Simultaneous extraction of the weak radius and the weak mixing angle from parity-violating electron scattering on C12

We study the impact of nuclear structure uncertainties on a measurement of the weak charge of ${}^{12}\mathrm{C}$ at the future Mainz Energy Recovering Superconducting Accelerator (MESA) facility in Mainz. Information from a large variety of nuclear models, accurately calibrated to the ground-state properties of selected nuclei, suggest that a 0.3% precision measurement of the parity-violating asymmetry at forward angles will not be compromised by nuclear structure effects, thereby allowing a world-leading determination of the weak charge of ${}^{12}\mathrm{C}$. Furthermore, we show that a combination of measurements of the parity-violating asymmetry at forward and backward angles for the same electron-beam energy can be used to extract information on the nuclear weak charge distribution. We conclude that a 0.34% precision on the weak radius of ${}^{12}\mathrm{C}$ may be achieved by performing a 3% precision measurement of the parity-violating asymmetry at backward angles.