  We derive new effective field theory (EFT) positivity bounds on the elastic
$2\to2$ scattering amplitudes of massive spinning particles from the standard
UV properties of unitarity, causality, locality and Lorentz invariance. By
bounding the $t$ derivatives of the amplitude (which can be represented as
angular momentum matrix elements) in terms of the total ingoing helicity, we
derive stronger unitarity bounds on the $s$- and $u$-channel branch cuts which
determine the dispersion relation. In contrast to previous positivity bounds,
which relate the $t$-derivative to the forward-limit EFT amplitude with no $t$
derivatives, our bounds establish that the $t$-derivative alone must be
strictly positive for sufficiently large helicities. Consequently, they provide
stronger constraints beyond the forward limit and can be used to constrain
dimension-6 interactions with a milder assumption about the high-energy growth
of the UV amplitude.
