Kinked tracks from $\Sigma^+$ baryons as a probe of light quark polarizations

Jets initiated by energetic quarks carry in an obvious way approximate information about the original quark energy and momentum. In a less obvious way, they also carry information about the quark polarization. Previous works have shown how the polarization information can be extracted by ATLAS and CMS using events in which the quark hadronizes to an energetic baryon - $\Lambda_b$ for $b$ quarks, $\Lambda_c$ for $c$ quarks and $\Lambda$ for $s$ quarks. In this paper we extend these proposals to $\Sigma^+$ baryons, which can provide sensitivity to polarizations of $s$ and $u$ quarks. We analyze the various aspects of how the kinked track signature of the $\Sigma^+ \to p \pi^0$ decay can be used for this purpose. We evaluate the feasibility of such measurements in $t\bar t$ samples.