The Effective Chiral Lagrangian with Lorentz Violation

Despite its many successes, the Standard Model (SM) is still incomplete and is thought to be only a part of a broader picture that hides within it new physics. In the 1990s, a framework based on low-energy effective field theory (EFT) that allows for the investigation of Lorentz violation in any sector of the SM was developed. It is known as the Standard Model Extension (SME). The SME Lagrangian is written down using elementary particles degrees of freedom, namely quarks, leptons and gauge bosons. Using the chiral symmetry properties of the quark fields and matching them onto the hadronic degrees of freedom, we construct part of the SME Lagrangian employing hadronic fields, in particular pions and nucleons, within the framework of chiral EFT. Our construction includes both pion and pion-nucleon cases where chiral symmetry results in interaction terms between pions that have not been considered before.