Momentum transformation matrix for dielectron simulations in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76\ \mathrm{TeV}$

The measured invariant mass spectrum of dielectron pairs is affected by the finite momentum resolution of the detector, the energy loss of electrons and positrons in the detector material, and the tracking procedure. The unfolding of detector effects cannot be performed in multiple dimensions (invariant mass, pair-$p_{\mathrm{T}}$) simultaneously since $N$-dimensional detector response matrices with $N = 4$ would be required, for which an algebra cannot be defined. Moreover, a simplified approach based on one-dimensional unfolding methods cannot be performed due to instabilities of the existing algorithms in the resonance regions. A consistent comparison between the measured dielectron spectrum in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76\ \mathrm{TeV}$ and theoretical model calculations requires taking into account the detector effects on the generated dielectron spectrum. This note contains the description of the ALICE detector effects on electrons and positrons and illustrates how to transform the true momentum vector of electrons and positrons into its corresponding measurable momentum by using multidimensional detector response matrices obtained from Monte Carlo simulations. The detector response matrices described in this note are valid for the 2011 data taking period.