On the Existence of Angular Correlations in Decays with Heavy Matter Partners

If heavy partners of the Standard Model matter fields are discovered at the LHC it will be imperative to determine their spin in order to uncover the underlying theory. In decay chains, both the spin and the mass hierarchy of all particles involved can influence the resulting angular correlations. We present the necessary conditions for decays involving the matter partners to exhibit angular correlations. In particular we find that when the masses are not degenerate, a heavy fermionic sector always displays angular correlations in cascade decays. When the masses are closely degenerate the size of spin effects is controlled by a global phase parameter. In a large region of the parameter space, correlations are strongly suppressed. In other regions, such as in UED model where this phase is fixed by 5-d Lorentz invariance, the correlations are pronounced. In addition, we show that in certain cases one may even have enough information to determine the spin of other heavy partners involved in the decay (such as the Lightest Stable Partner or a heavy gluon).