  We continue the program of extending the scattering equation framework by
Cachazo, He and Yuan to a double-cover prescription. We discuss how to apply
the double-cover formalism to effective field theories, with a special focus on
the non-linear sigma model. A defining characteristic of the double-cover
formulation is the emergence of new factorization relations. We present several
factorization relations, along with a novel recursion relation. Using the
recursion relation and a new prescription for the integrand, any non-linear
sigma model amplitude can be expressed in terms of off-shell three-point
amplitudes. The resulting expression is purely algebraic, and we do not have to
solve any scattering equation. We also discuss soft limits, boundary terms in
BCFW recursion, and application of the double-cover prescription to other
effective field theories, like the special Galileon theory.
