Electric dipole moment of theρmeson

Abstract

At an 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 ≥ 4. Using a global-symmetry-preserving truncation of QCD's Dyson-Schwinger equations, we compute the ρ-meson's electric dipole moment (EDM), dρ, as generated by the leading dimensionfour and -five CP-violating operators and an example of a dimension-six four-quark operator. The two dimension-five operators; viz., quark-EDM and -chromo-EDM, produce contributions to dρ whose coefficients are of the same sign and within a factor of two in magnitude. Moreover, should a suppression mechanism be verified for the θ-term in any beyond-Standard-Model theory, the contribution from a four-quark operator can match the quark-EDM and -chromo-EDM in importance. This study serves as a prototype for the more challenging task of computing the neutron's EDM.

Magnetic moment of the ρ meson in instant-form relativistic quantum mechanics

“…These approaches are the most close in spirit to our approach. There are approaches based on the Dyson-Schwinger equation [51][52][53][54][55], on the Nambu-Jona-Lasinio model [56,57]. Some authors use QCD sum rules [58,59], Feynmann diagrams in the light front formalism [60], the bag model [61], relativistic composite model [62], the constructed relativistic Hamiltonian [63], a low-energy effective field theory [64], or lattice QCD calculations [65][66][67][68][69].…”

Dimension-5CP-odd operators: QCD mixing and renormalization

“…While interesting model-independent statements can be made within a nucleon-level chiral effective theory approach [13][14][15][16][17][18], ultimately the computation of a number of hadronic matrix elements is necessary. Existing calculations of the impact of BSM operators on hadronic EDMs typically rely on modeling the strong dynamics in ways consistent with the Quantum Chromodynamics (QCD) symmetries, using methods such as QCD sum rules [19][20][21][22] and the Dyson-Schwinger equations [23,24] (see Refs. [3,12] for reviews).…”

Contact-interaction Faddeev equation and,inter alia, proton tensor charges

“…[20]. Namely, since one generally finds that systematic treatments of the contact interaction yield results for low-momentumtransfer observables which are practically indistinguishable from those produced by RL studies that employ more sophisticated interactions [14,[35][36][37][38][39][40][41][42][43][44]; and analyses of hadron physics observables using the RL truncation and one-loop QCD renormalisation-group-improved (RGI) kernels for the gap and bound-state equations produce results that are normally within 15% of the experimental value [59], we therefore attach a relative error of 15% to the results in Table IV. Hence, our predictions are: (8) 1.05 (16) .…”

“…A drastic approach is to replace the Bethe-Salpeter kernel for the quark-quark system by a momentum-independent interaction, a motivation for which may be found in the Nambu-Jona-Lasinio model [33,34]. On the other hand, following a body of re- cent work [14,[35][36][37][38][39][40][41][42][43][44] it may also be viewed differently. Namely, since gluon propagation is characterised by a mass-scale m g ≃ 0.5 GeV, which screens infrared field modes [25,[45][46][47][48][49][50][51][52][53][54][55][56], a vector ⊗ vector contact-interaction can be a realistic representation of the quark-quark scattering kernel in QCD so long as the momentum scales being resolved are smaller than m g .…”