Distributive law between monads

In category theory, an abstract branch of mathematics, distributive laws between monads are a way to express abstractly that two algebraic structures distribute one over the other one.
Suppose that formula_1 and formula_2 are two monads on a category C. In general, there is no natural monad structure on the composite functor "ST". However, there is a natural monad structure on the functor "ST" if there is a distributive law of the monad "S" over the monad "T".
Formally, a distributive law of the monad "S" over the monad "T" is a natural transformation
such that the diagrams
commute.
This law induces a composite monad "ST" with