Simultaneous extraction of the weak radius and the weak mixing angle from parity-violating electron scattering on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">C</mml:mi><mml:mprescripts/><mm

We study the impact of nuclear structure uncertainties on a measurement of the weak charge of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mmultiscripts><a:mi mathvariant="normal">C</a:mi><a:mprescripts/><a:none/><a:mn>12</a:mn></a:mmultiscripts></a:math> 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mmultiscripts><c:mi mathvariant="normal">C</c:mi><c:mprescripts/><c:none/><c:mn>12</c:mn></c:mmultiscripts></c:math>. 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mmultiscripts><e:mi mathvariant="normal">C</e:mi><e:mprescripts/><e:none/><e:mn>12</e:mn></e:mmultiscripts></e:math> may be achieved by performing a 3% precision measurement of the parity-violating asymmetry at backward angles. Published by the American Physical Society 2024