragmentation of up and down quarks [12] into π ± provides this possibility. Because up and down quark polarizations are reasonably well known, the ordering of the positive, neutral and negative pion asymmetries immediately informs about the sign of the gluon spin. A positive gluon spin, coupled with the positive up quark polarization and negative down quark polarization would result in π + asymmetries to be the largest, followed by π 0 and, then, π − . The charge-separated pion asymmetry results at √ s = 200 GeV have already been published [5]. In this paper, we report the charged pion longitudinal double spin asymmetries at √ s = 510 GeV that were extracted by the PHENIX experiment at midrapidity. The paper is organized as follows. In Sec. II, the PHENIX experiment and the detector components relevant for this result are described. In Sec. III, the analysis procedure for extracted charged pions and their double spin asymmetries at midrapidity is discussed. In Sec. IV, the results are presented. Summary is given in Sec. V.

II. EXPERIMENTAL SETUP
In 2013, the PHENIX experiment at RHIC collected data from longitudinally polarized p+p collisions at √ s = 510 GeV with an average polarization of ≈0.55. An integrated luminosity of 108 pb −1 was used for charged pion asymmetry measurements at midrapidity. The PHENIX detector is described in detail in Ref. [13]. Each of two nearly back-to-back arms of the central spectrometer covers a rapidity range |η| < 0.35 and an azimuthal range of ∆φ = π 2 . The PHENIX de-tector elements used in this analysis include the drift chambers (DC), the pad chambers (PC), the ring imag-ingČerenkov (RICH) detector and the electromagnetic calorimeters (EMCal). The RICH, filled with CO 2 gas radiator, is used for charged-pion identification. The EM-Cal comprises two different types of calorimeters. Six sectors are constructed with lead-scintillator (PbSc) towers in sampling configuration with depth of 0.85 interaction lengths. Two sectors are made of lead-glass towers with depth of 1.05 nuclear interaction lengths. The events sampled for this analysis are triggered via energy deposit thresholds in the EMCal and only events in the PbSc are analyzed because of low background fraction from higher energy thresholds of the trigger. Charged particle tracks are reconstructed with the DC and PC tracking system. These detectors also provide the momentum information of the tracks. A match between a projected track onto the EMCal and the location of deposited energy is required to veto charged tracks with mis-reconstructed momenta. The silicon-vertex detector was placed around the beam pipe with layers at nominal radii 2.6, 5.1, 11.8, 16.7 cm with an acceptance of |η| < 1 and ∆φ = 0.8π. The total material budget is 0.13 radiation lengths and the detector was not in operation in 2013. This created a large source of electron background from conversions of direct and decay photons. Additionally, two sets of 64 quartz-crystal radiators attached to photomultipliers located at z positions of ±144 cm and rapidities between 3.1 to 3.9 were used to trigger hard collision events and to select events within ±30 cm of the collision vertex in the asymmetry analysis. These beam-beam-counters and the zero-degree calorimeters were used together to evaluate the luminosities seen by the PHENIX detector. The zero-degree calorimeters comprise three sections of a hadronic calorimeter located at ±18 m from the PHENIX interaction point are also used to monitor the polarization orientation and confirm that the polarization direction of the beams has been rotated to the longitudinal direction.

III. ANALYSIS PROCEDURE
The 2013 configuration was similar to the published results at √ s = 200 GeV [5] in 2009, except that the hadron-blind detector (HBD) was no longer installed. In 2013, the energy threshold of the trigger was increased by a factor of ≈2-3 compared to in 2009 and events were triggered by particles leaving at least 2.2, 3.7, 4.7 or 5.6 GeV energy deposits in the EMCal for the various trigger types. The lower energy threshold triggers were prescaled such that only a fraction of events satisfying the trigger requirements was recorded. An OR of all these triggers was used for the transverse momentum bins in the range 5 GeV/c < p T < 11 GeV/c, where the less prescaled higher threshold triggers are dominant. For the highest transverse momentum bin (11 GeV/c < p T < 15 GeV/c), the 2.2 GeV threshold trigger was not used in order to minimize the background contribution. The trigger efficiency curves as a function of transverse momentum with energy threshold of 3.7 GeV for the PbSc are displayed in Fig. 1 for π ± candidates. High p T charged pions punch through the EMCal with approximately a 50% chance, depositing only a small fraction of their energy corresponding to the minimum-ionizing particles (MIPs) at ≈0.3 GeV due to their low probability of nuclear interactions in the detector. Pre-selection cuts of the energy for π ± are blind to the MIPs interactions and consequently result in higher trigger efficiencies than the case where all types of interactions taken into account. Nonetheless, this analysis does not include MIPs, and the approach properly takes into account the p T dependence of trigger efficiency after applying pre-selection cuts. 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 pre-selection of the π ± sample. The charge difference seen at higher pT originates from the momentum reconstruction which could not be perfectly calibrated in the high rate conditions of the 2013 data taking period.
