Measurement of the longitudinal spin asymmetries for weak boson production in proton-proton collisions at root s=510 GeV

We report new STAR measurements of the single-spin asymmetries A L for W þ and W − bosons produced in polarized proton-proton collisions at ﬃﬃﬃ s p ¼ 510 GeV as a function of the decay-positron and decay-electron pseudorapidity. The data were obtained in 2013 and correspond to an integrated luminosity of 250 pb − 1 . The results are combined with previous results obtained with 86 pb − 1 . A comparison with theoretical expectations based on polarized lepton-nucleon deep-inelastic scattering and prior polarized proton-proton data suggests a difference between the ¯ u and ¯ d quark helicity distributions for 0 . 05 < x < 0 . 25 . In addition, we report new results for the double-spin asymmetries A LL for W (cid:2) , as well as A L for Z= γ (cid:3) production and subsequent decay into electron-positron pairs.

We report new STAR measurements of the single-spin asymmetries AL for W + and W − bosons produced in polarized proton-proton collisions at √ s = 510 GeV as a function of the decay-positron and decay-electron pseudorapidity. The data were obtained in 2013 and correspond to an integrated luminosity of 250 pb −1 . The results are combined with previous results obtained with 86 pb −1 . A comparison with theoretical expectations based on polarized lepton-nucleon deep-inelastic scattering and prior polarized proton-proton data suggests a difference between theū andd quark helicity distributions for 0.05 < x < 0. 25. In addition, we report new results for the double-spin asymmetries ALL for W ± , as well as AL for Z/γ * production and subsequent decay into electron-positron pairs. PACS numbers: 13.38.Be, 13.38.Dg, 13.88.+e, 14.20.Dh,24.85.+p Understanding the spin structure of the proton in terms of its quark, antiquark, and gluon constituents is of fundamental interest. This description is commonly done using polarized parton distribution functions (PDFs), which can be determined using perturbative QCD techniques and global analyses of data from polarized deep-inelastic lepton-nucleon scattering (DIS) experiments and from high-energy polarized proton-proton scattering experiments at the Relativistic Heavy-Ion Collider (RHIC). Recent examples of such PDFs are given in Refs. [1,2]. The data from leptonic W -decays in polarized proton-proton collisions at RHIC [3][4][5][6][7] provide constraints in these global analyses, which now show a flavor asymmetry in the light sea-quark polarizations for parton momentum fractions, 0.05 < x < 0.25, at hard perturbative scales. The existence of such an asymmetry in the polarized PDFs has been searched for directly in semi-inclusive DIS experiments [8][9][10] but had thus far been established only in the case of the unpolarized PDFs. There, Drell-Yan measurements [11,12] and DIS measurements [13,14], in particular, have reported large enhancements in the ratio ofd overū antiquark distributions. This has provided a strong impetus for theoretical modeling [15] and renewed measurement [16]. Considerable progress is being made also in lattice-QCD [17].
The leptonic W + → e + ν and W − → e −ν decay channels provide sensitivity to the helicity distributions of the quarks, ∆u and ∆d, and antiquarks, ∆ū and ∆d, that is free of uncertainties associated with non-perturbative fragmentation. The cross-sections are well described [18]. The primary observable is the longitudinal single-spin asymmetry A L ≡ (σ + − σ − )/(σ + + σ − ) where σ +(−) is the cross-section when the helicity of the polarized proton beam is positive (negative). At leading order, where x 1 (x 2 ) is the momentum fraction carried by the colliding quark or antiquark in the polarized (unpolarized) beam. A W + L (A W − L ) approaches −∆u/u (−∆d/d) in the very forward region of W rapidity, y W 0, and ∆d/d (∆ū/ū) in the very backward region of W rapidity, y W 0. The observed positron and electron pseudorapidities, η e , are related to y W and to the decay angle of the positron and electron in the W rest frame [19]. Higher-order corrections to A L (η e ) are known [20][21][22] and have been incorporated into the aforementioned global analyses.
