Helicity Decomposition of Ghost-free Massive Gravity
  We perform a helicity decomposition in the full Lagrangian of the class of
Massive Gravity theories previously proven to be free of the sixth (ghost)
degree of freedom via a Hamiltonian analysis. We demonstrate, both with and
without the use of nonlinear field redefinitions, that the scale at which the
first interactions of the helicity-zero mode come in is $\Lambda_3=(M_Pl
m^2)^{1/3}$, and that this is the same scale at which helicity-zero
perturbation theory breaks down. We show that the number of propagating
helicity modes remains five in the full nonlinear theory with sources. We
clarify recent misconceptions in the literature advocating the existence of
either a ghost or a breakdown of perturbation theory at the significantly lower
energy scales, $\Lambda_5=(M_Pl m^4)^{1/5}$ or $\Lambda_4=(M_Pl m^3)^{1/4}$,
which arose because relevant terms in those calculations were overlooked. As an
interesting byproduct of our analysis, we show that it is possible to derive
the Stueckelberg formalism from the helicity decomposition, without ever
invoking diffeomorphism invariance, just from a simple requirement that the
kinetic terms of the helicity-two, -one and -zero modes are diagonalized.
