Self energies of the pion and the delta isobar from the ^3He(e,e'pi^+)^3H reaction

Abstract

In a kinematically complete experiment at the Mainz microtron MAMI, pion angular distributions of the ${}^3$He(e,e'${\pi }^{+}{)}^3$H reaction have been measured in the excitation region of the $\Delta$ resonance to determine the longitudinal ($L$), transverse ($T$), and the $LT$ interference part of the differential cross section. The data are described only after introducing self-energy modifications of the pion and $\Delta$-isobar propagators. Using Chiral Perturbation Theory (ChPT) to extrapolate the pion self energy as inferred from the measurement on the mass shell, we deduce a reduction of the ${\pi }^{+}$ mass of $\Delta m_{{\pi }^{+}}=(-1.7_{-2.1}^{+1.7})$ MeV/c${}^2$ in the neutron-rich nuclear medium at a density of $\rho =(0.057_{-0.057}^{+0.085})$ fm${}^{-3}$. Our data are consistent with the $\Delta$ self energy determined from measurements of ${\pi }^0$ photoproduction from ${}^4$He and heavier nuclei.

arXiv commentElsart, 12 pages and 4 figures, Correspondent: Professor Dr. Dr. h.c. mult. Achim Richter, [email protected], submitted to Phys. Rev. Lett

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