Single Spin Asymmetries of Inclusive Hadrons Produced in Electron Scattering from a Transversely Polarized He Target
We report the first measurement of target single-spin asymmetries (A) in the inclusive hadron production reaction, +, using a transversely polarized He target. The experiment was conducted at Jefferson Lab in Hall A using a 5.9-GeV electron beam. Three types of hadrons (, and proton) were detected in the transvere hadron momentum range 0.54 0.74 GeV/c. The range of for pions was -0.29 -0.23 and for kaons -0.25 -0.18. The observed asymmetry strongly depends on the type of hadron. A positive asymmetry is observed for and . A negative asymmetry is observed for . The magnitudes of the asymmetries follow . The K and proton asymmetries are consistent with zero within the experimental uncertainties. The and asymmetries measured for the He target and extracted for neutrons are opposite in sign with a small increase observed as a function of .
pacs:14.20.Dh, 25.30.Fj, 25.30.Rw, 24.85.+p
The Jefferson Lab Hall A Collaboration
The study of the transverse single spin asymmetries (TSSAs) is one of the most active areas of research in modern hadronic physics. TSSA is an important tool to advance our understanding of the nucleon spin, to reveal the role of the quark orbital angular momentum (OAM), and to access the three-dimensional structure of the nucleon in momentum space Barone et al. (2010). Current research on TSSA focuses on the polarized proton-proton () and lepton-nucleon () reaction channels.
An early observation of large left-right SSAs (A) in the reaction by the Fermilab E704 experiment at =19.4 GeV Adams et al. (1991a, b) revealed a strong dependence on the hadron type. In the center-of-mass frame of the polarized collision, viewed along the momentum direction of the polarized proton, favors the left side of the spin vector, whereas favors the right side of the spin vector. More recently, such non-vanishing TSSAs were observed for and K at =62.4 GeV by BRAHMS Arsene et al. (2008), and for neutral pions at =200 GeV by the STAR experiment at RHIC Abelev et al. (2008). Although TSSAs have been observed in reactions for more than two decades, measurement in semi-inclusive deep inelastic scattering (SIDIS) is regarded as one of the cleanest ways to understand them at the partonic level. TSSAs have been measured in the SIDIS reaction () by HERMES Airapetian et al. (2005, 2009, 2010, 2014) with a polarized proton target, and by COMPASS Alekseev et al. (2010, 2009); Adolph et al. (2012a, b) using polarized proton and deuteron targets. Recently, they have been measured at Jefferson Lab in Hall A using a polarized He target Qian et al. (2011); Huang et al. (2012).
The origin of TSSAs is currently interpreted using two theoretical approaches Anselmino et al. (2010). The first approach is based on the transverse-momentum-dependent distribution and fragmentation functions (TMDs) in the framework of the TMD factorization, and is mostly used to explain TSSAs in the SIDIS process. There are two reaction mechanisms: the Collins effect Collins (1993) and the Sivers effect Sivers (1990). In the Collins effect, the TSSA is generated by the transversity distribution, which represents the probability of finding a transversely polarized parton inside a transversely polarized nucleon, and the Collins fragmentation function, which correlates the transverse polarization of the quark with the transverse momentum of the outgoing hadron (). In the Sivers effect, the TSSA is generated by the Sivers distribution function, which correlates the quark’s transverse momentum and the nucleon’s spin, and is sensitive to the quark OAM. More specifically, the observed asymmetry due to the Sivers function arises from the final-state interaction between the struck quark and the nucleon remnant in SIDIS. On the other hand, the Sivers function in the Drell-Yan process is expected to arise from the initial-state interactions Brodsky et al. (2002). Taking gauge links into consideration, the Sivers distribution is predicted to be process dependent in the sense that it differs in sign between SIDIS and Drell-Yan processes Collins (2002); Brodsky et al. (2002). Furthermore, in models such as the di-quark model Lu and Schmidt (2007), one can connect the Sivers distribution for each quark to its contribution to the anomalous magnetic moment of the nucleon.
