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I know that higher point scattering amplitudes at a sufficiently high loop level have branch cuts and discontinuities. I wonder whether the number of scattering particles plays a role in this?

Is there a quick way to argue whether three-point scattering amplitudes (in any example theory) have branch cuts at a sufficiently high loop order?

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Considering that simple one-loop integrals as evaluated in the paper Scalar one-loop integrals feature functions such as square roots and logarithms for two- and three-point cases, it is clear that three-point amplitudes may develop branch cuts as soon as at one-loop level.

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