  New physics contributions to the (anti)neutrino-nucleon elastic scattering
process can be constrained by precision measurements, with controlled Standard
Model uncertainties. In a large class of new physics models, interactions
involving charged leptons of different flavor can be related, and the large
muon flavor component of accelerator neutrino beams can mitigate the lepton
mass suppression that occurs in other low-energy measurements. We employ the
recent high-statistics measurement of the cross section for $\bar{\nu}_\mu p
\to \mu^+ n$ scattering on the hydrogen atom by MINERvA to place new confidence
intervals on tensor and scalar neutrino-nucleon interactions: $\mathfrak{Re}
C_T = -1^{+14}_{-13} \times 10^{-4}$, $|\mathfrak{Im} C_T| \le 1.3 \times
10^{-3}$, and $|\mathfrak{Im} C_S| = 45^{+13}_{-19} \times 10^{-3}$. These
results represent a reduction in uncertainty by a factor of $2.1$, $3.1$, and
$1.2$, respectively, compared to existing constraints from precision beta
decay.
