Semi-Inclusive $\pi_0$ target and beam-target asymmetries from 6 GeV electron scattering with CLAS

We present precision measurements of the target and beam-target spin asymmetries from neutral pion electroproduction in deep-inelastic scattering (DIS) using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. We scattered 6-GeV, longitudinally polarized electrons off longitudinally polarized protons in a cryogenic $^{14}$NH$_3$ target, and extracted double and single target spin asymmetries for $ep\rightarrow e^\prime\pi^0X$ in multidimensional bins in four-momentum transfer ($1.0<Q^2<3.2$ GeV$^2$), Bjorken-$x$ ($0.12<x<0.48$), hadron energy fraction ($0.4<z<0.7$), transverse pion momentum ($0<P_T<1.0$ GeV), and azimuthal angle $\phi_h$ between the lepton scattering and hadron production planes. We extracted asymmetries as a function of both $x$ and $P_T$, which provide access to transverse-momentum distributions of longitudinally polarized quarks. The double spin asymmetries depend weakly on $P_T$. The $\sin 2\phi_h$ moments are zero within uncertainties, which is consistent with the expected suppression of the Collins fragmentation function. The observed $\sin\phi_h$ moments suggest that quark gluon correlations are significant at large $x$.

partially account for the total proton spin of 1/2, leaving the deficit to be found in quark and gluon orbital angular momenta. The orbital motion of quarks about the proton's spin axis can be observed in deep-inelastic lepton scattering (DIS) when a knocked-out quark has momentum transverse to the direction of momentum transfer. Although the struck quark acquires transverse momentum in the hadronization process, there remains enough of a remnant of the original quark orbital motion to probe quark spin-orbit correlations. The theoretical motivations and early experiments measuring these transverse-momentum distributions (TMDs) have demonstrated that the theory is sound and the experiments are feasible [2]. In this Letter we report results of unprecedented accuracy in measurements of spin-azimuthal asymmetries in neutral pion production in semi-inclusive DIS (SIDIS), which provides important information on the quark structure of the proton, complementary to that from charged pions.
DIS experiments have mapped the unpolarized structure function f 1 and the polarized structure function g 1 over a wide range of longitudinal momentum fraction x and momentum transfer Q 2 . These provide a one-dimensional picture of nucleon structure. SIDIS provides access to the three-dimensional structure of the nucleon via a new set of structure functions that depend on the transverse motion of the quarks. The scattered lepton and the leading hadron are detected in coincidence. Eight leading-order (i.e. leading twist) [3] transverse-momentum distributions (TMDs) exist for the different beam and target polarizations, which describe the correlations between a quark's transverse momentum and the spin of the quark or the parent nucleon. These correlations manifest themselves in different spin-dependent azimuthal moments of the cross section, generated either by correlations in the distribution of quarks or in the fragmentation process, often referred as the Sivers [4] and Collins mechanisms [5], respectively.
For a longitudinally polarized nucleon, we have access to two leadingtwist TMDs, g 1L and h ⊥ 1L , which respectively describe longitudinally and transversely polarized quarks in a longitudinally polarized nucleon, and four higher-twist TMDs, f ⊥ L , g ⊥ L , h L , and e L [6] that describe various quark-gluon correlations that vanish as Q 2 → ∞.
The HERMES Collaboration made the first observation of a single-spin asymmetry (SSA) in semi-inclusive DIS pion electroproduction [7]. This spawned a number of additional measurements of SSAs and double spin asymmetries (DSAs) using polarized hydrogen and deuterium targets [8,9]. The target SSAs for proton and deuteron targets published by HERMES [10,11,12,13] and COMPASS [14,15], provided the first, direct indication of significant interference terms beyond the simple s-wave (L = 0) picture. These asymmetries become larger with increasing x, suggesting that spinorbit correlations are more relevant for the valence quarks.
Measurements of SSAs at Jefferson Lab (JLab) with longitudinally polarized proton [16] and transversely polarized neutron [17,18,19,20] targets suggest that spin-orbit correlations are significant for certain combinations of quark and nucleon spins and transverse momenta. Large spin-azimuthal asymmetries were observed at JLab using a longitudinally polarized beam [21,22] in one case and a transversely polarized 3 He target in the other [23]. These results are consistent with the corresponding HERMES [24] and COMPASS [25] measurements, which were interpreted in terms of highertwist contributions related to quark-gluon correlations.
