SIDIS CLASNOTE 2013

Abstract

Semi-inclusive deep inelastic scattering (SIDIS) experiments may be used to identify the flavor of the quark that participates in the scattering process. Semi-inclusive scattering is defined as an electron scattering experiment in which the scattered electron and one hadron are detected in the final state. Ex- periments at Jefferson Lab have used longitudinally polarized electron beams to probe longitudinally polarized Hydrogen (15NH3) and Deuterium (15ND3) targets to investigate the quark’s contribution to the properties of a nucleon. This work reports a measurement of SIDIS pion asymmetries using the CEBAF Large Acceptance Spectrometer (CLAS) at Thomas Jefferson National Labo- ratory. The incident electron’s energy was 4.2 GeV and covered a kinematic region where the struck quark carries at least 30% of the nucleons total mo- mentum (xB ≥ 0.3). The electrons scatter mostly from valence quarks in this kinematic region allowing measurements which are less sensitive to the ocean of quark-antiquark pairs that are also inside a nucleon.

Data Analysis

Semi-inclusive deep inelastic scattering experiments using longitudinally polarized hydrogen (15NH3) and deuterium (15ND3) targets and a longitudinally polarized electron beam can be used to measure the ratio of the polarized va- lence quark distribution function to the unpolarized. Semi-inclusive scattering identifies an electron scattering experiment in which the scattered electron and one hadron are detected in the final state. This chapter describes the techniques used to analyze the data collected during the EG1b experiment and calculate semi-inclusive cross sections for the following reactions: ⃗e−N⃗ → e−π+X and ⃗e−N⃗ → e−π−X using NH3 and ND3 polarized targets respectively. The goal of this work is to measure charged pion asymmetries defined according to the incident electron helicity and the target polarization. This work focuses on a kinematic region where the struck quark carries at least 30% of the nucleons total momentum (xb > 0.3). The leptons scatter mostly from valence quarks in this kinematic region allowing contributions from sea quarks to be neglected. The above measurements are able to distinguish between the predictions made by the hyperfine perturbed quark constituent model (pQCM) and perturbative Quantum Chromodynamics (pQCD). As a result, the following study can be used to test the validity of the above models describing the structure of the nucleon.

The CLAS Data Selection

The data files from the EG1b experiment chosen for this analysis are listed in Table 1.1. During the experiment, 2.2 GeV, 4.2 GeV and 5.7 GeV longitudinally polarized electron beams were used to probe the polarized frozen ammonia NH3 and ND3 targets. This work will discuss the analysis of the 4.2 GeV electron beam data set as this energy provided the most statistics. The restrictions applied to the reconstructed events are described below. Run Set Target Type Torus Current(A) Target Polarization HWP 28100 - 28102 ND3 +2250 -0.18 +1 28106 - 28115 ND3 +2250 -0.18 -1 28145 - 28158 ND3 +2250 -0.20 +1 28166 - 28190 ND3 +2250 +0.30 +1 28205 - 28217 NH3 +2250 +0.75 +1 28222 - 28236 NH3 +2250 -0.68 +1 28242 - 28256 NH3 +2250 -0.70 -1 28260 - 28275 NH3 +2250 +0.69 -1 28287 - 28302 ND3 -2250 +0.28 +1 28306 - 28322 ND3 -2250 -0.12 +1 28375 - 28399 ND3 -2250 +0.25 -1 28407 - 28417 NH3 -2250 +0.73 -1 28456 - 28479 NH3 -2250 -0.69 +1 Table 1.1: EG1b runs analyzed for this work.

Particle Identification

Additional tests were performed on the electron and a pion candidates reconstructed by the standard CLAS software package. Electrons are identified by matching the charged particle hits in the Cherenkov counter, electromagnetic calorimeter, and the time of flight system. Geometrical and timing cuts are applied to improve electron identification [3]. In addition, cuts are applied on the energy deposited by the particle into the calorimeter and the number of photoelectrons produced in the Cherenkov counter. Charged pions are identi- fied by matching the hits in the drift chamber and ToF counter, along with a Cherenkov cut requiring that the number of photons for pions be less than two.

