Sunset diagram

A sunset diagram is a two-point diagram with two interaction vertices joined by three internal propagators. Its dependence on the external momentum produces wave-function renormalization in scalar quartic theory.

In a massive two-dimensional quartic scalar field theory, the two-loop sunset diagram is ultraviolet finite but changes the pole mass. Feynman parameters give, below the three-particle threshold,At $s=m^2$ the denominator is positive in the interior of the simplex, and its corners are integrable. Thus the result is finite and nonzero for $g_4\ne 0$. Absence of new divergent counterterms does not imply absence of finite mass counterterms in an on-shell renormalization scheme.