Scale-dependent bias with higher order primordial non-Gaussianity: Use of the integrated perturbation theory

We analytically derive a more accurate formula for the power spectrum of the biased objects with the primordial non-Gaussianity parametrized not only by the nonlinearity parameter fNL, but also by gNL and τNL which characterize the trispectrum of the primordial curvature perturbations. We adopt the integrated perturbation theory which was constructed in Matsubara [Phys. Rev. D 83, 083518 (2011)]. We discuss an inequality between fNL and τNL in the context of the scale-dependent bias, by introducing a stochasticity parameter. We also mention higher order loop corrections in the scale dependency of the bias parameter.