Electron Identification

The CLAS trigger system required a particle to deposit energy in the electromagnetic calorimeter and illuminate the Cherenkov counter within a 150 ns time window (Figure 1.1). Unfortunately, this trigger suffers from a back- ground of high energy negative pions that may be misidentified as electrons. The pion contamination of the electron sample is reduced using cuts on the energy deposited in the electromagnetic calorimeter and the momentum mea- sured by reconstructing the particles track in the known magnetic field. The energy deposition mechanism for the pions and electrons in the electromagnetic calorimeter is different. The total energy deposited by the electrons in the EC is proportional to their kinetic energy, whereas pions are minimum ionizing parti- cles and the energy deposition is independent of their momentum (Figure 1.2). The pion background is further suppressed using geometrical and time match- ing cuts between the Cherenkov counter hit and the measured track in the drift chamber.

Fig. 1.1: Example of electron passing through the drift chambers and creating the signal in the Cherenkov counter and electromagnetic calorimeter. Electron track is highlighted by the blue line (Run number 27095, Torus Current +2250 (inbending)). EC CUTS The CLAS electromagnetic calorimeter was used to reduce the misidenti- fication of electron and negative pion candidates. The electromagnetic calorime- ter contains thirteen layers of lead-scintillator sandwiches composed of ∼ 2 mm thick lead and 10 mm thick scintillator. Each set of thirteen layers are subdi- vided into five inner and eight outer layers that are named the inner and outer calorimeter respectively. Electrons interact with the calorimeter producing electromagnetic show- ers that release energy into the calorimeter. The deposited energy is propor- tional to the momentum of the electrons. Figure 1.3 shows the correlation of

Fig. 1.2: Momentum versus ECtotal. the inner and outer calorimeter electron candidate’s energy measured by the calorimeter and divided by the particles momentum reconstructed by the drift chamber. As shown in the Figure 1.3, there is an island near E/p = 0.2, which contains most of the electron candidates as well as some regions below 0.2 which will be argued to be negative pions misidentified as electrons. Pions entering the calorimeter are typically minimum ionizing parti- cles, loosing little of their incident energy in the calorimeter at a rate of 2 MeV g−1cm2. Electrons, on the other hand, deposit a larger fraction of their momentum into the calorimeter. As a result, the energy deposited into the elec- tromagnetic calorimeter is different for electrons and pions. Pions loose about 0.08 GeV of energy traversing the calorimeter independent their momentum thereby producing the constant signal in the calorimeter around 0.08 GeV. In order to reduce misidentified pions from the electron sample, the following cut

ECinner > 0.08 × p, (1.1) where p represents a particle’s momentum and ECinner the energy deposited into the inner part of the calorimeter. Since the energy loss of pions is related to the calorimeter thickness, a correlation can be established between the energy deposited into the inner and outer layers of the calorimeter: ECtot = 13, (1.2) ECinner 5 and results in the following cut for the energy deposition into the outer layer of the calorimeter: ECtot > 0.2 × p. (1.3) Cherenkov Counter Cut The Cherenkov counter has been used to further reduce the negatively charged pion background in the reconstructed electron sample. When the veloc- ity of a charged particle is greater than the local phase velocity of light or when it enters a medium with different optical properties, the charged particle will emit photons. Cherenkov light is emitted at the critical angle θc representing the angle of Cherenkov radiation relative to the particle’s direction. It can be

has been applied:  (a) Before cuts. (b) After cuts. Fig. 1.3: ECinner/p versus ECtot/p before and after EC cuts (ECtot > 0.2p and ECinner > 0.08p). After applying EC cuts about 46% of the events have been removed from the electron sample. shown that the cosine of the Cherenkov radiation angle is inversely proportional to the velocity of the charged particle cosθc = 1 , (1.4) nβ

where βc is the particle’s velocity and n the index of refraction of the medium. The charged particle in time t travels a distance βct, while the electromagnetic waves travel c t. For a medium with given index of refraction n, there is a n threshold velocity βthr = 1 , below which no radiation is emitted. This process n may be used to distinguish between the highly relativistic electrons and the less relativistic pions based on the number of photons produced in the Cherenkov detector. The number of photons produced per unit path length of a particle with charge Ze and per unit energy interval of the photons is proportional to the sine of the Cherenkov angle [2] d2NPE αz2 2 αz2􏰝 1 􏰞 dEdx = 􏱯c sin θc = 􏱯c 1− β2n2(E) d2NPE 2παz2 1 dλdx = λ2 [1 − β2n2(λ)] (1.5) (1.6) β=v=􏰦 pc . (1.7) c (pc)2 + (mc2)2 Taylor expanding Eq. 1.6 and keeping only the first two terms we get following d2NPEαz22 αz222 dEdx = 􏱯c sin θc = 􏱯c [β n (E)−1]. (1.8) The gas used in the CLAS Cerenkov counter is perfluorobutane C4F10 with index of refraction equal to 1.00153. Approximately thirteen photoelec- trons are produced by electrons traversing the Cherenkov detector. On the

