Mixed non-gaussianity from axion-gauge field dynamics

We study scalar-tensor-tensor cross correlation ≤ ζ hh ≤ generated by the dynamics of interacting axion and SU(2) gauge fields during inflation. We quantize the quadratic action and solve the linear equations by taking into account mixing terms in a non-perturbative manner. Combining that with the in-in formalism, we compute contributions from cubic interactions to the bispectrum B_{ζ hh}. We find that the bispectrum is peaked at the folded configuration, which is a unique feature encoded by the scalar mixing and localized production of tensor modes. With our parameter choice, the amplitude of the bispectrum is k⁶ B_{ζ hh} ∼ 10^-16. The unique shape dependence, together with the parity-violating nature, is thus a distinguishing feature to search for in the CMB observables.