Simultaneous measurements of the $\beta$ -neutrino angular correlation in $^{32}$Ar pure Fermi and pure Gamow-Teller transitions using $\beta$ -proton coincidences

We report first time measurements of the beta-neutrino angular correlation based on the kinetic energy shift of protons emitted in parallel or anti-parallel directions with respect to the positron in the beta decay of $^{32}$Ar. This proof of principle experiment provided simultaneous measurements for the superallowed 0$^+$~$\rightarrow$~0$^+$ transition followed by a 3356~keV proton emission and for a Gamow-Teller transition followed by a 2123~keV proton emission. The results, respectively ${\tilde a_{\beta\nu}}=1.01(3)_{(stat)}(2)_{(syst)}$ and ${\tilde a_{\beta\nu}}=-0.22(9)_{(stat)}(2)_{(syst)}$, are found in agreement with the Standard Model. A careful analysis of the data shows that future measurements can reach a precision level of 10$^{-3}$ for both pure Fermi and pure Gamow-Teller decay channels, providing new constraints on both scalar and tensor weak interactions.