Probing novel scalar and tensor interactions from (ultra)cold neutrons to the LHC

Scalar and tensor interactions were once competitors to the now well-established $V\ensuremath{-}A$ structure of the standard model weak interactions. We revisit these interactions and survey constraints from low-energy probes (neutron, nuclear, and pion decays) as well as collider searches. Currently, the most stringent limit on scalar and tensor interactions arise from ${0}^{+}\ensuremath{\rightarrow}{0}^{+}$ nuclear decays and the radiative pion decay $\ensuremath{\pi}\ensuremath{\rightarrow}e\ensuremath{\nu}\ensuremath{\gamma}$, respectively. For the future, we find that upcoming neutron beta decay and LHC measurements will compete in setting the most stringent bounds. For neutron beta decay, we demonstrate the importance of lattice computations of the neutron-to-proton matrix elements to setting limits on these interactions, and provide the first lattice estimate of the scalar charge and a new average of existing results for the tensor charge. Data taken at the LHC is currently probing these interactions at the ${10}^{\ensuremath{-}2}$ level (relative to the standard weak interactions), with the potential to reach the $\ensuremath{\lesssim}{10}^{\ensuremath{-}3}$ level. We show that, with some theoretical assumptions, the discovery of a charged spin-0 resonance decaying to an electron and missing energy implies a lower limit on the strength of scalar interactions probed at low energy.