Backward-angle ($u$-channel) production at an electron-ion collider

In backward photoproduction of mesons, the produced vector meson takes most of the struck nucleon momentum. The nucleon loses most of its momentum, and so is shifted several units of rapidity. Thus the Mandelstam $u$ is small, while the squared momentum transfer $t$ is typically large, near the kinematic limit. In a collider geometry, backward production transfers the struck baryon by many units of rapidity, in a striking similarity to baryon stopping. We explore this similarity, and point out the similarities between the Regge theories used to model baryon stopping with those that are used for backward production. We then explore how backward production can be explored at higher energies than are available at fixed target experiments, by studying production at an electron-ion collider. We calculate the expected $ep$ cross sections and rates, finding that the rate for backward $\omega$ production is about 1/300 that of forward $\omega \mathrm{s}$. We discuss the kinematics of backward production and consider the detector requirements for experimental study. We demonstrate that an experiment at the proposed U.S. Electron-Ion Collider will have the capability to detect backward-production events and may provide a test for models of stopping in high-energy $ep$ collisions including the baryon-junction model.

Figure 1

Schematic diagrams showing (a) forward $\omega$ production and (b) backward $\omega$ production. In backward production, the $\omega$ and the proton essentially swap places (in rapidity, with respect to the $\gamma p$ center of mass). The right-hand plot shows the cross sections as a function of $W$ for forward and backward $\omega$ production.

Figure 2

The proton and meson rapidities for $\omega$ (top row) and ${\rho }^0$ (bottom row) $u$-channel photoproduction and electroproduction at several EIC energies. The magenta distributions are for photoproduction, while the black are for electroproduction. The shaded histograms show the vector meson, while the unshaded ones are for the scattered proton. The nonzero photon $Q^2$ shifts both distributions slightly toward negative rapidity.

Figure 3

Proton $p_T$ spectra for $u$-channel $\omega$ and ${\rho }^0$ electroproduction (black) and photoproduction (magenta).

Figure 4

Proton $p_T$ for $u$-channel $\omega$ electroproduction (black) and photoproduction (magenta) as a function of the proton rapidity.

Figure 5

Pion pseudorapidity distributions from polarized (red) and unpolarized (blue) $u$-channel $\rho$ photoproduction at $10\times 100$ GeV.

Figure 6

Vector-meson decay daughter pseudorapidity distributions for $u$-channel $\omega \to {\pi }^0\gamma$ and ${\rho }^0\to {\pi }^{+}{\pi }^{-}$ electroproduction (black) and photoproduction (magenta).

Figure 7

Pseudorapidity distributions of photons from $u$-channel $\omega$ production at three EIC $ep$ collision energies. The shaded colored regions show the acceptance in pseudorapidity of the central, B0, and forward detectors. The top row two-dimensional scatter plots show the pseudorapidity of the photon from the $\omega$ decay and one of the photons from the ${\pi }^0$, while the bottom row shows the pseudorapidities of the two photons from the daughter ${\pi }^0$.

Figure 8

Scatter plot of the pseudorapidity distribution of ${\pi }^{\pm }$ from $u$-channel ${\rho }^0$ production at three EIC energies. The shaded colored regions show the acceptance in pseudorapidity of the central and B0 detectors.