In addition to the trigger, a matching track in the drift chamber is required to be pointing to the EMCal tower that fired the trigger. The transverse momentum of the particle is determined by the bending of the track in the magnetic field before the DC. In addition, the reconstructed tracks are required to fire more than one photomultiplier byČerenkov light in the RICH. The threshold for pions is around 4.9 GeV and until the kaon threshold of 17.3 GeV is reached the RICH fires only for pions and electrons (muons are not dominant and are already eliminated by the energy cut from the high energy threshold of trigger). To remove electrons as well as accidental track -EMCal cluster coincidences, the ratio between  cluster energy and track momentum (E/p) is required to be larger than 0.2 and smaller than 0.8, taking into account that most pions do not deposit all their energy in the electromagnetic calorimeter in contrast to electrons.
For the further rejection of electron background from the charged pion candidates, the probability of a cluster developed via electromagnetic shower processes (shower shape) determined from fitting the well understood electromagnetic shower shape in the EMCal to the cluster. The shower shape was required to be less than 0.1. The succession of the selection criteria on the raw charged particle spectra can be seen in Fig. 2. A clear bump can be seen once the momentum is large enough for pions to emitČerenkov light. The contribution at momenta below the bump indicates remaining electrons and other accidental coincidences. After applying electron rejection cuts, their contributions are substantially reduced (≈ 0.01-0.085). The remaining background in the higher transverse momentum range is studied with full MC simulations using pythia [14] as event generator and geant3 [15] for the detector description as shown in Fig  3. One can see that at low transverse momenta below 5 GeV/c, the distribution is dominated by electrons, accidental pion coincidences and, to a smaller extent, kaons and protons. At higher transverse momenta, electrons are the dominant, but small compared to pion signals, background until the RICH hit requirement becomes fulfilled by kaons as well. The simulated contributions describe both the signal-dominated region at higher transverse momenta as well as the background-dominated region below 5 GeV/c reasonably well.
The relative size of pion signal and electron back- grounds is then further compared with data by studying the full E/p range including the electron peak at ratios around unity where it is quite prominent. Based on this comparison, as seen in Fig. 4, the nonpion background is found to be below a few percent. A Gaussian function for the electron peak and an Error function for the pion signal are fit to the E/p distribution in each p T bin. The extracted parameter of the Gaussian was used to scale the electron background from the simulation. As the background level was found to be small, the scaling factor was varied by a factor of two in the background corrected asymmetries, variation was assigned as systematic uncertainty and the effect of the scale variation found to be small.
The selected pions are then separated by spin pattern, which determines whether the protons collided with the same or opposite helicities. These asymmetries are normalized for the fluctuations in luminosity from the bunch crossings with the same (++) helicity and opposite (+−) helicity, known as relative luminosity, R = L ++ /L +− (≈1.002): where P Y and P B are the average beam polarizations for the two beams, referred to as Yellow and Blue beam respectively, and N is the number of charged pions from the bunch crossings with the same and opposite helicities. During the 2013 RHIC running period P Y and P B were 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 decayin-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.
0.55 ± 0.02 and 0.56 ± 0.02 for Blue and Yellow beams, respectively [16]. The uncertainty on the asymmetries based on the relative luminosity extraction is δA LL = 3.8×10 −4 , which is shown as uncertainty bands in Figures  5 and 6.
