Abstract: Physics of the up-type flavor offers unique possibilities of testing the standard model (SM) compared to the down-type flavor sector. Here, we discuss SM and new physics (NP) contributions to the rare charmmeson decay D0 -> x+x- l+l-. In particular, we discuss the effect of including the lightest scalar isoscalar resonance in the SM picture, namely, the f0(500), which manifests in a big portion of the allowed phase space. Other than showing in the total branching ratio at an observable level of about 20%, the f0(500) resonance manifests as interference terms with the vector resonances, such as at high invariant mass of the leptonic pair in distinct angular observables. Recent data from LHCb optimize the sensitivity to P-wave contributions that we analyze in view of the inclusion of vector resonances. We propose the measurement of alternative observables that are sensitive to the S-wave and are straightforward to implement experimentally. This leads to a new set of null observables that vanish in the SM due to its gauge and flavor structures. Finally, we study observables that depend on the SM interference with generic NP contributions from semileptonic four-fermion operators in the presence of the S-wave.