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 ($\widehat{\Theta}$) explicitly, though invariance under $\widehat{C\Theta}$ and a mirror fermion symmetry $\widehat{T\Theta}$ 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 $\mathcal{O}(a^2)$.