Hadron electric dipole moments from CP-odd operators of dimension five via QCD sum rules: the vector meson

Abstract

We present a complete analysis of the electric dipole moment (EDM) of the ρ-meson induced by CP violating operators of dimension 4 and 5 within the QCD sum rules approach. The set of CP-odd operators includes the theta term and the electric and chromoelectric dipole moments of the three light quarks. We find that the ρ-meson EDM induced purely by the EDMs of quarks is smaller, but still in reasonable agreement, with the predictions of a naive constituent quark model. However, the chromoelectric dipole moments, including that of the strange quark, give comparable and sometimes larger contributions. We also consider the effect on the hadronic EDM of the existence of Peccei-Quinn symmetry. When this symmetry is active, chromoelectric dipole moments induce a linear term in the axion potential which leads to a numerically important vacuum contribution to the hadronic EDM. * pospelov@mnhepw.hep.umn.edu † a.ritz@damtp.cam.ac.uk ‡ Present address 1

Electric dipole moment of theρmeson

“…The third contribution to d ρ is generated by the quark's chromoelectric dipole moment. Its subcompo- [15], however, our result is an order of magnitude larger, has the opposite sign and contains a sizeabled + -term. At least the first two of these marked discrepancies are insensitive to reasonable variations in µ acm .…”

“…Our result may directly be compared with that obtained in a sum rules analysis; viz., herein : −2.9 × 10 −3 µ acm eθ ∼ 0.7 × 10 −3 eθ Ref. [15] : 4.4 × 10 −3 eθ .…”

“…The quark chromoelectric dipole moment interaction is one such operator. In its case, within a sum rules calculation [15], the net effect of this mixing is elimination ofθ in favour of a modest enhancement in magnitude of the coefficients of d ± in Eq. (60), with no change in sign.…”

“…Not that there is any hope of measuring a ρ-meson EDM but because the nonperturbative methods necessary can most readily be illustrated in the case of systems defined by two valence-quark degrees-of-freedom. In taking this path, we follow other authors [13][14][15] but will nonetheless expose novel insights, especially because we consider more operator structures than have previously been considered within a single unifying framework. It is worth remarking here that particles with spin also possess a magnetic dipole moment.…”

Electric dipole moments as probes of new physics

“…Using the same PCAC-type reduction of the pion in Nπ a |O CP |N ′ as in (3.42), one can reduce the calculation ofḡ πN N to the matrix elements of dimension five CP -even operators. In doing this, one has to take into account a subtlety for CEDM sources, first pointed out in [59,58,60], namely that a second class of contributions, the pion-pole diagrams (Fig. 3b), now contribute at the same order in chiral perturbation theory.…”