Mixed meson masses with domain-wall valence and staggered sea fermions

Mixed action lattice calculations allow for an additive lattice-spacing-dependent mass renormalization of mesons composed of one sea and one valence quark, regardless of the type of fermion discretization methods used in the valence and sea sectors. The value of the mass renormalization depends upon the lattice actions used. This mixed meson mass shift is an important lattice artifact to determine for mixed action calculations; because it modifies the pion mass, it plays a central role in the low-energy dynamics of all hadronic correlation functions. We determine the leading order, $\mathcal{O}(a^2)$, and next-to-leading order, $\mathcal{O}(a^2{m}_{\pi }^2)$, additive mass shift of valence-sea mesons for a mixed lattice action with domain-wall valence fermions and rooted staggered sea fermions, relevant to the majority of current large scale mixed action lattice efforts. We find that, on the asqtad-improved coarse MILC lattices, this additive mass shift is well parametrized in lattice units by $\Delta (am{)}^2=0.034(2)-0.06(2)(a{m}_{\pi }{)}^2$, which in physical units, using $a=0.125\mathrm{fm}$, corresponds to $\Delta (m{)}^2=(291\pm 8\mathrm{MeV}{)}^2-0.06(2)m_{\pi }^2$. In terms of the mixed action effective field theory parameters, the corresponding mass shift is given by $a^2{\Delta }_{\mathrm{Mix}}=(316\pm 4\mathrm{MeV}{)}^2$ at leading order plus next-to-leading order corrections including the necessary chiral logarithms for this mixed action calculation, determined in this work. Within the precision of our calculation, one cannot distinguish between the full next-to-leading order effective field theory analysis of this additive mixed meson mass shift and the parametrization given above.