A general method for model-independent measurements of particle spins, couplings and mixing angles in cascade decays with missing energy at hadron colliders

We outline a general strategy for measuring spins, couplings and mixing angles in the case of a heavy partner decay chain terminating in an invisible particle. We consider the common example of a heavy scalar or fermion D decaying sequentially to other heavy particles C, B and A by emitting a quark jet j and two leptons ℓ _n and ℓ ^± _f. We derive analytic formulas for the dilepton (ℓ ⁺ℓ ^-) and the two jet-lepton (jℓ _n and jℓ _f) invariant mass distributions for the case of most general couplings and mixing angles of the heavy partners. We then consider various spin assignments for the heavy particles A, B, C and D, and for each case, derive the relevant functional basis for the invariant mass distributions which contains the intrinsic spin information and does not depend on the couplings and mixing angles. We propose a new method for determining the spins of the heavy partners, using the three experimentally observable distributions ℓ ⁺ℓ ^-, jℓ ⁺+jℓ ^- and jℓ ⁺-jℓ ^-. We show that the former two only depend on a single model-dependent parameter α, while the latter may depend on two other parameters β and γ. By fitting these distributions to our set of basis functions, we are able to do a pure measurement of the spins per se. Our method is also applicable at a p collider such as the Tevatron, for which the previously proposed lepton charge asymmetry is identically zero and does not contain any spin information. In the process of determining the spins, we also end up with an independent measurement of the parameters α, β and γ, which represent certain combinations of the couplings and the mixing angles of the heavy partners A, B, C and D.