  We study higher genus Fan--Jarvis--Ruan--Witten theory of any chain
polynomial with any group of symmetries. Precisely, we give an explicit way to
compute the cup product of Polishchuk and Vaintrob's virtual class with the top
Chern class of the Hodge bundle. Our formula for this product holds in any
genus and without any assumption on the semi-simplicity of the underlying
cohomological field theory.
