Transverse-single-spin asymmetries of charged pions at midrapidity in transversely polarized $p{+}p$ collisions at $\sqrt{s}=200$ GeV

In 2015, the PHENIX collaboration has measured single-spin asymmetries for charged pions in transversely polarized proton-proton collisions at the center of mass energy of $\sqrt{s}=200$ GeV. The pions were detected at central rapidities of $|\eta|<0.35$. The single-spin asymmetries are consistent with zero for each charge individually, as well as consistent with the previously published neutral-pion asymmetries in the same rapidity range. However, they show a slight indication of charge-dependent differences which may suggest a flavor dependence in the underlying mechanisms that create these asymmetries.

In 2015, the PHENIX collaboration has measured single-spin asymmetries for charged pions in transversely polarized p+p collisions at the center of mass energy of √ s = 200 GeV. The pions were detected at central rapidities of |η| < 0.35. The single-spin asymmetries are consistent with zero for each charge individually, as well as consistent with the previously published neutral-pion asymmetries in the same rapidity range. However, they show a slight indication of charge-dependent differences which may suggest a flavor dependence in the underlying mechanisms that create these asymmetries.

I. INTRODUCTION
Single-spin asymmetries have been measured in hadronic collisions over a wide range of energies for a number of final state particles [1][2][3][4] and at various rapidity regions. Initially, calculations that were based entirely on perturbative quantum chromodynamics (pQCD) expected such asymmetries to be suppressed as they generally required a helicity-flip which would be proportional to the parton mass over the hard scale of the scattering process [5], though recent calculations suggest that perturbative contributions may be possible [6]. In contrast to the pQCD calculations, the measured single-spin asymmetries, A N for pion production in the forward direction were found to be quite sizeable [1][2][3].
Initially, two different mechanisms were suggested to describe these asymmetries that attribute the effect to the nonperturbative parts of either the parton distribution functions [7] or the fragmentation functions [8].
To do so, the traditional concept of parton distribution and fragmentation functions had to be extended to allow for explicit-transverse-momentum degrees of freedom. In the transverse-momentum-dependent (TMD) framework, it is however necessary that at least two scales are observed, the large scattering scale and a smaller scale related to the intrinsic transverse momenta of parton distribution and fragmentation. Both can be observed in semi-inclusive deeply inelastic scattering (SIDIS), as was first successfully demonstrated in [9] for both suggested effects.
Single-hadron final-state measurements in hadronic collisions have only one scale, typically given by the transverse momentum of the detected hadron. As such, a collinear framework that only relies on a single hard scale was suggested to describe these asymmetries [10,11]. In this framework, nonzero asymmetries require nonperturbative higher-twist correlations either in the initial state or the final state [12,13]. Subsequently, it was suggested that some of these correlation functions can be related to transverse-momentum moments of the TMD functions [14], which unifies both approaches. Thus, global fits of asymmetry measurements from SIDIS and hadron collisions have become possible and provide additional precision on the underlying functions of interest such as the quark transversity [15] or the Sivers [7] function in the * PHENIX Spokesperson: akiba@rcf.rhic.bnl.gov † Deceased proton. The latest of these comes from [16], in which are found sizeable contributions from both initial and final state effects. However, the final-state effects dominate in hadronic collisions where the measured asymmetries are large.
Pion transverse-single-spin asymmetries pick up both initial-and final-state effects. While at forward rapidities, the asymmetries are quite sizeable in the energy range of the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory [2,3], neutral-pion and η mesons have been shown to have vanishing asymmetries at central rapidities where the valence effects are expected to be less pronounced [17]. In addition, in neutralparticle asymmetries, potential cancellations between different parton flavors could also cause these asymmetries to vanish. Charged pion asymmetries provide different flavor sensitivity via the fragmentation functions and could test whether such cancellations happen, as the dominant hard process at the transverse momenta of this measurement is given by quark-gluon scattering. The PHENIX detector at RHIC has measured charged pion single-spin asymmetries at central rapidities in transversely polarized p+p collisions at a center-of-mass energy of √ s = 200 GeV. In the following sections, the relevant detector systems and the accumulated data sets will be described. The documentation of the charged pion selection criteria, reconstruction efficiencies and various background corrections follow before evaluating the various systematic uncertainties for the asymmetry results which are then discussed.

