Locally s-arc-transitive graphs arising from product action

We study locally s-arc-transitive graphs arising from the quasiprimitive product action (PA). prove that, for any (G,2)-arc-transitive graph with G acting quasiprimitively type PA on both G-orbits of vertices, group does not act primitively either orbit. Moreover, we construct first examples that are standard double covers type, answering existence question these graphs.