The second approach is based on the twist-3 collinear factorization Efremov and Teryaev (1982, 1985); Qiu and Sterman (1991, 1998), where the SSAs are interpreted in terms of higher-twist quark-gluon correlations, and is mainly used to explain the TSSAs in the channel. It was also shown that the TMD factorization and twist-3 methods are related Ji et al. (2006); Boer et al. (2003); Yuan and Zhou (2009). However, the Sivers function extracted from data with the twist-3 approach is shown to have a “sign mismatch” when compared to the Sivers function extracted from SIDIS data. The sign mismatch indicates a potential inconsistency in the current theoretical formalism Kang et al. (2011a), and needs to be further investigated. In order to understand the underlying mechanism producing TSSA it is crucial to study additional reaction channels Anselmino et al. (2010); Kang et al. (2011b).
In this letter, we study TSSA from one of the experimentally least explored reactions, inclusive hadron production using a lepton beam on a transversely polarized nucleon () Anselmino et al. (2000, 2010). An early study of this process was done by Anselmino et al., under the assumption that the underlying mechanism that generates TSSA is either Collins or Sivers effect Anselmino et al. (2000). More recently, this study was re-evaluated using newly available SIDIS data on Sivers and Collins moments assuming that the TMD factorization is valid in processes at large values. Due to the presence of only one hard scale in this process, estimation of the asymmetries is generally done at large values (typically 1 GeV/c). They predicted asymmetries between 5-10% for 4.9 GeV, =1.5 GeV/c, and 0.1 with a contribution from the Sivers mechanism to A, whereas the contribution from the Collins mechanism was negligible Anselmino et al. (2010).
Non-zero SSAs were also estimated based on the twist-3 distribution and fragmentation functions in the framework of collinear factorization Koike (2003a, b); Kang et al. (2011b), and in the SIDIS process by integrating over the scattered electron’s azimuthal angle Sun et al. (2010). These studies of TSSAs in the process are performed under the assumption of a SIDIS reaction, in which hard scattering occurs between a virtual photon and a quark. However, since the process is dominated by the cross-section at Q near zero, it was also pointed out that the process will have significant contributions from soft processes, such as vector meson dominance, especially at lower values Sivers (1991). Experimental data for TSSA in this process have recently been reported by the HERMES Collaboration using beams on a transversely polarized hydrogen target Airapetian et al. (2014).
We report the first measurement of target single-spin asymmetries (A) in inclusive hadron (, K, and proton) production at fixed-target e+N center-of-mass energy 3.45 GeV, using an unpolarized electron beam and a transversely polarized He target as an effective polarized neutron target. The kinematical variables for this process are: , where is the momentum of the outgoing hadron along the polarized nucleon’s momentum direction in the e+N center-of-mass frame, and , the transverse momentum of the outgoing hadron. The kinematical configuration in the laboratory coordinate system is shown in Fig 1.
The target spin “up”() was defined to be along the + direction, parallel to the vector , where and are the momentum vectors of the incoming beam and outgoing hadron, respectively.
The target SSA is defined as Anselmino et al. (2010),
where is the differential cross-section in the target “up”(“down”) state, and is the target polarization. The spin-dependent part of the cross-section is proportional to the term ), which gives rise to a modulation in the definition of the asymmetry. This term makes A parity-conserving, but T-odd under “naïve” time reversal, in which the initial and final states do not interchange. Note that the sign of in the laboratory coordinate system of this experiment (Eq. 1) differ by a factor -1 from the definition in the phenomenological study of this process in Anselmino et al. (2010), where the authors used the center-of-mass coordinate system with the lepton moving in the - direction.
The data were collected using a singles trigger during the E06-010 experiment in Hall A at Jefferson Lab Allada (2010). A beam energy of 5.9 GeV was provided by the CEBAF accelerator with an average current of 12 . The produced hadrons were detected in a high-resolution spectrometer (HRS) Alcorn et al. (2004) at a central angle of 16 on beam left side. Positively and negatively charged particles were detected separately by changing the magnet polarity of the HRS. The central momentum of the HRS was fixed at 2.35 GeV/c, with a momentum acceptance of 4.5 and solid angle of 6 msr. The average transverse momentum of the detected hadrons () was 0.64 GeV/c. We note that if the pions are produced through virtual or real-photon exchange (+N or +N), the minimum photon energy is E2.6 GeV, corresponding to an invariant mass of W2.4 GeV for the +N system, well above the region of nucleon resonances.
The data from the two helicity states from the polarized electron beam were summed over to achieve an unpolarized beam. The residual helicity-sorted beam-charge difference was less than 100 ppm in a typical run. The target spin direction was automatically reversed () at a rate of once every 20 minutes, which allowed control of the combined systematic uncertainty due to luminosity fluctuations and time depedence to below 50 ppm in this experiment.
