Recoil proton polarization: A new discriminative observable for deeply virtual Compton scattering

Generalized parton distributions describe the correlations between the longitudinal momentum and the transverse position of quarks and gluons in a nucleon. They can be constrained by measuring photon leptoproduction observables, arising from the interference between Bethe-Heitler and deeply virtual Compton scattering (DVCS) processes. At leading-twist/leading-order, the amplitude of the latter is parametrized by complex integrals of the GPDs $\{H,E,\tilde{H},\tilde{E}\}$. As data collected on an unpolarized or longitudinally polarized target constrains $H$ and $\tilde{H}$, $E$ is poorly known as it requires data collected with a transversely polarized target, which is very challenging to implement in fixed-target experiments. The only alternative considered so far has been DVCS on a neutron with a deuterium target, while assuming isospin symmetry and absence of final-state interactions. Today, we introduce the polarization of the recoil proton as a new DVCS observable, highly sensitive to $E$, which appears feasible for an experimental study at a high-luminosity facility such as Jefferson Lab.

Figure 1

Diagrams of Bethe-Heitler (top) and DVCS (bottom). For Bethe-Heitler, the nucleon structure is parameterized by the form factors depending on $\mathrm{t}=|p^{\prime }-p{|}^2$. In DVCS, the GPDs parametrize the nucleon structure. In addition to t, they depend on $x$ and $\xi$ being respectively the average longitudinal momentum carried by the active quark and half the longitudinal momentum transfer to the proton.

Figure 2

The coordinate system in which $P^{\prime }$ is computed. The center of mass system of the hadronic plane, spanned by the directions of the recoil proton and the produced photon, is used. The $z^{\prime }$-axis is along the direction of the produced photon. The $y^{\prime }$-axis is normal to the hadronic plane, its direction given by the cross product of the directions of the virtual photon and the produced photon. The $x^{\prime }$-axis is in the hadronic plane, forming a right-handed coordinate system with the two other axes. The angle between the hadronic plane and the leptonic plane, spanned by the directions of the incident electron and the final electron, is denoted ${\varphi }_h$.

Figure 3

Top: the polarization along the $x$-axis (left), $y$-axis (middle), and $z$-axis (right) as a function of beam energy for the configuration $Q^2=1.8{\mathrm{GeV}}^2$, $x_B=0.17$, $t=-0.45{\mathrm{GeV}}^2$, ${\varphi }_h=180°$. The curves show the prediction from the GK model (plain black with $h_e=1$), and with one of the coefficients at a time switched off. Bottom: the difference between the polarization using all CFFs and the polarization setting a CFF to 0.

Figure 4

Top: the polarization along the $x$-axis (left), $y$-axis (middle) and $z$-axis (right) as a function of $Q^2$ for the configuration $E_k=10.6\mathrm{G}\mathrm{e}\mathrm{V}$, $x_B=0.17$, $t=-0.45{\mathrm{GeV}}^2$, ${\varphi }_h=180°$. The curves show the prediction from the GK model (plain black with $h_e=1$), and with one of the coefficients at a time switched off. Bottom: the difference between the polarization using all CFFs and the polarization setting a CFF to 0.

Figure 5

Top: the polarization along the $x$-axis (left), $y$-axis (middle) and $z$-axis (right) as a function of $x_B$ for the configuration $E_k=10.6\mathrm{G}\mathrm{e}\mathrm{V}$, $Q^2=1.8{\mathrm{GeV}}^2$, $t=-0.45{\mathrm{GeV}}^2$, ${\varphi }_h=180°$. The curves show the prediction from the GK model (plain black with $h_e=1$), and with one of the coefficients at a time switched off. Bottom: the difference between the polarization using all CFFs and the polarization setting a CFF to 0.

Figure 6

Top: The polarization along the $x$-axis (left), $y$-axis (middle) and $z$-axis (right) as a function of $t$ for the configuration $E_k=10.6\mathrm{G}\mathrm{e}\mathrm{V}$, $Q^2=1.8{\mathrm{GeV}}^2$, $x_B=0.17$, ${\varphi }_h=180°$. The curves show the prediction from the GK model (plain black with $h_e=1$), and with one of the coefficients at a time switched off. Bottom: The difference between the polarization using all CFFs and the polarization setting a CFF to 0.

Figure 7

Separation of the BH, interference and DVCS contributions to the recoil proton polarization for the configuration $E_k=10.6\mathrm{G}\mathrm{e}\mathrm{V}$, $Q^2=1.8\mathrm{G}\mathrm{e}{\mathrm{V}}^{\mathrm{2}}$, ${\mathrm{x}}_B=0.17$ and $t=-0.45\mathrm{G}\mathrm{e}{\mathrm{V}}^{\mathrm{2}}$. The top row displays the beam-helicity independent polarization ($P^u$) while bottom row shows the beam-helicity dependent terms ($P^h$) as a function of ${\varphi }_h$.

Figure 8

Top: the polarization along the $x$-axis (left), $y$-axis (middle) and $z$-axis (right) as a function of ${\varphi }_h$ for the configuration $E_k=10.6\mathrm{G}\mathrm{e}\mathrm{V}$, $Q^2=1.8{\mathrm{GeV}}^2$, $x_B=0.17$, $t=-0.45{\mathrm{GeV}}^2$. The curves show the prediction from the GK model (plain black with $h_e=1$, dashed gray for $h_e=-1$) and with one of the coefficients at a time switched off. Bottom: the difference between the polarization using all CFFs and the polarization setting a CFF to 0.

Figure 9

The derivative of $P_x^m$ (left), $P_y^m$ (middle) and $P_z^m$ with respect to the real part (top) or imaginary part (bottom) of each CFF as a function of ${\varphi }_h$ for $E_k=10.6\mathrm{G}\mathrm{e}\mathrm{V}$, $Q^2=1.8{\mathrm{GeV}}^2$, $x_B=0.17$, $t=-0.45{\mathrm{GeV}}^2$ and $h_e=1$.

Figure 10

The azimuthal rescattering angle ${\varphi }_{\mathrm{pol}}$ for ${\theta }_{\mathrm{pol}}$ in the range 4°–19° when subtracting over helicities, which gives sensitivity to $P_x^m$ (left) and when adding all events, which gives sensitivity to $P_y^m$ (right). The dotted lines show the NN replicas, with the 68% confidence level band shown in turquoise. The pseudodata is shown in black dots and the fit to pseudodata (referred to as PoPEx) in blue, with the blue band illustrating the statistical uncertainty on the fit result. The GK, VGG and KM15 models are shown for comparison in red, purple and green respectively.

Figure 11

A scan over differential efficiency (left), analyzing power (center), and $F^2$ (right) as a function of the kinetic energy in the center of the analyzer. The shown range corresponds to a proton momentum of $320–1290\mathrm{MeV}/\mathrm{c}$ at the center of the analyzer.

Figure 12

The differential efficiency (left) and analyzing power (right) as a function of ${\theta }_{\mathrm{pol}}$ for a proton with kinetic energies of 90, 190 and 290 MeV at the center of the carbon analyzer.