Universal bounds for SU(3) low energy constants

In this paper bounds for L1, L2, and L3 are obtained in chiral perturbation theory with three flavors. At the same time we test the compatibility of this theory with axiomatic principles. Following a recent paper we use dispersion relations to write positivity conditions that translate into bounds for the chiral low energy constants. As a first approach we consider the exact SU(3)V limit and notice that if a common mass of the order of that of the kaon is adopted for the octet of pseudo-Goldstone bosons the bounds have very large O(p6) corrections. Once the positivity conditions are adapted to account for different masses, we correct the previous bounds for a physical kaon mass and find that they tighten. We observe an overlap between the experimentally determined region and the first principles forbidden region, in the space of parameters.