Electric dipole moment of theρmeson

Abstract

At a hadronic scale the effect of CP-violating interactions that typically appear in extensions of the Standard Model may be described by an effective Lagrangian, in which the operators are expressed in terms of lepton and partonic gluon and quark fields and ordered by their mass dimension, $k\ensuremath{\geqslant}4$. Using a global-symmetry-preserving truncation of QCD Dyson-Schwinger equations, we compute the $\ensuremath{\rho}$-meson's electric dipole moment (EDM), ${d}_{\ensuremath{\rho}}$, as generated by the leading dimension-four and dimension-five CP-violating operators and an example of a dimension-six four-quark operator. The two dimension-five operators, i.e., the quark EDM and quark chromo-EDM, produce contributions to ${d}_{\ensuremath{\rho}}$ whose coefficients are of the same sign and within a factor of 2 in magnitude. Moreover, should a suppression mechanism be verified for the $\ensuremath{\theta}$ term in any beyond-Standard-Model theory, the contribution from a four-quark operator can match the quark EDM and quark chromo-EDM in importance. This study serves as a prototype for the more challenging task of computing the neutron's EDM.