other hand, calculations show that the number of photons produced by the negatively charged pions in the Cherenkov detector is approximately two. The theoretical results of the number of photons produced by the electrons and pions when passing through the Cherenkov counter are shown on Figure 1.4. (a) For electrons. (b) For pions. Fig. 1.4: Theoretical Calculation of the Number of Photoelectrons for electrons and pions. The distribution of the number of photoelectrons measured in the Cherenkov detector and the energy deposition dependence on number of photoelectrons are shown on Figure 1.5 and Figure 1.6. Pions, misidentified as electrons appear on Figure 1.5 at nphe<2.5.

Fig. 1.5: The number of photoelectrons without cuts. Fig. 1.6: The total energy deposited into the Calorimeter versus the Number of Photoelectrons. Geometric and Timing cuts Negative pions may be produced when the lepton scatters at a polar angle close to zero and is not observed by the detector. In order to reduce the electron sample contamination by those pions, geometrical cuts on the location of the particle at the entrance to the Cherenkov detector and time matching cuts have been developed by Osipenko [3]. For each CLAS Cherenkov detector segment the following cut has been applied |θp − θpcenter − θpoffset| < 3σp, (1.9) where θp represents the measured polar angle with respect to a projectile plane for each electron event and σp the width of the polar angle θp. The Cherenkov counter’s projective plane is an imaginary plane behind the Cherenkov detector where Cherenkov radiation would have arrived if it had moved the same distance from emission point to the PMT, without reflections in the mirror system. θpcenter is the polar angle from the CLAS detector center to the image of Cherenkov counter segment center and θpoffset is the shift in the segment center position. In addition to geometrical cuts, timing cuts have been applied to match the time between a Cherenkov counter hit and the time of flight system. The pion contamination in an electron sample was estimated by fitting the photoelectron distribution using two Gaussian distributions convoluted with a Landau distribution [4]: −0.5“ x−p1 ”2 1 −0.5“ x−p7 ”2 Npe =p0e p2 +p4 􏰙x−p5􏰚+p6e p8 . (1.10) 1− p6 The fits in Figure 1.7.(a) suggest that the pion contamination in the electron sample is 9.63% ± 0.01% before applying the OSI cuts and after the OSI cuts the contamination is about 4.029% ± 0.003% (Figure 1.7.(b)).

(a) Before Cuts. (b) After OSI Cuts. Fig. 1.7: The number of photoelectrons before and after geometrical and time matching cuts.

Pion Identification

Charged pions are identified using a coincidence hit in the drift chamber and Time-of-Flight (ToF) counter. Pions are separated from the other charged particles by looking at the particle momentum versus the β distribution. The particle velocity, β = v , is calculated from the difference of the RF time and the c time-of-flight measurement in the ToF system with the path length from the

vertex to the ToF counters. The mass of the charged particle can be identified by combining the particle’s β with the particle momentum obtained from the track measured by the drift chamber in the known magnetic field. The particle mass in a magnetic field is given as mβ p = 􏰦􏰦1 − β2 m=p (β2−1) β = Lpath, tflight (1.11) (1.12) (1.13) where m is the mass of the charged particle, β its velocity, p particle momentum, Lpath the path length from the vertex to scintillators and tflight the time of flight from the interaction vertex to the ToF system. Using the above information (particle momentum from the drift cham- bers and the timing information from the ToF system), the mass squared of the charged particle was calculated and is shown on Figure 1.9. The pion mass band is distributed around zero. To isolate charged pions from the rest of the particles, a 3σ cut on the momentum versus β distribution has been applied [5]. In addition to the charged particle velocity (β), the fiducial volume cuts have been applied for the charged pion identification. Since the drift chambers and scintillators are used for pion detection, the polar angle range where pions are detected is much larger than for electrons. For the EG1b experiment, pi- ons were detected from 8◦ to 180◦ [5]. The pion identification code has been

Fig. 1.8: The charged particle momentum versus β distribution. The pion and proton bands are clearly separated. developed by Joshua Pierce [6].

