Abstract
We derive new convergent series representations for the two-loop sunset diagram with three different propagator masses m_1,, m_2 and m_3 and external momentum p by techniques of analytic continuation on a well-known triple series that corresponds to the Lauricella F_C^{(3)} function. The convergence regions of the new series contain regions of interest to physical problems. These include some ranges of masses and squared external momentum values which make them useful from Chiral Perturbation Theory to some regions of the parameter space of the Minimal Supersymmetric Standard Model. The analytic continuation results presented for the Lauricella series could be used in other settings as well.
Highlights
The sunset integral is among the simplest of two-loop integrals that appear in the perturbation expansion of quantities in various quantum field theories, including the Standard Model (SM)
We return to the most general massive sunset and we show that, as discussed in the conclusion and outlook section of [1], an analytic continuation procedure applied to the expressions presented in terms of Lauricella series in the latter paper allows one to provide new series representations of the sunset diagram, giving access to some ranges of values of the masses and squared external momentum which are not accessible using the results of [1]
We have provided new series representations Si (i = 5, ..., 10) for the two-loop sunset diagram with four mass scales, following an analytic continuation procedure that we have applied to an old series representation of the sunset diagram given in [1] in terms of Lauricella FC(3) series
Summary
The sunset integral is among the simplest of two-loop integrals that appear in the perturbation expansion of quantities in various quantum field theories, including the Standard Model (SM). Instead of considering the most general two-loop sunset integral as in [1], we have focused on the particular sunset configurations needed in ChPT: we have developed the Mellin-Barnes approach to evaluate the ChPT sunsets and analytical results were presented in terms of double series of Kampé de Fériet type (details of this derivation will be given in [14]). We return to the most general massive sunset and we show that, as discussed in the conclusion and outlook section of [1], an analytic continuation procedure applied to the expressions presented in terms of Lauricella series in the latter paper allows one to provide new series representations of the sunset diagram, giving access to some ranges of values of the masses and squared external momentum which are not accessible using the results of [1].
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