Superallowed 0^+ rightarrow 0^+ β decay studies at GANIL and upcoming opportunities with DESIR and S³-LEB

Corrected transition rates ($\mathcal{F}t^{0^+ \rightarrow 0^+}$) of $0^+ \rightarrow 0^+$ superallowed $\beta$ decays currently give the most precise value of $V_{ud}$, the dominant term of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix. By setting stringent constrains on the CKM unitarity, these decays allow probing physics beyond the Standard Model in the electroweak sector. A recent global reevaluation of the $\mathcal{F}t^{0^+ \rightarrow 0^+}$ values has indicated a violation of CKM unitarity prompting reassessment of the theoretical radiative and isospin symmetry breaking corrections applied on the experimental transition rates $ft$. In this article we briefly discuss this current situation and the experimental program at GANIL geared towards constraining isospin symmetry breaking corrections. We conclude by presenting the opportunities that will be available at DESIR and S$^3$-LEB, the upcoming low-energy radioactive ion beam facilities at GANIL.