Event Reconstruction Efficiency

The goal of this work is to measure the semi-inclusive asymmetry when an electron and a pion are detected in the final state. For this analysis, pions of opposite charge will be observed using the same scintillator paddles by flipping

Fig. 1.9: The charged particle momentum versus mass squared distribution for the ⃗ep → ⃗e′π+n electroproduction process. The bands around zero and one represent pions and protons respectively [5]. the CLAS torus magnetic field direction. Although pions will be detected by the same detector elements, electrons will intersect different detector elements. As a result, the electron reconstruction efficiency was evaluated in terms of the electron rate observed in two different scintillator paddles detecting the same electron kinematics.

Inclusive Electron Event Reconstruction Efficiency

The electron reconstruction efficiency for individual scintillator detec- tors using the 4.2 GeV EG1b data set is investigated below. Only the electron is detected in the final state (inclusive case). The pion contamination in the electron sample was removed by applying the cuts described above. The elec-

tron paddle numbers 10 (B<0) and 5 (B>0) were chosen respectively, because they contained the most electron events in a first pass semi-inclusive pion anal- ysis of the data set. The electron kinematics (momentum, scattering angle and invariant mass) for these scintillators is shown on Figure 1.10. Ratios of the inclusive electron rate, normalized using the gated Faraday cup and detected in scintillator paddles # 5 and # 10, were measured. The two ratios are constructed to quantify the CLAS detector’s ability to reconstruct electrons in scintillator paddle #5 using a positive Torus polarity and scintillator #10 using the negative Torus polarity. ND3, B > 0, Paddle Numbere− = 5 = 1.57 ± 0.16 (1.14) ND3, B < 0, Paddle Numbere− = 10 NH3, B > 0, Paddle Numbere− = 5 = 1.76 ± 0.17. (1.15) NH3, B < 0, Paddle Numbere− = 10 Notice the above ratios are statistically the same. The semi-inclusive analysis to be performed in this work will be taking ratios using an ND3 and NH3 target. Below is the observed ratio comparing the inclusive electrons observed in scintillator #5 for a positive torus polarity and an ND3 target to the electrons observed in scintillator #10 when the torus polarity is negative and the target is NH3. ND3, B > 0, Paddle Numbere− = 5 = 1.55 ± 0.15. (1.16) NH3, B < 0, Paddle Numbere− = 10 The above ratios, which have been observed to be ammonia target inde- pendent, indicate a difference in an electron detector efficiency when the torus polarityisflipped. Anelectrondetectionefficiency”correctioncoefficient”isde-

(a) (b) (c) Fig. 1.10: Electron Kinematics. (a) Electron Momentum((NH3, B>0), (NH3, B<0), (ND3, B>0) and (ND3, B<0)), (b) Electron Scattering Angle θ ((NH3, B>0), (NH3, B<0), (ND3, B>0) and (ND3, B<0)) and (c) W Invariant mass((NH3, B>0), (NH3, B<0), (ND3, B>0) and (ND3, B<0)) fined in terms of the above ratio and measured to be ND3,B>0,Paddle Numbere− =5 = NH3,B<0,Paddle Numbere−=10 0.645 and ND3,B<0,Paddle Numbere−=10 = 1.82. The impact of these correc- NH3,B>0,Paddle Numbere−=5 tions on the data is illustrated in the next section.

