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We perform the leading one-loop renormalization of the chiral Lagrangian forspinless matter fields living in the fundamental representation of SU(N). TheLagrangian can also be applied to any theory with a spontaneous symmetrybreaking of $SU(N)_L\times SU(N)_R$ to $SU(N)_V$ and spinless matter fields inthe fundamental representation. For QCD, the matter fields can be kaons orpseudoscalar heavy mesons. Using the background field method and heat kernelexpansion techniques, the divergences of the one-loop effective generatingfunctional for correlation functions of single matter fields are calculated upto $\mathcal{O}(p^3)$. They are absorbed by counterterms not only from thethird order but also from the second order chiral Lagrangian.

One-loop renormalization of the chiral Lagrangian for spinless matter fields in the SU(N) fundamental representation