In 2013, nominal beam fills from injection to dump of beams at RHIC lasted eight hours. PHENIX DAQ system collected data in runs within the fill. Because the pre-scale of the trigger as well as the polarization values, which were calculated by the initial polarization and the rate of decrease of polarization as a function of time, changed on a run-by-run basis, the analysis is carried out separately for each run. The asymmetries are calculated for each run and each transverse momentum bin and are fit by a constant over all runs. During the data-taking 16 different spin pattern combinations for the two beams were utilized in order to minimize systematic effects. These several patterns were found to provide consistent asymmetries, based on T-tests between them, and therefore no systematic uncertainty was assigned due to the different patterns.
To test for other potential systematic effects, the asymmetry calculation is repeated many times with randomized spin patterns for each run. The resulting asymmetry distributions for all iterations peak around zero with a Gaussian width given by the statistical uncertainties and the corresponding χ 2 /n.d.f. distributions of the fits center around unity. Other systematic uncertainties include a global scale uncertainty of 6.5% due to the accuracy of the beam polarization determination [16] and the transverse component of the beams, which has been found to be negligible for the double longitudinal spin asymmetries. The momentum scale uncertainty of the hadron transverse momentum has also been taken into account, but given the size of the transverse momentum bins used for the asymmetries, bin migration is minimal. The nonpion background has also been considered based on the background yields evaluated by comparing MC with data. The background asymmetry is estimated based on an electron enhanced data sample, which is found to be consistent with zero. The systematic uncertainty from the background asymmetry is evaluated by varying the background fraction after taking into account the evaluated background asymmetry mentioned above. These systematic uncertainties range from 2 × 10 −5 to 10 −3 .

IV. RESULTS
The resulting final double spin asymmetries are displayed in Fig. 5 as a function of transverse momentum for positive and negative pions and compared to the previously published neutral pions. As can be seen, the results are consistent with the DSSV [6] fit that has considered only the 200 GeV data but not the 510 GeV data. Due to the large statistical uncertainties, the sign of the gluon polarization in the probed x region cannot directly be inferred from the ordering of the asymmetries for the three charges. However, it was found that the present results are consistent with the positive gluon polarization from the global fits. The reason for the comparatively low statistics for charged pions compared to neutral pions is the trigger requirement of having substantial energy deposited in the electromagnetic calorimeter, which happens only for a small fraction of charged pions.
In addition, one can also compare these data to the previously published measurements of charged pions at √ s = 200 GeV. They are complementary because the hadrons detected at the same transverse momenta but at different center-of-mass energies probe different momentum fraction region. Therefore, the exact same measurement at higher collision energy of √ s = 510 GeV probes a lower value of x than what was possible with the previously published data at √ s = 200 GeV. While the experimentally measured transverse momentum contains a convolution of x for both partons and the mo-  mentum fraction z from the fragmentation process, the variable x T = 2p T / √ s can act as a proxy for the x ranges probed. Fig. 6 shows the measurements at 200 and 510 GeV and one can see the substantially lower x T reach. Based on pythia [14] simulations of charged pions in the rapidity range and transverse momentum ranges probed in this publication, mean x values of ≈ 0.04-0.09 can be accessed. Despite the limited statistical precision, this additional information at lower x will improve global fits of the gluon polarization when this data is included. The asymmetries are tabulated in Table I.

V. SUMMARY
In summary, PHENIX has measured the charged pion double spin asymmetries at midrapidity (|η| < 0.35) in longitudinally polarized p+p collisions at √ s = 510 GeV. These measurements are sensitive to the gluon spin contribution to the total spin of the proton in x range ≈ 0.04-0.09. The asymmetries are found to be consistent with global fits that have included only 200 GeV RHIC data, and a nonzero, positive gluon polarization in the x region probed by RHIC has been found. In the proposed sPHENIX experiment [17], the hadronic calorimeter will greatly enhance triggering efficiency for charged hadrons and, therefore, significantly improve the statistical precision for charged pion measurements and make such direct evaluation of the gluon spin contribution possible.