Weak charge and weak radius of ${}^{12}$C

We present a feasibility study of a simultaneous sub-percent extraction of the weak charge and the weak radius of the ${}^{12}$C nucleus using parity-violating electron scattering, based on a largely model-independent assessment of the uncertainties. The corresponding measurement is considered to be carried out at the future MESA facility in Mainz with $E_{rm beam} = 155$ MeV. We find that a combination of a $0.3%$ precise measurement of the parity-violating asymmetry at forward angles with a $10%$ measurement at backward angles will allow to determine the weak charge and the weak radius of ${}^{12}$C with $0.4%$ and $0.5%$ precision, respectively. These values could be improved to $0.3%$ and $0.2%$ for a $3%$ backward measurement. This experimental program will have impact on precision low-energy tests in the electroweak sector and nuclear structure.