Theta vacua, QCD sum rules, and the neutron electric dipole moment

Abstract

We present a detailed study of the electric dipole moment of the neutron induced by a vacuum theta angle within the framework of QCD sum rules. At next-to-next-to leading order in the operator product expansion, we find the result d n (θ) = 2.4 × 10 −16θ e · cm, to approximately 40% precision. With the current experimental bound this translates into a limit on the theta parameter of |θ| < 3 × 10 −10 . We compare this result with the long-standing estimates obtained within chiral perturbation theory, and observe a numerical similarity, but also significant differences in the source of the dominant contribution.

A comprehensive analysis of electric dipole moment constraints on CP-violating phases in the MSSM

“…For the neutron EDM, the uncertainty arises from hadronic physics, while for the Mercury EDM the source of uncertainty is associated with (i) atomic physics in extracting the nuclear Schiff moment from d Hg , (ii) the nuclear physics going into extracting T-and Podd pion-nucleon couplingsḡ πN N from the Schiff moment, and (iii) the hadronic physics in computing theḡ πN N in terms of quark Chromo-EDM operator, Weinberg three-gluon operator, and CP-violating four fermion operators. 6 In utilizing the CPsuperH2.0 package to estimate the relevant EDMs from the EDMs of quarks and leptons we are relying on QCD sum rule computations [59,[62][63][64][65][66] of strong interaction matrix elements. For a discussion of the systematic uncertainties in our results for these quantities when different hadronic model approximations are employed we refere the reader to e.g.…”

“…7 These CP-odd operators are responsible for the EDMs of the neutron, as well as of that of the Thallium and Mercury atoms, as summarized in table 2. In particular, in the MSSM the Thallium EDM is dominated by the electron EDM operator d e , and possibly by the four-fermion operator C f f ′ if tanβ > 30 [59]; the neutron EDM, which we compute here using QCD sum rule results [62][63][64][65], mainly stems from the EDM and chromo-EDM operators of the u and d quarks, d u,d andd u,d , and from the 3-gluon term d 3G ; lastly, the Mercury EDM is generated primarily by the chromo-EDM operatorsd u,d [29]. A combination of table 2 and table 2 provides information on how each CP-violating phase is constrained by which experimental EDM bound.…”

Vacuum energy and θ-vacuum

“…Notice that the partition function Z θ is always real because CP symmetry transforms FF into −FF and preserves the effective gauge action S eff (g). The inequality (1) implies that the free energy density E θ = E θ /V of the θ-vacuum is bounded below by that of the 0-vacuum, i.e. E 0 ≤ E θ ; from this property Vafa-Witten argued implicitly assuming that E θ is smooth at θ = 0 that E ′ θ = FF 0 = 0.…”

“…However, since thi term breaks CP invariance there are severe constraints in the value of its θ-coefficient. In particular, the absence of a significant electric dipolar momentum of the neutron requires that θ < 10 −9 [1].…”

Neutron electric dipole moment: Constituent dressing and compositeness

“…It will increase when using any reasonable Ansatz that incorporates strong interaction dressing in Γ ± µ , analogous to that described by Σ F , ∆ F in the CP and T preserving part of the vertex. We can estimate the scale of this effect by comparing ω − u (p)(= ω − d (n)) and ω − d (p)(= ω − u (n)) with lattice estimates [57] of the proton's tensor charges: δu = 0.839(60), δd = −0.180 (10). It is thus apparent that Eq.…”