Exclusive and Semi-Inclusive Event Reconstruction Efficiencies

The measured single pion electroproduction rate was compared to the MAID 2007 unitary model [7], that has been developed using the world data of pion photo and electro-production to determine the impact of using the above electron reconstruction efficiency ”correction coefficient”. The MAID 2007 model has predictions of the total cross section for the following two cases that are related to our work: γ∗ + proton(NH3) → π+ + neutron (1.17) γ∗ + neutron(ND3) → π− + proton. (1.18) The ratio of the pions detected in the scintillator paddles, located be- tween the Cherenkov counter and electromagnetic calorimeter, is shown in Fig- ure 1.11. Ratios were measured for four different cases. The intrinsic assump- tion is that, for the inbending case, positive pions and for the outbending case negative pions have the same trajectories with the same kinematics. In ad- dition, negatively charged pions in the inbending field and positively charged pions in the outbending fields are detected by the same detector elements. Using MAID 2007, the total cross section was calculated for the following invariant mass and four momentum transfer squared values: 1.7 GeV < W<1.8 18 CLAS-NOTE 2012  CLAS-NOTE 2012 Fig. 1.11: Pion paddle number versus Ratio for Semi-Inclusive case. GeV and Q2=1.1 GeV2 [7]. σ=σT+εσL+􏰦2ε(1+ε)σLT cosφπCM++εσTTcos2φπCM+h􏰦2ε(1−ε)σLT′ sinφπCM, (1.19) where φπCM is the pion azimuthal angle in the CM frame, ε = (1 + 2(1 + ν2 ) tan2 θe )−1 is the virtual photon polarization, ν = E − E the energy dif- Q2 2 i f ference of the initial and final state electron, Q2 = 4EiEf sin2 θe the four mo- 2 mentum transferred squared, θe the electron scattering angle and h the electron helicity. After applying corrections from the inclusive cases, the ratios have been compared to the results from MAID2007. The difference of the measured and MAID2007 model ratios for each pion paddle number is shown in Figure 1.12. 19 CLAS-NOTE 2012 One can argue using from Figure 1.12 that the ”inclusive corrections” do not impact single pion production rates for the exclusive cases. Fig. 1.12: Pion Paddle Number versus MAID2007 - Experiment(N (π−, ND3) / N(π+, NH3)). The Black and red data represent B>0/B<0 and B<0/B>0 cases respectively before corrections. The green and blue points represent the ratios for B>0/B<0 and B<0/B>0 after inclusive corrections.

Asymmetries

The double spin asymmetry measurements in this work are performed by comparing scattering events that occur when the incident probe spin and nuclear target spin are parallel to the scattering events that occur when the spins are anti-parallel.

Beam Charge Asymmetry

The helicity of the electron beam was flipped at a rate of 1 Hz. The helicity is prepared at the source such that helicity pairs are produced pseudo randomly. Fig. 1.13: The Helicity State: A one bit signal from the beam injector gives the helicity information, whereas a sync bit with a 2 Hz frequency is generated at the same time and is equal to the helicity flip time. If the first electron bunch is pseudo randomly chosen to be positive (negative) then it is labeled as the original helicity state and denoted in software by a 2 (1). The next helicity state is prepared to be a complement to the first state and labeled in the software as either a 4, if the original helicity state was a 1 (negative), or 3 if the original helicity state was a 2 (positive). The helicity selection process is then repeated. Figure 1.13 illustrates the signals used to label the helicity states. The 21 CLAS-NOTE 2012  CLAS-NOTE 2012 clock pulse (SYNC) is used to indicate that a change in the pockel cell used to define the helicity state may have occurred. The helicity bit identifies the helicity state that was set. The original/complement pulse identifies if the state is an original or complement helicity state. All three bits are recorded in the raw data file for each event and then converted to the labels 1, 2, 3, 4 during DST file production once the particles have been reconstructed. Two scalers were used to record several ancillary detectors, such as a Faraday cup and several PMTs mounted on the beam line, according to their helicity label. One of the scalers was gated by the DAQ live time in order to record beam conditions when the DAQ was able to take data and not busy recording data. The second scaler remained ungated. Both scalers recorded the SYNC and Helicity signals from the injector along with the counts ob- served from ancillary detectors during the SYNC interval. The Faraday cup signal recorded by the gated helicity scaler is used to normalize the events reconstructed during the same helicity interval. The beam charge asymmetry is defined in Eq. 1.21 and measured using the gated helicity scaler. For each run number, a gaussian fit was used to fit the beam charge asymmetry distributions as in Figure 1.14. The beam charge asymmetry is defined as ΣF C hel1,hel2 − ΣF C hel4,hel3 ABeam Charge = ΣF C hel1,hel2 + ΣF C hel4,hel3 , (1.20) where FChel1,hel2 (FChel4,hel3) represents the Faraday cup counts observed for the original helicity 1 and 2 states (the complement helicity 3 and 4 states). 22  CLAS-NOTE 2012 Fig. 1.14: Beam charge asymmetry for run #28101 using the gated Faraday cup counts for two helicity pairs (1-4 and 2-3 helicity pairs). A1−4 = (11.5 ± 4.4) × 10−5 and A2−3 = (−2.3 ± 4.4) × 10−5. EG1b data sets, with the same half wave plane, target type, target po- larization and beam torus, have been combined. The beam charge asymmetries have been calculated for the each run group and are listed in Table 1.2. A1−4 × 10−4   A2−3 × 10−4  Run Group Half wave plane(HWP) 28100 – 28105 +1 28106 – 28115 -1 28145 – 28240 +1 28242 – 28284 -1 28286 – 28324 +1 28325 – 28447 -1 28449 – 28479 +1  5.88 ± 34.40 7.53 ± 22.30 31.70 ± 7.99 49.6 ± 10.8 36.3 ± 11.6 21.1 ± 13.4 −11.6 ± 16.5 4.03 ± 34.36 8.28 ± 22.30 30.40 ± 7.99 47.9 ± 10.8 37.0 ± 11.5 22.2 ± 13.4 −21.6 ± 16.5       Table 1.2: Run Group versus Beam Charge Asymmetry.

