Chiral perturbation theory at O(a^2) for lattice QCD

Details Chiral perturbation theory at O(a^2) for lattice QCD Chiral perturbation theory at O(a^2) for lattice QCD

2003-06-17

arxiv.org/abs/hep-lat/0306021v2

Phys.Rev.D70:034508,2004

Physics

High Energy Physics

High Energy Physics - Lattice

25 pages, LaTeX2e; references added

Scientific paper

10.1103/PhysRevD.70.034508

We construct the chiral effective Lagrangian for two lattice theories: one with Wilson fermions and the other with Wilson sea fermions and Ginsparg-Wilson valence fermions. For each of these theories we construct the Symanzik action through order $a^2$. The chiral Lagrangian is then derived, including terms of order $a^2$, which have not been calculated before. We find that there are only few new terms at this order. Corrections to existing coefficients in the continuum chiral Lagrangian are proportional to $a^2$, and appear in the Lagrangian at order $a^2 p^2$ or higher. Similarly, O(4) symmetry breaking terms enter the Symanzik action at order $a^2$, but contribute to the chiral Lagrangian at order $a^2 p^4$ or higher. We calculate the light meson masses in chiral perturbation theory for both lattice theories. At next-to-leading order, we find that there are no order $a^2$ corrections to the valence-valence meson mass in the mixed theory due to the enhanced chiral symmetry of the valence sector.

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