Mass splittings in a linear sigma model for multiflavor gauge theories

We calculate the tree-level mass spectrum for a linear sigma model describing the scalar and pseudoscalar mesons of a SU(3) local gauge theory with Dirac fermions in the fundamental representation. N1 fermions have a mass m1 and N2 a mass m2. Using recent lattice data with m1=m2 and N1+N2=8 or 12, we predict the mass splittings for m2=m1+δm. At first order in δm, an interesting inverted pattern appears in the 0++ sector, where mesons with lighter fermions are heavier. This feature could be tested in ongoing calculations provided that m1 and δm are sufficiently small. We discuss possible improvements of the approach.