In this Rapid Communication, we report new measurements of the single-spin asymmetries for decay positrons and electrons from W ± bosons produced in longitudinally-polarized proton-proton collisions at a center-of-mass energy of √ s = 510 GeV. In addition, we report new results for the double-spin asymmetries A LL for W ± and A L for Z/γ * production. The data were recorded in the year 2013 by the STAR collaboration and correspond to an integrated luminosity of about 250 pb −1 . The polarizations of the two incident proton beams were measured using Coulomb-nuclear interference proton-carbon polarimeters, which were calibrated with a polarized hydrogen gas-jet target [23]. The luminosity-weighted beam polarization was P = 0.56, with a relative scale uncertainty of 3.3% for the singlebeam polarization and 6.4% for the product of the polarizations from both beams. The figure-of-merit, P 2 L for single-spin asymmetry measurements, is higher by a factor of three for the 2013 data compared to the results [4] from the 2011 and 2012 data. This measurement and analysis made use of essentially the same apparatus and techniques as described in Refs. [3,4,18]. As before, the subsystems of the STAR detector [24] used in this measurement are the Time Projection Chamber [25] (TPC), which provides charged particle tracking for pseudorapidities |η| < ∼ 1.3, and the Barrel [26] and Endcap [27] Electromagnetic Calorimeters (BEMC, EEMC). These lead-scintillator sampling calorimeters are segmented into optically isolated towers that cover the full azimuthal angle, φ, for mid and forward pseudorapidity, |η| < 1.0 and 1.1 < η < 2.0, respectively. They provide the online triggering requirements to initiate the data recording. The trigger accepted events if a transverse energy E T > 12 (10) GeV was observed in a region ∆η×∆φ 0.1×0.1 of the BEMC (EEMC). Events were kept in the analysis if their collision vertex along the beam axis, determined from tracks reconstructed in the TPC, was within ± 100 cm of the center of the STAR detector. The vertex distribution along the beam axis was approximately Gaussian with an RMS width of 47 cm.
The W ± bosons were detected via their decay into positrons and electrons, W + → e + ν and W − → e −ν . These events are characterized by an isolated e + or e − with high transverse momentum, p T , accompanied by a high p T neutrino, ν, or antineutrino,ν. Since the ν and ν escape detection, this leads to a characteristically large p T imbalance in these events.
Candidate W -decay positrons or electrons were identified at mid-rapidity (forward rapidity) by a high p T TPC track associated with the primary event collision vertex pointing to a matching tower cluster in the BEMC (EEMC) with high energy. Candidate tracks at midrapidity (forward rapidity) were required to have at least 15 (5) TPC hits to ensure good track quality, and the ratio of the number of hits in the fit to the number of possible hits was required to be more than 0.51 to avoid splitting tracks. A threshold was imposed on the transverse momentum of the particle track, p T > 10 (7) GeV/c.
Of the four possible 2 × 2 calorimeter tower clusters containing the tower that was hit at its front face by the high-p T positron or electron, the cluster with the largest total energy was used to determine the positron or electron transverse energy, E e T . This energy was required to exceed 14 GeV. The distance between the track and the center position of the tower cluster was required to be less than 7 (10) cm at the front face of the BEMC (EEMC).
Unlike background events, signal events have a characteristic isolated transverse energy deposit from the decay positron or electron of about 40 GeV, approximately half the W mass, and a large imbalance in the total observed transverse energy as mentioned above. QCD backgrounds were suppressed using selections based on kinematic and topological differences between leptonic W -decay events and QCD processes. To identify isolated high-p T decay positrons or electrons, and discriminate against jets, the ratio of E e T to the total energy in a 4 × 4 BEMC (EEMC) cluster centered on and including the candidate 2 × 2 tower cluster was required to be greater than 95 (96)%. In addition, the ratio of E e T to the transverse energy E ∆R<0.7 T in a cone of radius of ∆R = ∆η 2 + ∆φ 2 < 0.7 around the candidate track was required to be greater than 88%. The transverse energy E ∆R<0.7 T was determined by summing the BEMC and EEMC E T and the TPC track p T within the cone. This selection thus suppressed jet-like events. In addition, in the EEMC acceptance, an isolation cut based on the energy deposited in the two layers of the EEMC Shower Maximum Detector (ESMD) [27] was used. The ESMD can be used to measure the transverse profile of the electromagnetic shower and thereby discriminate between the narrow transverse profile of an isolated (signal) positron or electron shower and the typically wider distribution observed in QCD (background) events. This was done by requiring that the ratio of total energy deposited in ESMD strips within ±1.5 cm of the central strip pointed to by a TPC track to the energy deposited in strips within ±10 cm, R ESMD , was greater than 0.7.