II. DATA-SETS
In 2015, the PHENIX experiment accumulated 60 pb −1 of transversely polarized p+p collision data. As both beams were polarized with average polarizations of 60% (counter-clockwise, yellow beam) and 58% (clockwise, blue beam) [18], two independent measurements were initially performed using the spin information of one beam and averaging over the spin information of the second beam. After confirming the consistency of the single-spin asymmetries for each individual beam, the results were combined.
The PHENIX detector comprises a central Helmholtz double coil magnet that is surrounded by two central detector arms that cover 90 degrees azimuthally each, and a pseudorapidity range of |η| < 0.35. A detailed detector description can be found at [19], while only the detector sub-systems relevant for this analysis will be presented in this paper. The central arms comprise drift (DC) and pad chambers (PC) at radii of 2.02-2.46 m (DC), 2.50 m (PC1), 4.00 m (PC2), and 5.00 m (PC3) that measure charged-particle momenta via the bending in the magnetic field. Between them, the gas ring-imagingČerenkov (RICH) detector is situated that helps identifying electrons, pions, and kaons at momentum thresholds of 0.03, 4.7, and 16 GeV/c, respectively. Downstream of the PCs, two types of electromagnetic calorimeters, EMCal, are located. Six of eight sectors are instrumented with a lead-scintillator (PbSc) shashlik calorimeter while the remaining two sectors are instrumented with a lead-glass (PbGl) calorimeter. The EMCal measures the energy of electrons and photons, as well as in part the energy of hadrons that start showering within the EMCal detector. The PbSc (PbGl) EMCal corresponds to 0.85 (1.05) nuclear interaction lengths. It also serves as a trigger detector for these particles, where typically three different energy thresholds are set up with different suppression factors in the data-taking.
Additionally, the beam-beam counters (BBCs), which comprise 64 quartz crystals and photo-multipliers each, located at the forward and backward rapidities of 3.1< |η| < 3.9 register hard collisions and the collision vertex position and the start time for time-of-flight measurements. The BBCs also serve to log the relative luminosities that have been accumulated in different spin states. Zero-degree-calorimeters at rapidities of |η| > 6 are used to cross check these relative luminosities as well as the correct beam spin orientation using the nonzero neutron single-spin asymmetries [20].

III. EVENT AND PARTICLE SELECTION CRITERIA
Pion-candidate events were selected if the lowest threshold of the EMCal trigger condition was satisfied, which required that at least 1.4 GeV of energy was deposited by the candidate particle in any of 4 × 4 EMCal towers. The BBC reconstructed event vertex had to be within 30 cm of the nominal beam interaction point along the beam axis. Pions were then selected if their momentum was between 5 and 15 GeV/c and the track matched the energy deposit in the EMCal. The track had to fire the RICH, and the shower shape in the EMCal had not to resemble that of an electromagnetic particle as given by a likelihood ratio between electromagnetic and other particles. To reduce the contamination by electrons in the pion data sample, the ratio of deposited energy, E, in the EMCal and reconstructed momentum, p, had to be 0.2 < E/p < 0.8. At low E/p values, electrons that are produced in decays close to the EMCal and appear to have higher reconstructed momenta get rejected. While other electrons deposit all of their energy in the EM-Cal and typically get reconstructed at E/p values around unity, pions only deposit a fraction of their energy in the EMCal and can thus be selected.
To estimate the asymmetries for electron background an electron-enhanced sample is selected in addition to the pion enhanced sample. For this sample the E/p and shower shape selections are inverted and even more RICH activity was required. These two types of samples will be denoted as pion-enhanced and electron-enhanced samples.

IV. ASYMMETRY EXTRACTION
The charged-pion yields were extracted starting by selecting them with the aforementioned criteria.
The single-spin asymmetries are then calculated for each beam, particle charge and signal type as: where N ↑/↓ L/R are the count rates to the left and right with respect to the polarized beam direction and spin orientation, for beams polarized up or down, respectively. P is the average beam polarization. Additionally, as the detector sits not exactly at 90 degrees to the spin orientation, the asymmetry needs to be normalized with the average cosine of the azimuthal angle | cos φ| of all particle candidates n, | cos φ| = i | cos φ i |/n, where φ i is defined for each candidate i relative to the spin orientation of the polarized beam, along its beam axis.
To evaluate the signal and background fractions in each sample, the raw candidate yields were corrected for the general reconstruction and acceptance efficiencies that were evaluated in single-particle simulations in geant3 [21]. The trigger efficiencies were corrected by calculating the fraction of minimum-bias events, for which pion candidates were also triggered by the EM-Cal based trigger. The RICH efficiency was calculated similarly by comparing the ratio of pion candidates that require the RICH selection criterion over all candidates. Because electrons also fulfill the RICH requirements for lower transverse momenta, the RICH efficiencies were corrected for this background using pythia6 [22] simulations.
Given that pion candidates are triggered using an electromagnetic calorimeter, the overall reconstruction efficiencies are much lower than for neutral pions or electrons, see for example [23] for more details on pion cross section measurements using PHENIX.
The composition of the raw data yields as a function of the transverse momentum based on a pythia6 [22] Monte-Carlo (MC) simulation is shown in Fig. 1, which shows that overall the data is well-described by the MC. The thresholds in the RICH for pions and kaons to emiť Cerenkov light are clearly visible at momenta of around 5 and 16 GeV/c, respectively. The simulations, confirm that the selected sample is clearly dominated by pions, with electrons being the main background. To calibrate the actual signal and background fractions in the pion and electron enhanced data samples, the E/p distributions in both pion and electron enhanced data samples were fit by the shapes obtained from MC over an enlarged E/p range. In particular, the electron contribution can be obtained by fitting a Gaussian close to unity which corresponds to the well-reconstructed electrons, that lose all their energy in the calorimeter, while the shape for the pions was directly taken from the simulation. The example for the raw yields and fits to the pion-enhanced data sample can be seen in Fig. 2. The MC obtains the overall magnitude of signal and background well, although slight differences between MC and data based electron peaks are visible that are used to rescale the background fraction. The background level in the pionenhanced sample ranges from 1 to 8% for the different transverse-momentum bins and charges.
Using the extracted electron background fractions in pion-enhanced (r π ) and electron-enhanced (r e ) samples, as well as the sample's respective asymmetries (A Sig N , A BG N ), the charged-pion asymmetries A π N can be obtained: The background asymmetries are consistent with zero, but their measured values were taken and the statistical errors propagated. The uncertainties on the signal to background fractions are assigned as systematic uncertainties as described below. Energy-over-momentum ratio distribution for negative pion and electron candidates from data and MC simulation for the pion-enhanced data sample.

