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The electroweak interaction in the Standard Model (SM) is described by a pure vector-axial-vector structure, though any Lorentz-invariant component could contribute. In this work, we present the most precise measurement of tensor currents in the low-energy regime by examining the $\beta$-$\bar{\nu}$ correlation of trapped $^{8}$Li ions with the Beta-decay Paul Trap. We find $a_{\beta\nu} = -0.3325 \pm 0.0013_{stat} \pm 0.0019_{syst}$ at $1\sigma$ for the case of coupling to right-handed neutrinos $(C_T=-C_T')$, which is consistent with the SM prediction., Comment: 6 pages, 3 figures, 1 table

We place unprecedented constraints on recoil corrections in the $\beta$ decay of $^8$Li, by identifying a strong correlation between them and the $^8$Li ground state quadrupole moment in large-scale ab initio calculations. The results are essential for improving the sensitivity of high-precision experiments that probe the weak interaction theory and test physics beyond the Standard Model (BSM). In addition, our calculations predict a $2^+$ state of the $\alpha+\alpha$ system that is energetically accessible to $\beta$ decay but has not been observed in the experimental $^8$Be energy spectrum, and has an important effect on the recoil corrections and $\beta$ decay for the $A=8$ systems. This state and an associated $0^+$ state are notoriously difficult to model due to their cluster structure and collective correlations, but become feasible for calculations in the ab initio symmetry-adapted no-core shell-model framework., Comment: Accepted version