Inclusive e$^+$e$^-$ production in collisions of pions with protons and nuclei in the second resonance region of baryons

TL;DR

This study investigates inclusive dielectron production in pion-proton and pion-nucleus collisions near the baryon resonance region, highlighting the importance of vector meson dominance models and baryon transition form factors.

Contribution

It provides a detailed comparison of vector meson dominance models and baryon transition form factors against experimental data, revealing the significance of the pion cloud in dielectron yields.

Findings

VMD1 model fits data well, VMD2 overestimates yields

Baryon contribution shows up to sevenfold deviation from QED point-like expectation

Time-like baryon transition form factors are strongly momentum-dependent

Abstract

Inclusive e$^+$e$^-$ production has been studied with HADES in $\pi^-$ + p, $\pi^-$ + C and $\pi^- + \mathrm{CH}_2$ reactions, using the GSI pion beam at $\sqrt{s_{\pi p}}$ = 1.49 GeV. Invariant mass and transverse momentum distributions have been measured and reveal contributions from Dalitz decays of $\pi^0$, $\eta$ mesons and baryon resonances. The transverse momentum distributions are very sensitive to the underlying kinematics of the various processes. The baryon contribution exhibits a deviation up to a factor seven from the QED reference expected for the dielectron decay of a hypothetical point-like baryon with the production cross section constrained from the inverse $\gamma$ n$\rightarrow \pi^-$ p reaction. The enhancement is attributed to a strong four-momentum squared dependence of the time-like electromagnetic transition form factors as suggested by Vector Meson Dominance (VMD). Two versions of the VMD, that differ in the photon-baryon coupling, have been applied in simulations and compared to data. VMD1 (or two-component VMD) assumes a coupling via the $\rho$ meson and a direct coupling of the photon, while in VMD2 (or strict VMD) the coupling is only mediated via the $\rho$ meson. The VMD2 model, frequently used in transport calculations for dilepton decays, is found to overestimate the measured dielectron yields, while a good description of the data can be obtained with the VMD1 model assuming no phase difference between the two amplitudes. Similar descriptions have also been obtained using a time-like baryon transition form factor model where the pion cloud plays the major role.