Beam spin asymmetries in deeply virtual Compton scattering (DVCS) with CLAS at 4.8 GeV

We report measurements of the beam spin asymmetry in deeply virtual Compton scattering (DVCS) at an electron beam energy of $4.8$ GeV using the CLAS detector at the Thomas Jefferson National Accelerator Facility. The DVCS beam spin asymmetry has been measured in a wide range of kinematics, $1.0<Q^2<2.8$ (GeV/$c$)${}^2$, $0.12<x_B<0.48$, and $0.1<-t<0.8$ (GeV/$c$)${}^2$, using the reaction $\overrightarrow{e}p\to e^{\text{'}}\mathit{pX}$. The number of $\mathrm{H}(e,e^{\text{'}}\gamma p)$ and $\mathrm{H}(e,e^{\text{'}}{\pi }^{0}p)$ events are separated in each $(Q^2,x_B,t)$ bin by a fit to the line shape of the $\mathrm{H}(e,e^{\text{'}}p)X$ $M_x^2$ distribution. The validity of the method was studied in detail using experimental and simulated data. It was shown that with the achieved missing mass squared resolution and the available statistics, the separation of DVCS–Bethe-Heitler and ${\pi }^0$ events can reliably be done with less than 5% uncertainty. Also, the $Q^2$ and $t$ dependences of the $\sin \varphi$ moments of the asymmetry are extracted and compared with theoretical calculations.

Figure 1

Feynman diagrams for DVCS and Bethe-Heitler processes contributing to the amplitude of $\mathit{ep}\to e^{\text{'}}p\gamma$ scattering.

Figure 2

Distribution of the number of photoelectrons detected in the CC vs the sampling fraction of the EC.

Figure 3

Vertex time distribution as a function of momentum for positive tracks. The particle velocity is deduced from the momentum using the proton mass.

Figure 4

Distribution of the energy measured in the EC vs $\beta$ for neutral particles detected in the EC. The vertical band at $\beta =1$ corresponds to photons.

Figure 5

Selection of the BH events. (a) Distribution of the $x$ and $y$ components of the missing momentum. The strong peak at zero corresponds to BH events. (b) Electron and proton azimuthal angle difference before (dashed line histogram) and after (solid line histogram) the cut on the $x$ and $y$ components of the missing momentum.

Figure 6

(a) Missing mass squared of $\mathit{ep}\to \mathit{epX}$ for the BH events before (dashed line histogram) and after (solid line histogram) momentum corrections are applied. (b) Dependence of the Gaussian means of the missing mass squared distributions on the CLAS sector before (stars) and after (crosses) the momentum corrections.

Figure 7

Kinematical coverage of the data set. (a) $Q^2$ vs $x_B$ distribution with our $Q^2$ bin divisions. (b) $Q^2$ vs $t$ distribution. The boxes indicate the kinematical bins used for this analysis (see Tables 3 and 4).

Figure 8

Kinematics of electroproduction in the target rest frame. The azimuthal angle ${\varphi }_{p\gamma }$ is the angle between the proton-photon production plane and the electron scattering plane. The azimuthal angle defined in Ref. [8] and presented in Eq. (15) is $\varphi =\pi -{\varphi }_{p\gamma }$.

Figure 9

Fits to identified (a) $\mathit{ep}\gamma$ and (b) $\mathit{ep}{\pi }^0$ final states to determine the mean values and standard deviations of the Gaussian functions $G_{\gamma }$ and $G_{{\pi }^0}$. The solid line is the fit function, the dashed line is the fitted Gaussian function, and the dashed-dotted line is the polynomial fit to the radiative tail and the background.

Figure 10

Example of fits obtained using Eq. (23) for one ${\varphi }_{p\gamma }$ bin. (a) Fit to the background using the end points of the $M_x^2$ distribution. (b), (c), and (d) are fits to the $M_x^2$ distributions corresponding to positive, negative, and summed beam helicity states, respectively. In (b)–(d), the fit parameters are the number of single photon and ${\pi }^0$ events; the solid lines are the fit functions as defined in Eq. (23), the dashed lines are the Gaussian functions for the single photon events, the dashed-dotted lines are the Gaussian functions for the single ${\pi }^0$ events, and the dashed-dot-dot-dot lines are the polynomial background.

Figure 11

Ratios of initial to reconstructed single photon events (a) for a constant $N_{\gamma }/N_{{\pi }^0}$ ratio and (b) for a constant number of events in the mixed distribution. In (a) the numbers under each point on the plot correspond to the initial number of $\mathit{ep}\gamma$ events. In (b) the numbers under each point show the ratios of the $\mathit{ep}\gamma$ to $\mathit{ep}{\pi }^0$ events in the mixed sample.

Figure 12

Simulated missing mass squared distributions for (a) positive and (b) negative helicity for one ${\varphi }_{p\gamma }$, $Q^2$, and $t$ bin. The open circles with error bars correspond to the mixed event distributions. The solid line is the fit using the function in Eq. (23) to these points. The open squares represent the $M_x^2$ distributions of the initial photon events. The dashed lines are the resulting $G_{\gamma }$ from the fit to the mixed distributions. The stars and dashed-dotted lines are the same for the single pion final state. The dashed-dot-dot-dotted line in (b) corresponds to the fitted polynomial background.

Figure 13

${\varphi }_{p\gamma }$ dependence of ratios of the number of single photon events extracted using the fits to the missing mass squared distribution of the mixed events to the number of single photon events that passed the analysis cuts for the positive (open circles) and negative (crosses) beam helicity states. The stars represent the ratio of the two ratios.

Figure 14

Simulated and extracted $A_{\mathrm{LU}}$. The crosses are the extracted asymmetries and the solid line is the fit to these points using the function in Eq. (22). The open circles and the dotted line are the same for the simulated asymmetry.

Figure 15

Distribution of the means and standard deviations of the Gaussian functions for the photon and pion peaks for sub-bins of one kinematical bin: $1.7<Q^2<2.8$ (GeV/$c$)${}^2$ and $0.1<\left|t\right|<0.8$ (GeV/$c$)${}^2$.

Figure 16

Distribution of the (a) $\sin {\varphi }_{p\gamma }$ and (b) $\sin 2{\varphi }_{p\gamma }$ moments of the beam spin asymmetries for the $Q^2$ bin of $1.35\text{−}1.7$ (GeV/$c$)${}^2$ and $0.1<\left|t\right|<0.4$ (GeV/$c$)${}^2$, extracted from the fits to the missing mass squared distributions using different values of means and standard deviations of $G_{\gamma }$ and $G_{{\pi }^0}$ within $\pm 1$ rms.

Figure 17

Asymmetry $A_{\mathrm{LU}}$ as a function of azimuthal angle fitted according to Eq. (22) to extract the $\sin \varphi$ and $\sin 2\varphi$ moments in three $Q^2$ bins, see Table 3.

Figure 18

Asymmetry $A_{\mathrm{LU}}$ as a function of azimuthal angle fitted according to Eq. (22) to extract the $\sin \varphi$ and $\sin 2\varphi$ moments in three $t$ bins, see Table 4.

Figure 19

(a) $Q^2$ and (b) $t$ dependences of the $\sin {\varphi }_{p\gamma }$ moments of the DVCS asymmetry. The cross symbol is the asymmetry measured by CLAS with the $4.2$ GeV data. The curves are model calculations based on a Regge model for the photon-proton interaction (solid and dashed-dotted lines) [24] and on the GPD-based model (dashed and dotted lines) [25, 29]. Each curve represents different parameter settings (see text for details). In the plots the error bars are the combined statistical and systematical uncertainties added in quadrature.