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Chiral perturbation theory at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">O</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:math>for lattice QCD
We construct 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 $\mathcal{O}{(a}^{2}).$ The chiral Lagrangian is then derived, including terms of $\mathcal{O}{(a}^{2}),$ which have not been …