In addition, the characteristic transverse energy imbalance of signal events was used to further suppress backgrounds. A p T -balance vector, p bal T , defined as the vector-sum of the decay positron or electron candidate p e T vector plus the sum of the p T vectors for all reconstructed jets whose axes are outside a cone radius of ∆R = 0.7 around the candidate decay positron or electron, was computed for each event. Jets were reconstructed for this purpose using an anti-k T algorithm [28] with a resolution parameter R = 0.6 from towers (tracks) with E T (p T ) > 0.2 GeV(/c). Reconstructed jets were required to have p T > 3.5 GeV/c. A scalar signed p T -balance variable, defined as ( p e T · p bal T )/| p e T |, was then computed and required to be larger than 14 (20) GeV/c for candidate events in the BEMC (EEMC) to be retained in the analysis. Complementary to the signed p T -balance cut, it was required that the total transverse energy opposite in azimuth to the candidate positron or electron in the BEMC, −0.7 < ∆φ − π < 0.7, did not exceed 11 GeV. This further reduced QCD dijet background in cases when a sizable fraction of the energy for one of the jets was not observed due to detector effects. Candidate positrons or electrons that passed the above selection cuts were then sorted by charge-sign, determined from the curvature of the TPC tracks in the solenoidal magnetic field. Figure 1a (b) shows the distribution of the reconstructed charge-sign, Q = ±1, multiplied by the ratio of E e T observed in the BEMC (EEMC) to p e T determined with the TPC for events in the signal region, 25 < E e T < 50 GeV. The relative yields of the W + and W − follow the pseudorapidity dependence of the cross-section ratio. The distributions were each fitted with two double-Gaussian template shapes, determined from a Monte Carlo simulated W sample, to estimate the reconstructed charge-sign purity. The amplitudes of the Gaussians were fitted to the data, as was the central position of the narrower Gaussian in each of the templates. The remaining parameters were fixed by studies in which simulated W + → e + ν and W − → e −ν events were embedded (c.f. the paragraph below) in zero-bias data. The hatched regions, |Q·E T /p T | < 0.4 and |Q·E T /p T | > 1.8, were excluded to remove tracks with poorly reconstructed p T and to reduce contamination from events with opposite charge-sign. This contamination is negligible at midrapidity, but increases to 9.6% and 12.0% for W + and W − candidate events, respectively, in the EEMC region. The forward A L values were corrected for this contamination using the asymmetries observed in the data.  Figure 2 shows the distributions of W + and W − yields as a function of E e T for the four central η e intervals considered in this analysis, along with the estimated residual background contributions from electroweak and QCD processes. The residual electroweak backgrounds are predominantly due to W ± → τ ± ν τ and Z/γ * → e + e − . These contributions were estimated from Monte Carlo simulations, using events generated with pythia 6.4.28 [29] and the "Perugia 0" tune [30] that passed through a geant 3 [31] model of the STAR detector, and were subsequently embedded into STAR zero-bias data. The simulated samples were normalized to the W data using the known integrated luminosity. The tauola package was used for the polarized τ ± decay [32]. Residual QCD dijet background in which one of the jets pointed to uninstrumented pseudorapidity regions was estimated using two separate procedures. The contribution from e ± candidate events with an opposite-side jet fragment in the uninstrumented region −2 < η < −1.1 was estimated by studying such data in the EEMC, which instruments the region 1.1 < η < 2. This is referred to as the "Second EEMC" procedure. Residual background from the uninstrumented region |η| > 2 was estimated by studying events that satisfy all isolation criteria, but do not satisfy the cuts on the scalar signed p T -balance variable. This is referred to as the "Datadriven QCD" procedure. To assess the background remaining in the signal region, the E T distribution of this background-dominated sample was normalized to the signal candidate distribution that remained after all other background contributions had been removed for E T values between 14 GeV and 18 GeV. Additional aspects of both procedures are described in Refs [3,18].  Figure 3 shows the charge-separated distributions in the EEMC region as a function of the signed p T -balance variable, together with the estimated residual background contributions. Residual electroweak backgrounds for these regions were estimated in the same way as for the mid-rapidity data. Residual QCD backgrounds were estimated using the ESMD, where the isolation parameter R ESMD was required to be less than 0.6 for QCD background events. The shape was determined for each charge-sign separately and normalized to the measured yield in the region where the signed p T -balance variable was between -8 and 8 GeV/c. This region is dominated by QCD backgrounds.
At RHIC, there are four helicity configurations for the two longitudinally-polarized proton beams: ++, +−, −+, and −−. The data from these four configurations can be combined such that the net polarization for one beam effectively averages to zero, while maintaining high polarization in the other. The longitudinal single-spin asymmetry A L for the combination in which the first beam is polarized and the second carries no net polarization was determined from: where β is the signal purity, P is the average beam polarization, and R and N are the normalizations for relative luminosity and the raw W ± yields, respectively, for the helicity configurations indicated by the subscripts. The relative luminosities were obtained from a large QCD sample that exhibits no significant single-spin asymmetry. Typical values were between 0.993 and 1.009. The purity was evaluated from the aforementioned signal and background contributions and was found to be between 83% and 98%. A L was determined in a similar way for the combination in which the second beam is polarized and the first carries no net polarization, and the values for the two combinations were then combined.
The A L results for W + and W − from the data sample recorded by STAR in 2013 are shown in Fig. 4 as a function of η e . The vertical error bars show the size of the statistical uncertainties, including those associated with the correction for the wrong charge-sign in the case of the points at |η e | 1.2. The previously published STAR data [4] are shown for comparison. Shown also are the A L data on high-energy forward decay muons and mid-rapidity positrons or electrons from combined W and Z/γ * production by the PHENIX experiment with their statistical and systematic uncertainties as a function of η µ and η e , respectively [6,7].