Electron Asymmetry

A measurement of the electron cross section helicity difference needs to account for a possible helicity dependence of the incident electron flux (charge Asymmetry). Figure 1.15 shows the reconstructed electron rate asymmetry, before it is normalized by the gated Faraday Cup, as a function of the run number for the 4.2 GeV data set. The reconstructed electron asymmetry can be defined following way: CLAS-NOTE 2012 or A+− = NES+ −NES− ≡(2−3), NES NES+ + NES− −+ NES− −NES+ ANES = NES− + NES+ ≡ (1 − 4), (1.21) (1.22) where NES+ (NES−) represents number of electron scattered for the positive (negative) beam helicity. Systematic effects on the asymmetry measurement may be investigated by separating the data into two groups based on which helicity state is set first. The first group (black data points) represents the electron asymmetry observed when the first (original) helicity state is negative and its complement state is positive (helicity state #1 – state #4). The second group (red data points) represents the asymmetry observed when the first state is positive and the complement state is negative (helicity state #2 – #3). Both groups were divided into two subgroups based the target type used. The diamond points on the histogram represent the data for the NH3 target and the squares for 24 CLAS-NOTE 2012 Fig. 1.15: Run Number versus Electron Asymmetry before FC normalization. The black and red points represent reconstructed electron asymmetry for the helicity 1-4 pair for ND3 and NH3 target respectively. The blue and green points represent the helicity pair 2-3 for ND3 and NH3 respectively. The green line shows the sign of the half wave plane (HWP) and the purple line is the sign of the target polarization (TPol). the ND3 target. Two lines on the histogram are used to identify the sign of the half wave plate (HWP) and the target polarization (TPol). The relative spin orientation can be changed by either inserting a half wave plane (HWP) or by populating a different target polarization state with a different RF fre- quency. One would expect the asymmetry to change sign if either the HWP is inserted or the target polarization is rotated 180 degrees. As one can see for Figure 1.15 and Figure 1.16, the electron asymmetry (sign(hel1-hel4), sign(hel3- hel2) and sign(hel42-hel13)) changes sign if the HWP or Target Polarization sign is changed. 25  (a) NH3, Tpol>0 and HWP>0. CLAS-NOTE 2012 (b) NH3, Tpol<0 and HWP>0. Fig. 1.16: W versus (NEShel42 − NEShel13). The electron asymmetry (sign(hel42-hel13)) changes sign when the HWP or Target Polarization sign is changed. The un-normalized reconstructed electron asymmetry has been calcu- lated as: 26 NEShel1,hel2 − NEShel4,hel3 ANES = NEShel1,hel2 + NEShel4,hel3, and normalized by the Faraday cup NEShel1,hel2 − NEShel4,hel3 AFCnormalized = F C hel1,hel2 F C hel4,hel3 . NES NEShel1,hel2 + NEShel4,hel3 F C hel1,hel2 F C hel4,hel3 (1.23) (1.24) CLAS-NOTE 2012 Fig. 1.17: Run number versus electron asymmetry after applying FC normaliza- tion. The black and red points represent the reconstructed electron asymmetry for the helicity 1-4 pair for ND3 and NH3 target respectively. The blue and green points are the helicity pair 2-3 for ND3 and NH3 respectively. The green line shows the sign of the half wave plane (HWP) and the purple line is the sign of the target polarization (TPol). 27

[SIDIS_PionAsym_EG2000]