Specifically, a xaio/s is a shepherd's staff or crook.
This entry = Lexicum Ambrosianum 75 (according to Adler), ps.-Herodian 149, ps.-Zonaras 1842. See also Etymologicum Magnum 807.46 and the scholia to Apollonius Rhodius, Argonautica 4.972 (where the headword appears: web address 1 below).