Strong isospin breaking with twisted mass lattice QCD

In this work we propose a method for including strong isospin breaking in twisted mass lattice calculations, while preserving flavor identification. We utilize a partially quenched construction in which the sea quarks are given by the standard twisted mass lattice action while the valence quarks have an additional strong isospin breaking mass term. This construction allows for a practical use with existing twisted-mass gauge ensembles. Additionally, we construct the relevant partially quenched twisted mass chiral perturbation theory for both mesons and baryons to O(m_q^2, m_q a, a^2). We provide explicit expressions for the pion, nucleon and delta masses, as well as the corresponding mass splittings, and discuss the resulting errors from including the strong isospin breaking in the valence sector only. Finally, we demonstrate how the application of this idea can be used, with mild approximations, to determine the values of both the up and down quark masses.