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We present a calculation of cut-off effects at tree-level of perturbationtheory for the K and D mesons using the twisted mass formulation of latticeQCD. The analytical calculations are performed in the time-momentum frame. Therelative sizes of cut-off effects are compared for the pion, the kaon and the Dmeson masses. In addition, different realizations of maximal twist conditionare considered and the corresponding cut-off effects are analyzed.

$N_f = 2+1+1$ flavours of twisted mass quarks: cut-off effects at tree-level of perturbation theory