The size of systematic uncertainties associated with BEMC and EEMC gain calibrations (5% variation) and the data-driven QCD background are indicated by the boxes. The gray band shown along the A L = 0 line indicates the size of the systematic uncertainty from the determination of relative luminosity, and is correlated among all the points. The 3.3% relative systematic uncertainty from beam polarization measurement is not shown. Table I gives the results for A L , as well as for the longitudinal double-spin asymmetry where the subscripts denote the helicity configurations.
The new W ± A LL data are consistent with previously published STAR data [4] and have better precision. W ± A LL is sensitive to quark and antiquark polarizations, albeit less so than A L , and has been proposed for tests of consistency and positivity constraints [36,37].
The new W ± A L data are consistent with the previously published results, and have statistical uncertainties Longitudinal single-spin asymmetries, AL, for W ± production as a function of the positron or electron pseudorapidity, ηe, separately for the STAR 2011+2012 (black squares) and 2013 (red diamonds) data samples for 25 < E e T < 50 GeV. The 2011+2012 results have been offset to slightly smaller η values for clarity. Shown also are the final asymmetries for high-energy decay leptons from W and Z/γ * production from the PHENIX central arms as a function of ηe and from the muon-arms as a function of ηµ with their statistical and systematic uncertainties [6,7]. that are 40 − 50% smaller. The combined STAR data are shown in Fig. 5 and compared with expectations based on the DSSV14 [2], NNPDFpol1.1 [1] and BS15 [33] PDFs evaluated using the next-to-leading order CHE [21] and fully resummed RHICBOS [22] codes. The NNPDF-pol1.1 analysis, unlike DSSV14 and BS15, includes the STAR 2011+2012 W ± data [4], which reduces in particular the uncertainties for W − expectations at negative η. To assess the impact, the STAR 2013 data were used in the reweighting procedure of Refs. [34,35] with the 100 publicly available NNPDFpol1.1 PDFs. The results from this reweighting, taking into account the total uncertainties of the STAR 2013 data and their correlations [38], are shown in Fig. 5 as the blue hatched bands. The NNPDFpol1.1 uncertainties [1] are shown as the green bands for comparison. Figure 6 shows the corresponding differences of the light sea-quark polarizations versus x at a scale of Q 2 = 10 (GeV/c) 2 . The data confirm the existence of a sizable, positive ∆ū in the range 0.05 < x < 0.25 [4] and the existence of a flavor asymmetry in the polarized quark sea.    In addition, A L was determined for Z/γ * production from a sample of 274 electron-positron pairs with 70 < m e + e − < 110 GeV/c 2 . The e + and e − were each required to be isolated, have |η e | < 1.1, and E e T > 14 GeV. The result, A Z/γ * L = −0.04 ± 0.07, is consistent with that in Ref. [4] but with half the statistical uncertainty. The systematic uncertainty is negligible compared to the statistical uncertainty. This result is also consistent with theoretical expectations, A Z/γ * L = −0.08 from DSSV14 [2] and A Z/γ * L = −0.04 from NNPDFpol1.1 [1]. In summary, we report new STAR measurements of longitudinal single-spin and double-spin asymmetries for W ± and single-spin asymmetry for Z/γ * bosons produced in polarized proton-proton collisions at √ s = 510 GeV. The production of weak bosons in these col-lisions and their subsequent leptonic decay is a unique process to delineate the quark and antiquark polarizations in the proton by flavor. The A L data for W + and W − , combined with previously published STAR results, show a significant preference for ∆ū(x, Q 2 ) > ∆d(x, Q 2 ) in the fractional momentum range 0.05 < x < 0.25 at a scale of Q 2 = 10 (GeV/c) 2 . This is opposite to the flavor asymmetry observed in the spin-averaged quark-sea distributions.
We thank the RHIC Operations Group and RCF at BNL, the NERSC Center at LBNL, and the Open Science Grid consortium for providing resources and support. This work was supported in part by the Office of Nuclear Physics within the U.S. DOE Office of Sci-ence, the U.S. National Science Foundation, the Ministry of High Education and Science of the Russian Federation, National Natural Science Foundation of China, Chinese Academy of Science, the Ministry of Science and Technology of China and the Chinese Ministry of Education, the National Research Foundation of Korea, Czech Science Foundation and Ministry of Education, Youth and Sports of the Czech Republic, Department of Atomic Energy and Department of Science and Technology of the Government of India, the National Science Centre of Poland, the Ministry of Science, Education and Sports of the Republic of Croatia, RosAtom of Russia and German Bundesministerium für Bildung, Wissenschaft, Forschung and Technologie (BMBF) and the Helmholtz Association. Table I contains the correlations of the quadrature sum of the statistical and total systematic uncertainties on A L (η e ) for W − and W + from the STAR 2013 data.