  Benchmark reactions involving molecular hydrogen, such as H$_2$+D or
H$_2$+Cl, provide the ideal platforms to investigate the effect of Near
Threshold Resonances (NTR) on scattering processes. Due to the small reduced
mass of those systems, shape resonances due to particular partial waves can
provide features at scattering energies up to a few Kelvins, reachable in
recent experiments. We explore the effect of NTRs on elastic and inelastic
scattering for higher partial waves $\ell$ in the case of H$_2$+Cl for $s$-wave
and H$_2$+D for $p$-wave scattering, and find that NTRs lead to a different
energy scaling of the cross sections as compared to the well known Wigner
threshold regime. We give a theoretical analysis based on Jost functions for
short range interaction potentials. To explore higher partial waves, we adopt a
three channel model that incorporates all key ingredients, and explore how the
NTR scaling is affected by $\ell$. A short discussion on the effect of the
long-range form of the interaction potential is also provided.