V. SYSTEMATIC STUDIES AND CROSS CHECKS
For the asymmetries, several methods were applied to ensure the validity of the results. Apart from the previously discussed square root formula (Eq. 1), the singlespin asymmetries were also extracted by the so-called relative luminosity formula, where the relative luminosity R = L ↑ /L ↓ between the luminosities of the two spin orientations is applied to the count rate differences and the count rate sum: and normalized by the acceptance factor | cos φ| . The asymmetries were additionally calculated as a function of the azimuthal angle and fitted with a sine modulation, although the azimuthal acceptance is limited at central rapidities in PHENIX. All three methods were compared using T-tests and were found to be consistent with each other such that no further systematic uncertainty was assigned.
The two polarized beams provide two independent measurements of the asymmetries at central rapidities and can therefore be compared with each other for consistency. Again using a T-test, the results were found to be consistent with each other, such that both results could be combined in the final result.
Another test is performed by randomizing the spin information of each of the beam crossings and fills to artificially remove any physical asymmetry. This so-called bunch-shuffling method is repeated many times and ideally should produce a Gaussian distribution centered at zero with a width as large as the statistical uncertainty. Any deviations would suggest additional systematic uncertainties that had not been included. While the bunchshuffled asymmetries were on average consistent with zero, their widths were in some bins slightly larger than the statistical uncertainties. This variation was assigned as additional systematic uncertainty.
Lastly, the signal and background fractions that were described in the previous section were varied according to the uncertainties obtained from the fits to the E/p distribution. These are the dominant systematic uncertainty, but the measurements are dominated by the statistical uncertainties for both charges and all transversemomentum bins. Additionally, a global 3.4% scale uncertainty exists due to the precision of the beam polarization evaluated by the RHIC polarimetry group [18].

VI. RESULTS
The asymmetries are displayed in Fig. 3 as a function of the transverse momentum and summarized in Table I. As can be seen, the results are statistically limited due to the fact that, in comparison to the neutral pions, only a fraction of charged pions shower in the EMCal and fire triggers. Nevertheless, smaller than one percent level precision can be reached at lower transverse momenta, and the systematic uncertainties are generally much smaller. While the asymmetries for each charge are consistent with zero, as well as consistent with the previously measured neutral-pion asymmetries, there are differences between positive and negative charges. The χ 2 between π + and π − asymmetries is 9.04 for all five data points together. This might indicate a dependence of the asymmetries on the participating flavors of up and down quarks in particular, given that gluon-related initial-state effects would show the same behavior for either pion charge. Higher statistical precision, as is envisioned to be extracted with the sPHENIX experiment [24], will tell whether different flavors produce different asymmetries. It is worth noting that while the knowledge on the higher-twist correlations is still very limited, both the Sivers functions as well as the combinations of quark transversity and Collins fragmentation functions, show clear differences for up-and down-quark related effects.
When comparing the asymmetries to the expected asymmetries based on the global fit of data from SIDIS, other (predominantly forward single-spin asymmetries in p+p collisions and e + e − data [16]), the PHENIX results at higher transverse momenta are well described. In the midrapidity range, these calculations are dominated by the higher twist quark-gluon-quark correlators in the nucleon that are related to the quark Sivers functions. However, at lower transverse momenta, the size and sign of the measured asymmetries, especially for negative pions, appear to be slightly different.
[GeV/c]  In summary, the PHENIX experiment has measured charged-pion transverse-single-spin asymmetries at central rapidities. The precision has been greatly improved from the previously published nonidentified chargedhadron asymmetries [25] to a one-percent-level precision of charged pions over a substantially larger range of transverse momenta. While the asymmetries overall are consistent with zero, as well as the previously published neutral-pion asymmetries in the same rapidity region, an indication for a charge-dependent separation of the asymmetries is visible. If confirmed with higher precision, it could indicate a flavor-dependent effect.