Previous CLAS measurements [16] improved the world data set in two ways: they showed the first hint of a non-zero sin 2φ h azimuthal moment for charged pions, and they extracted azimuthal moments in multi-dimensional kinematic bins. COMPASS extended the proton DSAs to low-x [26] using a muon beam and a polarized NH 3 target, and they were able to extract the dependence on P T , albeit with low statistical accuracy above x = 0.2.
The world's SSAs and DSAs are dominated by the charged pion results. High statistical accuracy is still needed to study asymmetries as two-dimensional functions of P T and x in order to access the transversemomentum dependence of different partonic distributions, most notably the helicity distribution, g q 1 . This is true especially for the case of the neutral pion. This paper presents new results intended to help correct this deficiency.
The electroproduction of neutral pions has several important advantages compared to charged pions: 1) suppression of higher-twist contributions at large hadron energy fraction z [27], which are particularly important at JLab energies where small-z events are contaminated by target fragmentation; 2) reduction of the background from diffractive ρ decays into pions, which mar the interpretation of the charged single-pion data; 3) similarity of fragmentation functions for u and d quarks leading to π 0 , which reduces the dependence of the DSAs on the fragmentation functions at large x, where valence quarks dominate; and 4) suppression of spin-dependent fragmentation for π 0 s, due to the roughly equal magnitude and opposite sign of the Collins fragmentation functions for up and down quarks [13,15,28,29,30]. These factors simplify the interpretation of π 0 SSAs and DSAs. Furthermore, neutral pions are straight-forward to identify with little background using the invariant mass of two detected photons.
The azimuthal angular dependence (φ h ) of the asymmetry in the yield for the observed hadron around the direction of momentum transfer provides our experimental observable. Longitudinally polarized beams and targets give access to longitudinal target SSAs and the longitudinal DSAs as a function of φ h , 4-momentum transfer Q 2 , Bjorken x, transverse hadron momentum P T , and hadron energy fraction z. These spin asymmetries are defined in the laboratory frame, for which beam and target polarizations are along the beam-line (L) or unpolarized (U). From the φ h -dependence of these asymmetries (defined on the left-hand side of Eq. 1 for SSAs and Eq. 2 for DSAs) we can extract the experimental azimuthal moments (given on the right-hand side of Eqs. 1 and 2) using the φ h -dependence: The first (second) superscript on the yield Y denotes the sign of the beam (target) polarization. The first (second) subscript on the azimuthal moment A denotes whether the beam (target) is polarized or not. The superscript on A denotes the azimuthal moment. No superscript, as in A LL , denotes a φ h -independent asymmetry. The angle φ h is the hadron azimuthal angle with respect to the lepton plane as defined in the Trento convention [31]. We normalized the asymmetries using experimentally determined beam and target polarizations, P b and P t , respectively, and the dilution factor f , which accounts for the unpolarized material in the target.
In this letter, we present the results for the target SSA A U L and the longitudinal DSA A LL for π 0 production in SIDIS using the CLAS detector at JLab [32] with the addition of a small-angle inner calorimeter (IC) for photons. The experiment (eg1-dvcs) took place from February to October, 2009 [33,34]. We scattered longitudinally polarized electrons off a longitudinally polarized solid 14 NH 3 target and collected a total of 30 mC of charge at a beam energy of 5.94 GeV. We detected scattered electrons and neutral pions in coincidence using CLAS. The present SIDIS data constitute a subset of our inclusive measurements [33], and they improve the older CLAS eg1b π 0 measurements [16] by an order of magnitude in integrated luminosity.
We determined the beam polarization (about 85%) using a Møller polarimeter [35] and deduced the target polarization from the product of beam and target polarization (about 65%) obtained from ep elastic scattering. We polarized the protons in 14 NH 3 via Dynamic Nuclear Polarization [36]. The CLAS acceptance for scattered electrons (17 • < θ < 50 • ) was constrained by the IC at small angles and the polarized target walls at large angles.
