Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2007-07-16
JHEP 0709:065,2007
Physics
High Energy Physics
High Energy Physics - Phenomenology
Typos corrected and minor changes in Table 2. Published version. 19 pages, 1 figure, 2 tables
Scientific paper
10.1088/1126-6708/2007/09/065
We derive a simplified representation for the pion mass to two loops in three-flavour chiral perturbation theory. For this purpose, we first determine the reduced expressions for the tensorial two-loop 2-point sunset integrals arising in chiral perturbation theory calculations. Making use of those relations, we obtain the expression for the pion mass in terms of the minimal set of master integrals. On the basis of known results for these, we arrive at an explicit analytic representation, up to the contribution from K-K-eta intermediate states where a closed-form expression for the corresponding sunset integral is missing. However, the expansion of this function for a small pion mass leads to a simple representation which yields a very accurate approximation of this contribution. Finally, we also give a discussion of the numerical implications of our results.
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