Deeply virtual meson production on neutrons

In this paper we analyze in detail how the measurements of exclusive electroproduction of mesons on neutrons would complement the studies of generalized parton distributions (GPDs) of the proton, providing independent experimental observables. Some of these processes on neutrons have very distinctive features, and thus we expect that measurements on liquid deuterium would allow to clearly distinguish them from similar processes on protons, giving a very clean probe of the GPD. In the case of charged meson production, all produced hadrons are charged, and for this reason we expect that the kinematics of this process could be easily reconstructed. We estimate the cross sections in the kinematics of the Jefferson Laboratory experiments using current phenomenological GPD models.

Figure 1

Leading-order contributions to the DVMP hard coefficient functions, $s$-channel (left) and $u$-channel (right). The horizontal green blob stands for the generalized parton distributions of the parton, and the upper (small) green blob is the wave function of the produced meson. In the next-to-leading order, we should add additional gluon in all possible ways to the upper part of the diagram. The two-parton twist-3 contributions have the same structure.

Figure 2

Left: Different components of charged pion production on a neutron, $en\to e{\pi }^{-}p$. The dominant contribution to the total cross section (solid line) comes from the longitudinal cross section $d{\sigma }_L/dt$ due to the $t$-channel pion pole. At larger $t$ the contributions of transversity GPDs become comparable to the leading-twist contribution $d{\sigma }_L/dt$. Right: Comparison of leading twist cross sections, taking into account the pole term (solid curve, marked with symbol “$L$”) and without it (dashed curve, marked with symbol “$L^{\prime }$”). Also, in the same plot we have shown the NLO corrections to the coefficient functions. For the ease of comparison, in both plots we have chosen the same values of $W$, $Q^2$ as in [55]. The value of Bjorken $x_B$ is $x_B\approx 0.2$.

Figure 3

Left: Different components of neutral pion production on the neutron, $en\to e{\pi }^{0}p$. The dominant contribution to the total cross section (solid line) comes from the transverse cross section $d{\sigma }_T/dt$. Other components (not shown) are negligible. Right: The same plot for the incoherent process on the deuteron, $eD\to e{\pi }^{0}pn$. For ease of comparison, in both plots we have chosen the same values of $W$, $Q^2$ as in [55]. The value of the Bjorken $x_B$ is $x_B\approx 0.2$.

Figure 4

Cross sections for the strangeness production on the neutron. In case of ${\gamma }^{*}n\to K^{+}{\mathrm{\Sigma }}^{-}$ and ${\gamma }^{*}n\to K^0{\mathrm{\Sigma }}^0$ the dominant contribution to the total cross section (solid line) comes from the transverse cross section $d{\sigma }_T/dt$. In the process ${\gamma }^{*}n\to K^0\mathrm{\Lambda }$ the dominant contribution comes from $d{\sigma }_L/dt$ (dashed line) which is mildly enhanced at small-$t^{\prime }$ due to kaon pole (39). For the ease of comparison, in both plots we have chosen the same values of $W$, $Q^2$ as in [55]. The value of the Bjorken $x_B$ is $x_B\approx 0.2$.