Chiral perturbation theory with tensor sources

Abstract

We construct the most general chirally invariant Lagrangian for mesons in the presence of external sources coupled to the tensor current Ψ over-bar σ(μv) Ψ. In order to have only even terms in the chiral expansion, we consider the new source of O(p^2). With this choice, we build the even-parity effective Lagrangian up to the p^6-order (NLO). While there are only 4 new terms at the p^4-order, at p^6-order we find 78 terms for n(f) = 2 and 113 terms for n(f) = 3. We provide a detailed discussion on the different mechanisms that ensure that our final set of operators is complete and non-redundant. We also examine the odd-parity sector, to conclude that the first operators appear at the p^8-order (NNLO).