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Correlation functions with Karsten-Wilczek fermions

The Karsten-Wilczek action describes two chiral fermions but breaks the symmetries under both charge conjugation ($ \widehat{C}) $ and time reflection ($ \widehatΘ $) explicitly, though invariance under $ \widehat{CΘ} $ and a mirror fermion symmetry $ \widehat{TΘ} $ are maintained. These proceedings outline how the action's symmetries and the presence of the second fermion emerge in mesonic correlation functions. The residual symmetries explain the non-observation of broken time-reflection symmetry in a class of mesonic correlation functions. Time-reflection symmetry is enforced for correlation functions that are manifestly invariant under $ \widehat{C} $ or $ \widehat{T} $. Due to contributions from the second fermion, oscillating contributions arise in some mesonic correlation functions. A second condition for non-perturbative tuning of the relevant counterterm is obtained from these oscillations. Both non-perturbative tuning conditions are independent and agree within errors. Due to contributions from the second fermion, additional pseudoscalar states are observed in non-standard channels. Mass splittings between these additional states and the Goldstone boson vanish as $ \mathcal{O}(a^2) $.