  We develop a (largely conjectural) theory of p-adic L-functions interpolating
square roots of central L-values for automorphic forms on GSp(4) x GL(2) x
GL(2), and a relation between these p-adic L-functions and families of Galois
cohomology classes interpolating algebraic cycles. Our theory is a
generalisation of the theory of "diagonal cycles" developed by Darmon and
Rotger for the GL(2) triple product.
