Dilepton production in proton-proton and quasifree proton-neutron reactions at 1.25 GeV

We investigate the $\mathit{pp}\to {\mathit{ppe}}^{+}{e}^{-}$ and quasifree $\mathit{pn}\to {\mathit{pne}}^{+}{e}^{-}$ reactions within an effective Lagrangian model at a laboratory kinetic energy of $1.25$ GeV for which experimental data have recently been reported by the HADES Collaboration. The model uses a meson-exchange approximation to describe the initial nucleon-nucleon ($\mathit{NN}$) scattering. Contributions to the reaction amplitudes are included from the $\mathit{NN}$ bremsstrahlung as well as from the excitation, propagation, and radiative decay of the $\Delta (1230)$ isobar state. It is found that the HADES data on the $e^{+}{e}^{-}$ invariant mass distribution in the $\mathit{pp}\to {\mathit{ppe}}^{+}{e}^{-}$ reaction are excellently reproduced by our model where the $\Delta$ isobar term dominates the spectrum. In the case of the quasifree $\mathit{pn}\to {\mathit{pne}}^{+}{e}^{-}$ reaction, a strong sensitivity to the pion electromagnetic form factor is observed which helps to bring the calculated cross sections closer to the data in the higher dilepton mass region.

Figure 1

Graphical representation of our model to describe $e^{+}{e}^{-}$ production in $\mathit{pp}$ and $\mathit{pn}$ collisions. Diagrams (a) and (b) represent the $e^{+}{e}^{-}$ emission from an external nucleon line. (c) $e^{+}{e}^{-}$ emission from an internal charged meson line for the $\mathit{pn}$ reaction. (d) Diagrams representing processes where $e^{+}{e}^{-}$ is emitted directly from the charged meson-nucleon-nucleon-photon vertices.

Figure 2

(a) The invariant mass distribution of the dileptons produced in the $\mathit{pp}\to {\mathit{ppe}}^{+}{e}^{-}$ reaction at a beam energy of 1.25 GeV. The maximum allowed value of $M$ is 0.545 GeV for this beam energy. (b) The same for the quasifree $\mathit{pn}\to {\mathit{pne}}^{+}{e}^{-}$ reaction at the same incident energy. The Fermi smearing as discussed in the text has been applied to all the theoretical calculations shown in Fig. 2(b). Experimental data are from Ref. [19].

Figure 3

(a) and (b) The same reactions as in Figs. 2a and 2(b) but with electromagnetic form factors included at pion and nucleon vertices. Also shown are the contributions of meson Dalitz decays and subthreshold $\rho {}^0$ decay processes. Total QM cross sections obtained with (FF2) and without (NEFF) electromagnetic form factors are shown by dashed and dashed-dotted lines, respectively. The simple sum of the meson Dalitz decays, $\rho {}^0$ decay, and full quantum mechanical (with FF2 form factors) cross sections are shown by the solid line. The data are taken from Ref. [19].