New constraints on primordial non-Gaussianity from missing two-loop contributions of scalar induced gravitational waves

We analyze the energy density spectrum of scalar induced gravitational waves (SIGWs) using the NANOGrav 15-year data set, thereby constraining the primordial non-Gaussian parameter f(NL). For the first time, we calculate the seventeen missing two-loop diagrams proportional to f(NL)A(zeta)(3) that correspond to the two-point correlation function < h(k )(lambda,(3))h(k ')(lambda ',(2))> for local-type primordial non-Gaussianity. The total energy density spectrum of SIGWs can be significantly suppressed by these two-loop diagrams. If SIGWs dominate the stochastic gravitational wave backgrounds observed in pulsar timing array experiments, the parameter interval f(NL )is an element of [-5,-1] is notably excluded based on NANOGrav 15-year data set. After taking into account abundance of primordial black holes and the convergence of the cosmological perturbation expansion, we find that the only possible parameter range for f(NL) might be -1 <= f(NL) < 0.