Toward precise QEC values for the superallowed 0⁺→0 ⁺ β decays of T=2 nuclides: The masses of Na20, Al24, P28, and Cl32

High-precision measurements of superallowed 0⁺→0 ⁺ β decays of T=2 nuclides such as Mg20, Si24, S28, and Ar32 can contribute to searches for physics beyond the standard model of particle physics if the QEC values are accurate to a few keV or better. As a step toward providing precise QEC values for these decays, the ground-state masses of the respective daughter nuclei Na20, Al24, P28, and Cl32 have been determined by measuring the (He3,t) reactions leading to them with the Ar36(He3,t)K36 reaction as a calibration. A quadrupole-dipole-dipole-dipole (Q3D) magnetic spectrograph was used together with thin ion-implanted carbon-foil targets of Ne20, Mg24, Si28, S32, and Ar36. The masses of Na20 and Cl32 are found to be in good agreement with the values from the 2003 Atomic Mass Evaluation (AME03), and the precision has been improved by a factor of 6 in both cases. The masses of Al24 and P28 are found to be higher than the values from AME03 by 9.5 keV (3.2σ) and 11.5 keV (3.6σ), respectively, and the precision has been improved by a factor of 2.5 in both cases. The new Cl32 mass is used together with the excitation energy of its lowest T=2 level and the mass of Ar32 to derive an improved superallowed QEC value of 6087.3(22) keV for this case. The effects on quantities related to standard-model tests including the β-ν correlation coefficient a and the isospin-symmetry-breaking correction δC are examined for the A=32 case.