Johan Bijnens, Niclas Danielsson, Timo A. Lähde
The Pseudoscalar Meson Mass to Two Loops in Three-Flavor Partially Quenched ChPT

Phys.Rev. D70 (2004) 111503

This paper presents a first study of the pseudoscalar meson masses to two loops, or NNLO, within the supersymmetric formulation of partially quenched chiral perturbation theory (PQ$\chi$PT). The expression for the pseudoscalar meson mass in the case of three valence and three sea quarks with equal masses, but different from each other, is given to ${\cal O}(p^6)$, along with a numerical analysis.

LU TP 04-26, hep-lat/0406017