 B411 contribution to the one-loop matter bispectrum

ID: b411-contribution-to-the-one-loop-matter-bispectrum

The connected correlation of one fourth-order and two first-order density contrasts contracts a pair of inputs at the fourth-order vertex into a loop. For each choice of the fourth-order external field there are twelve Wick contractions. In one dimension,

B_{411} = 12 P_{L} (k_{1}) P_{L} (k_{2}) \int \frac{d q}{2 π} F_{4} (- k_{1}, - k_{2}, q, - q) P_{L} (q) + two cyclic terms .

F_{4} = - k_{3}^{4} / (24 k_{1} k_{2} q^{2})

exactly. Its leading cutoff dependence is therefore proportional to

k_{3}^{2} F_{2} (k_{1}, k_{2}) P_{L} (k_{1}) P_{L} (k_{2}) \int d q P_{L} (q) / q^{2}

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