Together, the CLAS electromagnetic calorimeter (EC) and the IC were able to detect photons from π 0 decay over a range of angles from 4 • to 50 • . We selected neutral pions by reconstructing the invariant mass of two photons, M γγ [37]. We analyzed separately three neutral pion topologies, EC-EC, EC-IC, and IC-IC, to take full advantage of the improved energy resolution of the IC and the larger angular range of the EC. Neutral pion mass cuts for EC-EC, EC-IC, and IC-IC were (0.10,0.17), (0.102,0.17), and (0.105,0.165) GeV, respectively.
Additionally, we applied fiducial cuts to both the EC and IC and removed tracks around the edges of the EC where there was a higher negative pion contamination in the electron sample. We also removed events on the inner edge of the IC (hot blocks close to the beam line), as well as blocks on the outer edges of the IC (blocks with incomplete energy reconstruction). Approximately 4.3M events survived these cuts.
We defined our variables using the Trento Convention [31], and selected SIDIS events by imposing kinematic cuts on the squared 4-momentum transfer (Q 2 > 1 GeV 2 ), Bjorken-x (0.12 < x < 0.48), the target plus virtual photon invariant mass (W > 2 GeV), the fractional energy of the π 0 (0.40 < z < 0.70), and the missing mass (M x > 1.5 GeV), which suppressed the contributions from target fragmentation and exclusive events. We divided the data into 4 bins in x, 9 bins in Q 2 , 4 bins in z, 6 bins in P T , and 12 bins in φ h . Here, φ h is the azimuthal angle around the direction of momentum transfer. Because beam and target polarization lie along the beam direction, all asymmetries were corrected by a depolarization factor.
We calculated the corresponding SIDIS yields by scaling the events by the charge measured with the Faraday Cup in Hall B. We scaled the raw asymmetries by the beam and target polarization for A LL and by the target polarization for A U L . In order to remove contributions from the unpolarized part of the 14 NH 3 target, we normalized the raw asymmetries by the dilution factor (about 3/17), which we calculated using a kinematically dependent model [38] optimized to fit the ratio of SIDIS events [39] from reference targets. The dilution model takes into account the SIDIS cross section per nucleon and an attenuation factor due to final state interactions of the π 0 in the target. The relative uncertainty in the dilution factor, due to the determination of the length of the frozen target, is 3%, and the uncertainty from the model dependence is 5%. Systematic uncertainties also resulted from the beam and target polarizations, background subtractions, and radiative corrections. Additionally, we studied the systematic fitting uncertainties for the moment extraction in detail. The strong dependence of the dilution factor for π 0 s on different kinematic variables is one of the main sources of systematic uncertainty. We also estimated via Monte Carlo simulation the uncertainties on the moment extraction, especially due to the imprecisely measured cos φ and cos 2φ dependence in the asymmetry denominators.
We performed radiative corrections on the data following the theoretical developments in Ref. [40]. We evaluated the spin-dependent radiative corrections using the Mo-Tsai formalism [41] in the angle peaking approximation (photon emission along the incident and scattered electron directions only) and the equivalent radiator approximation (radiation from the same nucleus as the hard scattering process is equivalent to an external radiator of a few percent). We used fits to the world data on spin-dependent exclusive and inclusive π 0 electroproduction cross sections and evaluated the radiative tails for each helicity combination separately using a Monte-Carlo integration technique. The net effect was relatively small in most kinematic bins, and is included in the systematic uncertainty budget.
