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We discuss the type of pairing in the hexagonal pnictide superconductorSrPtAs, taking into account its multiband structure. The topological chiral$d$-wave state with time-reversal-symmetry breaking has been anticipated fromthe spontaneous magnetization observed by the muon-spin-relaxation experiment.We point out in this paper that the recent experimental reports on thenuclear-spin-lattice relaxation rate $T_1^{-1}$ and superfluid density$n_s(T)$, which seemingly support the conventional $s$-wave pairing, are alsoconsistent with the chiral $d$-wave state. The compatibility of the gap andmultiband structures is crucial in this argument.

Possibility of chiral $d$-wave state in the hexagonal pnictide superconductor SrPtAs