Supertwistor formulation for massless superparticle in AdS₅ × S⁵ superspace

Starting with the first-order formulation of the massless superparticle model on the $Ad{S}_5\times S^5$ superbackground and presenting the momentum components tangent to $Ad{S}_5$ and $S^5$ subspaces as bilinear combinations of the constrained $SU\left(2\right)$-Majorana spinors allows to bring the superparticle's Lagrangian to the form quadratic in supertwistors. The $SU(2,2|4)$ supertwistors are assembled into a pair of $SU\left(2\right)$ doublets, one of which has even $SU(2,2)$ and odd $SU\left(4\right)$ components, while the other has odd $SU(2,2)$ and even $SU\left(4\right)$ components. They are subject to the first-class constraints that generate the $psu\left(2\right|2)\oplus u(1)$ gauge algebra. This justifies previously proposed group-theoretic definition of the $Ad{S}_5\times S^5$ supertwistors and allows to derive the incidence relations with the $\left(10\right|32)$ supercoordinates of the $Ad{S}_5\times S^5$ superspace. Whenever superparticle moves within the $Ad{S}_5$ subspace of the $Ad{S}_5\times S^5$ space-time, twistor formulation of its Lagrangian involves just one $SU\left(2\right)$ doublet of $SU(2,2|4)$ supertwistors with even $SU(2,2)$ and odd $SU\left(4\right)$ components. If in addition particle's 5-momentum is null, four first-class constraints which are the $su\left(2\right)\oplus u\left(1\right)$ generators single out upon quantization the states of $D=5$ $N=8$ gauged supergravity multiplet in the superambitwistor formulation.