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Résumé |
In this talk, we begin by showing how it is possible to
obtain full analytic results for the two-loop three distinct mass
scale sunset diagrams that appear in the expressions for the masses
and decay constants of the pion, kaon and eta particles in two-loop
SU(3) chiral perturbation theory. We then talk about two applications
of these results: a) how it allows one to obtain small quark mass
ratios to arbitrarily high powers, and b) how it allows one to make
fits to lattice data to extract greater information about low energy
constants. We then change track and discuss in more detail the
Mellin-Barnes method used in our calculations, and demonstrate how
this method can be extended using analytic continuation to obtain
results for Feynman diagrams whose mass value parameters are such that
it is impossible to use a direct calculation. We show how such methods
of analytic continuation can also be helpful in contexts where a
direct calculation does yield results, and thus set the stage for more
widespread application of this technique. |