The main goal of this experiment was the extraction of SSAs and DSAs in fine bins in x and transverse hadron momentum P T . We show here representative results. Fig. 1 shows A LL for π 0 as a function of P T , together with curves calculated for our kinematics using different theoretical approaches to parton distributions [42,43]. The general magnitude is predicted well by these calculations, while the P T -dependence is less well described. The dependence of the DSA on P T indicates that spin orbit correlations may be significant, and that these dependencies are sensitive to details of the momentum distributions of the polarized quarks. Because A LL is related to the ratio of polarized to unpolarized structure functions, this suggest that transverse momentum is correlated with spin orientation. Extraction of the underlying quark transverse momentum k T of the helicity distributions, however, will require an established framework for TMD extraction from a combination of measurements with unpolarized and polarized targets [44]. Studies of the Collins fragmentation functions at the e + e − machines, BELLE, [28,46,47], BABAR [48,29], and BESIII [30], indicate that the π ± Collins fragmentation functions H ⊥ 1 are large and have opposite signs for the favored and unfavored cases. Because fragmentation into π 0 is essentially the average of the π + and π − cases, this suggests a significant suppression of the Collins fragmentation function for π 0 . The measured sin 2φ h moment of the single target spin asymmetry A sin 2φ h U L , which at leading twist has only a contribution from the Collins function coupled to the chiral-odd TMD, h ⊥ The sin 2φ h moments for A UL plotted versus x (left) and P T (right) compared to previous CLAS measurements [16] (which had a lower z threshold of 0.3, no IC, and much lower integrated luminosity) and theory predictions (gray band) [42,43]. The error bars represent the statistical uncertainties, whereas the yellow bands represent the total experimental systematic uncertainties.
is shown in Fig. 2 for π 0 is consistent with zero as expected.
A significant sin φ h modulation of the target spin asymmetry has been observed for neutral pions by the HERMES Collaboration [8]. There have been several attempts to describe the sin φ h moment of this asymmetry using twist-3 contributions originating from the unpolarized fragmentation function The x-dependence of A U L is consistent with HERMES measurements [9] in both magnitude and x-dependence. The increasing P T -dependence is also consistent with HERMES. Precise direct comparisons, however, require taking out the kinematic factor 2ǫ(1 + ǫ) from the structure functions, and adding a factor of Q to account for the higher twist nature of this asymmetry, as defined in Ref. [6]. Tables with detailed relevant information on double and single target spin asymmetries for ep → e ′ π 0 X, extracted for multidimensional bins including x, z and P T -dependences, are available at arXiv:1709.10054.
In summary, kinematic dependencies of single and double spin asymmetries for neutral pions have been measured in multidimensional bins over a wide kinematic range in x and P T using CLAS with a polarized proton target. Measurements of the P T -dependence of the double spin asymmetry, performed for the first time for different x-bins, indicate the possibility of different average transverse momenta for quarks aligned or anti-aligned with the nucleon spin. A non-zero sin φ h target single-spin asymmetry was measured for neutral pions with high precision, indicating that the target SSA may be generated through the Sivers mechanism. A small sin 2φ h moment of the target SSA is consistent with expectations of strong suppression of the Collins effect for neutral pions, due to cancellation of roughly equal favored and unfavored Collins functions. The extent to which higher twist contributes to these extracted moments at relatively low Q 2 constitutes a large part of the upcoming CLAS program with 11 GeV beams.
We thank the accelerator staff, the Physics Division, the Target Group, and the Hall-B staff at JLab for their outstanding efforts that made this experiment possible. This work was supported in part by the U.S. Department of Energy and the National Science Foundation, the French Commissariatà l'Energie Atomique, the French Centre National de la Recherche Scientifique, the Italian Istituto Nazionale di Fisica Nucleare, the National Research Foundation of Korea, the United Kingdom's Science and Technology Facilities Council, and the Southeastern Universities Research Association (SURA), which operates the Thomas Jefferson National Accelerator Facility for the United States department of Energy under contract DE-AC05-06OR23177.    The table quotes the average value within a bin. %% P_T is the momentum of the pi0 transverse to the momentum transfer direction (in GeV). %% x is the Bjorken scaling variable. %% A_LL^cos is the measured cosine-phi moment of the double spin asymmetry for longitudinally polarized electrons and protons. %% Delta_stat is the statistical uncertainty on the moment. %% Delta_sys is the systematic uncertainty on the moment. %% y is the fractional energy transfer. %% z is the fractional energy of the pi0. %% Q^2 is the 4-momentum transfer squared. %% depol is the depolarization factor, which accounts for the mismatch between the beam and momentum transfer directions. %% dilut is the applied dilution factor.