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The two-channel Anderson lattice model which has $SU(2)\otimes SU(2)$symmetry is of relevance to understanding of the magnetic, quadrupolar andsuperconducting phases in U$_{1-x}$Th$_x$Be$_{13}$ or Pr base skutteruditecompounds such as PrFe$_4$P$_{12}$ or PrOs$_4$Sb$_{12}$. Possibleunconventional superconducting phases of the model are explored. They arecharacterized by a composite order parameter comprising of a local magnetic orquadrupolar moment and a triplet conduction electron Cooper-pair. This bindingof local degrees of freedom removes the entropy of the non Fermi-liquid normalstate. We find superconducting transitions in the intermediate valence regimewhich are suppressed in the stable moment regime. The gap function is nonanalytic and odd in frequency: a pseudo-gap develops in the conduction electrondensity of states which vanishes as $|\omega|$ close to $\omega=0$. In thestrong intermediate valent regime, the gap function acquires an additional$\k$-dependence.Comment: 20 pages, 12 figures, latex EPJ format. Accepted for publication as  Eur.Phys.J.

Composite spin-triplet superconductivity in an $ \mathsf {SU(2)\otimes SU(2)}$ symmetric lattice model