Polarized He targets have often been used as an effective polarized neutron targets, because in the ground state of the He nuclear wavefunction (dominated by the S-state) the two proton spins are opposite to each other, and the nuclear spin is carried by the remaining neutron Bissey et al. (2002). The polarized target used in this measurement was a 40-cm long glass cell filled with 8 atm of He gas and a small amount (0.13 atm) of N gas to reduce depolarizing effects Alcorn et al. (2004). The radiation lengths of the materials up to the center of the He target were: Be window (0.072%), He gas (0.004%), glass window (0.142%), and He gas (0.046%). The target was polarized via hybrid spin-exchange optical pumping of a mixture of Rb-K Babcock et al. (2005). The He polarization was measured every 20 minutes during the spin-reversal using Nuclear Magnetic Resonance (NMR). The NMR signal was calibrated with Electron Paramagnetic Resonance (EPR) measurements and a known NMR signal obtained from an identical water cell. The average in-beam polarization of the target was (55.42.8).
The HRS detector package consisted of four separate detectors for particle identification: (i) a light-gas threshold Čerenkov for electron identification, (ii) a two-layer electromagnetic calorimeter for electron-hadron separation, (iii) a threshold aerogel Čerenkov detector for pion identification, and (iv) a ring imaging Čerenkov (RICH) detector for , K, and proton identification. The electron and positron background were suppressed with a rejection factor of 10:1. After all the particle identification cuts the contamination due to leptons was negligible in the hadron sample. The pion sample had a contamination of 1% due to other hadrons. Kaons were identified using the RICH detector, in combination with a veto from the aerogel counter, to suppress the large pion background. To further improve the purity of the kaon sample, a probability distribution was constructed based on the reconstructed Čerenkov ring angle and the expected Čerenkov angle in the RICH detector for a known particle momentum Urciuoli et al. (2009). A cut on this distribution effectively suppresses the background events due to mis-identified particles. The contamination of the kaon sample from other hadrons was estimated to be (proton) and () for positive kaons, and () for negative kaons. Protons were identified using the same method that was used for charged kaons, producing a very clean sample with estimated background 1%.
The raw He target single-spin asymmetry () was obtained using the normalized yields in target spin up/down () states, as shown in Eq. 1. The yield in each spin state is normalized with the accumulated beam charge and livetime of the data acquisition system in that state. The dilution of the measured He asymmetries due to the presence of a small amount of N gas in the target cell was corrected using the factor,
where is the density of the gas in the cell and is the unpolarized inclusive hadron cross-section. The unpolarized N and He cross-sections were obtained from the data taken during the experiment using reference cells filled with pure N and He gas. The was extracted separately for all hadrons and was about 10% in each case.
The overall systematic uncertainty in this measurement was small due to frequent target spin flips. The false asymmetry due to luminosity fluctuations was less than 0.04 and was confirmed by measuring the target SSA in inclusive DIS reaction for in-plane transverse target ( = 0, 180). This configuration was achieved by rotating the target spin by 90 while keeping all other conditions the same. This type of asymmetry vanishes under parity conservation, assuming one-photon exchange. In addition, the inclusive pion asymmetry was measured to be zero with a precision of 0.05% in the same configuration ( = 0, 180). This asymmetry is expected to vanishes due to sin() moment.
There were two additional sources of systematic uncertainty associated with the RICH detector for kaons and protons. The first one was from a cut on the number of hits in the RICH detector. The relative change in asymmetry under variation of the cut threshold was assigned as a systematic uncertainty. For K it was 14% and for protons it was 3%, relative to the statistical uncertainty. The second source was local fluctuations in the kaon and proton yield arising from detector inefficiencies in certain periods of the data-taking. The systematic uncertainty was estimated using the change in the asymmetry obtained in the periods with and without these fluctuations, and was estimated to be 2%, 6%, and 1%, relative to the statistical uncertainty, for K, K and protons, respectively. Systematic uncertainties due to the target density fluctuations, vertex cuts, DAQ livetime, and HRS single-track events were negligible.
