Taste breaking in the minimally doubled Karsten-Wilczek action and its tree-level improvement

Minimally doubled fermion actions offer a discretization for two-flavor quantum chromodynamics without rooting, but retaining a U(1) chiral symmetry at the same time. The price to pay is a breaking of the hypercubic symmetry, which requires the inclusion and tuning of new counterterms. Similar to staggered quarks, these actions suffer from taste breaking. We perform a mixed-action numerical study with the Karsten-Wilczek formulation of minimally doubled fermions on 4stout staggered configurations, generated with physical quark masses, covering a broad range of lattice spacings. We consider a tree-level spatial Naik improvement to mitigate discretization errors. We carry out a nonperturbative tuning of the KW action with and without improvement and investigate the taste breaking and the approach to the continuum limit.