  We investigate the dynamical self-energy corrections of the electron-hole
plasma due to electron-electron and electron-phonon interactions at the band
edges of a quasi-one dimensional (1D) photoexcited electron-hole plasma. The
leading-order $GW$ dynamical screening approximation is used in the calculation
by treating electron-electron Coulomb interaction and electron-optical phonon
Fr\"{o}hlich interaction on an equal footing. We calculate the
exchange-correlation induced band gap renormalization (BGR) as a function of
the electron-hole plasma density and the quantum wire width. The calculated BGR
shows good agreement with existing experimental results, and the BGR normalized
by the effective quasi-1D excitonic Rydberg exhibits an approximate
one-parameter universality.
