Beam-spin asymmetries from semi-inclusive pion electroproduction

We have measured the moment $A_{LU}^{\sin \varphi }$ corresponding to the polarized electron beam-spin asymmetry in semi-inclusive deep inelastic scattering. $A_{LU}^{\sin \varphi }$ is a twist-3 quantity providing information about quark-gluon correlations. Data were taken with the CLAS Spectrometer at Jefferson Lab using a 5.498 GeV longitudinally polarized electron beam and an unpolarized liquid hydrogen target. All three pion channels (${\pi }^{+}$, ${\pi }^0$ and ${\pi }^{-}$) were measured simultaneously over a large range of kinematics within the virtuality range $Q^2\approx 1.0–4.5{\mathrm{GeV}}^2$. The observable was measured with better than 1% statistical precision over a large range of $z$, $P_T$, $x_B$, and $Q^2$, which permits comparison with several reaction models. The discussed measurements provide an upgrade in statistics over previous measurements, and serve as the first evidence for the negative sign of the ${\pi }^{-}$ $\sin \varphi$ moment.

Figure 1

The scattering diagram of the SIDIS process. The angle $\varphi$ is the angle between the plane described by the incident and scattered electron and that defined by the direction of the emitted hadron.

Figure 2

SIDIS scattering process including the parton distribution function and fragmentation function.

Figure 3

The CLAS detector, including drift chambers, Čerenkov counters, electromagnetic calorimeters, and time-of-flight detectors.

Figure 4

Number of photoelectrons detected in the CLAS Čerenkov counter. Events with the number of photoelectrons $\times 10$ greater than 25 were kept, while those below were subjected to further cuts. The blue (dotted) histogram shows the total measured events passing cuts in the EC, but without additional CC cuts applied. The black (solid) histogram shows those events passing all electron identification cuts, including those imposed using the CC measurements when $N_{\mathrm{pe}}\times 10<25$. The red line at $N_{\mathrm{pe}}\times 10=25$ delineates the two regions with different CC cuts (see text).

Figure 5

Sampling fraction $E/p$ vs $p$ for electron candidates in the CLAS electromagnetic calorimeter. Only events between the two solid (red) lines were kept. The dotted line indicates the mean of the distribution.

Figure 6

A two-dimensional histogram of the energy deposited in the outer vs inner parts of the CLAS electromagnetic calorimeter. Electron candidates depositing less than 55 MeV (as represented by the red line) were removed.

Figure 7

$\mathrm{\Delta }t$ vs momentum for positively charged tracks, where the cut shown removed proton and kaon tracks from the desired ${\pi }^{+}$ sample. The black dots define $\pm 3\sigma$ for $\mathrm{\Delta }t$ in each momentum bin, and the red curves are fits to those points, which were used to set maximum and minimum values on $\mathrm{\Delta }t$. The plots for ${\pi }^{-}$ look similar but without the strong proton contribution.

Figure 8

$\beta$ vs momentum for hits in the CLAS calorimeter. A momentum-dependent cut, shown by the solid red line, was used to separate photons from neutrons.

Figure 9

Invariant mass of two photons in a single bin in $x_B$, $P_T$, and $\varphi$ for the positive-helicity state. The invariant mass was fit with a Gaussian (red dotted curve) plus a polynomial background (grey curve), which is integrated to determine the number of neutral pions in the bin.

Figure 10

Kinematic coverage for SIDIS events. $A_{LU}^{\sin \varphi }$ was binned in $z$, $x_B$, $P_T$, and $Q^2$, so the upper panel shows $Q^2$ vs $x_B$ and the lower panel shows $z$ vs $P_T$, where $z$ has been constrained to the SIDIS region of $0.4<z<0.7$. The distributions are shown for ${\pi }^{+}$ events, but the kinematic coverage for ${\pi }^{-}$ and ${\pi }^0$ is similar.

Figure 11

$p$-value vs ${\chi }^2$. Fits for which the $p$-value $<0.003$ did not pass our hypothesis test and were removed.

Figure 12

Comparison between the measured (blue) and expected (red) ${\chi }^2$ distributions.

Figure 13

Beam-spin asymmetries for one bin in $z$, plotted in red, open symbols (blue, solid symbols) using measured (random) helicities. Both are fit using Eq. (9). An estimate of systematic uncertainty was made by fitting the BSA using a random helicity, which is expected to be zero, and comparing the result with the null hypothesis.

Figure 14

$A_{LU}^{\sin \varphi }$ vs $z$, $x_B$, $P_T$, and $Q^2$ after integration over the other kinematic variables for each pion channel. The integration range in $z$ for SIDIS kinematics is for $0.4<z<0.7$. The error bars represent statistical uncertainties and the shaded regions represent the systematic uncertainties. The top row shows ${\pi }^{+}$, the center row shows ${\pi }^{-}$, and the bottom row shows ${\pi }^0$.

Figure 15

$A_{LU}^{\sin \varphi }$ vs $x_B$ in different $P_T$ bins. The error bars represent statistical uncertainties and the shaded regions at the bottom represent systematic uncertainties. The top row is ${\pi }^{+}$, the middle is ${\pi }^{-}$, and the bottom is ${\pi }^0$. Each column represents a different bin in $P_T$. The results are integrated over all $Q^2$ and $0.4<z<0.7$.

Figure 16

Comparison of $A_{LU}^{\sin \varphi }$ vs $x_B$ between several data sets, each scaled by a factor of $⟨Q⟩/f(y)$, where $f(y)$ is given by Eq. (16). The left panel is ${\pi }^{+}$, the center is ${\pi }^{-}$, and the right is ${\pi }^0$. Here the solid (black) circles are this experiment, the open (red) squares are from HERMES [44], and the open (blue) triangles are from previous CLAS publications [45, 46, 47]. The error bars are statistical uncertainty and the solid bands show the systematic uncertainty for the current experiment.

Figure 17

Comparison of measurement to theoretical models taking into account either the contributions due to the $e\otimes H_1^{\perp }$ term as calculated in Ref. [14] (solid curves, red) or as calculated in Refs. [22, 53] (dashed, green). The $g^{\perp }\otimes D_1$ contribution (dashed-dot, blue curves) [22, 53] are also shown, which were calculated utilizing the spectator model described in Ref. [55].