Iwasawa $\lambda$ invariant and Massey product

We compute Iwasawa $\lambda$ invariant in terms of Massey products in Galois cohomology with restricted ramification. When applied to imaginary quadratic fields and cyclotomic fields, we obtain a new proof and generalization of results of Gold and McCallum-Sharifi. The main tool is the generalized Bockstein map introduced by Lam-Liu-Sharifi-Wake-Wang.