The final He asymmetry results are shown for different hadron species in Fig. 2. These results include a small correction due to particle contamination for each hadron species. In Fig. 2 the data were integrated in and (see Table 1). The error bars represents the statistical uncertainty. The systematic uncertainties are shown as a solid band. The measured A for (2) and K(6) are positive, and opposite in sign to that of (1). In addition, the magnitudes of these asymmetries follow . The measured A for K and protons was found to be small and consistent with zero. We note that the majority of the detected protons originate through a knock-out reaction from the He nucleus, whereas mesons are produced either through fragmentation process or in a photoproduction reaction. The SSAs for charged pions as a function of for a He target are shown in Fig. 3. The asymmetry grows as a function of and plateaus around GeV/c.
We extracted on neutron from the measured He asymmetry using the effective polarization approach, previously used for both inclusive and semi-inclusive DIS processes Scopetta (2007); Bissey et al. (2002). Using this method, for the neutron can be obtained from He results using the relation,
where is the measured He asymmetry. P = 0.86 and P = -0.028 are the effective polarization of the neutron and proton, respectively. Hence, the contribution of proton polarization () to is relatively small. The factor, = , in He was measured directly in this experiment using the yields obtained from unpolarized hydrogen and He targets. The average proton dilution (1-) for was 0.1560.007 and for it was 0.2680.005. The SSA from a polarized proton target (A) was assumed to be no more than 5% at 0.64 GeV/c, which is consistent with the HERMES data on Airapetian et al. (2014).
The final results for for charged pions on an effective neutron target are shown in Fig. 4. The extracted is below 20% for both and , with the asymmtry amplitude for being larger than those for . The for both and increase up to 0.63 GeV/c, before it plateaus. Currently there are no theoretical estimates for A at 3.45 GeV and 0.64 GeV/c for a neutron target. The existing predictions were done for a proton target at 1.5 GeV/c and Anselmino et al. (2010). However, the sign of A for in our experiment is consistent with the existing predictions dominated by the Sivers effect, assuming pn and .
We can compare the observed behavior of our data with existing TSSAs in both proton-proton () and lepton-nucleon () reaction channels. Our results show that in the center-of-mass frame of the polarized neutron-electron collision, viewed along the direction of the neutron’s momentum, favors the right side of the spin vector, whereas favors the left side of the spin vector. Assuming isospin symmetry, this behavior is the same as that observed in for the E704 Adams et al. (1991a, b) and BRAHMS Arsene et al. (2008) experiments. In addition, this behavior is also the same as the Collins asymmetry for , and the Sivers asymmetry for observed in SIDIS Airapetian et al. (2005, 2009, 2010); Adolph et al. (2012a, b); Qian et al. (2011). The A for is about 15% at =0.64 GeV/c, which is larger than that for HERMES proton data for ( 5% at =0.68 GeV/c) Airapetian et al. (2014). Similarly, we observed large A for ( 5%) compared to that for HERMES proton data (1%) Airapetian et al. (2014). Furthermore, we observed a large and positive amplitude for the K asymmetry compared to K asymmetry on He, a similar feature observed in reaction on proton target Airapetian et al. (2014), and also the Sivers amplitude for kaons in the SIDIS reaction at HERMES Airapetian et al. (2009).
In summary, we have reported the first measurement of SSAs in the inclusive hadron production reaction using unpolarized electrons on a transversely polarized He target at GeV/c. Clear non-zero asymmetries were observed for charged pions and positive kaons, showing a similar feature of flavor dependence to that observed in the Sivers asymmetry in SIDIS, and in A in collisions. Currently there are no estimates or theoretical interpretations of these asymmetries at the relatively low of 0.64 GeV/c used for this measurement. We hope that the results presented here will stimulate new theoretical and experimental efforts to pin-point the exact origin of the observed SSAs. Future experiments at Jefferson Lab Allada (2012); jla (), after the 12-GeV upgrade, will extend this measurement to higher values of on both proton and He targets, and will provide precision data for future theoretical studies. Moreover, if these non-zero asymmetries survive at high energy kinematics then they can be used as monitors of transverse target polarization in a fixed target experiment, or local transverse polarization of the He beam at a future Electron-Ion-Collider.
We acknowledge the outstanding support of the JLab Hall A staff and the Accelerator Division in accomplishing this experiment. This work was supported in part by the U. S. National Science Foundation, and by Department of Energy (DOE) contract number DE-AC05-06OR23177, under which the Jefferson Science Associates operates the Thomas Jefferson National Accelerator Facility.
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