New insights into the neutron electric dipole moment

Abstract

We analyze the CP-violating electric dipole form factor of the nucleon in the framework of covariant baryon chiral perturbation theory. We give a new upper bound on the vacuum angle, |θ0| 2.5 · 10 −10 . The quark mass dependence of the electric dipole moment is discussed and compared to lattice QCD data. We also perform the matching between its representations in the three-and two-flavor theories.Key words: CP violation, chiral Lagrangians, neutron electric dipole moment PACS: 11.30. Er, 12.39.Fe, 14.20.Dh 1. The neutron electric dipole moment (nEDM) is a sensitive probe of CP violation in the Standard Model and beyond. The current experimental limit d n ≤ 2.9 · 10 −26 e cm [1] is still orders of magnitude larger than the Standard Model prediction due to weak interactions. However, in QCD the breaking of the U (1) A anomaly allows for strong CP violation, which is parameterized through the vacuum angle θ 0 . Therefore, an upper bound on d n allows to constrain the magnitude of θ 0 . New and on-going experiments with ultracold neutrons strive to improve these bounds even further, see e.g. [2] for a very recent review. On the theoretical side, first full lattice QCD calculations of the neutron electric dipole moment are becoming available [3][4][5]. These require a careful study of the quark mass dependence of the nEDM to connect to the physical light quark masses. In addition, CP-violating atomic effects can be sensitive to the nuclear Schiff moment, which receives a contribution from the radius of the nucleon electric dipole form factor, see e.g. [6]. It is thus of paramount interest to improve the existing calculations of these fundamental quantities in the framework of chiral perturbation theory. In [7], the electric dipole moments of the neutron and the Λ were calculated within the framework of U (3) L × U (3) R heavy-baryon chiral perturbation theory and an estimate for θ 0 was given (for earlier works utilizing chiral Lagrangians, see [8,9]). In [10], the electric dipole form factor of the nucleon was analyzed to leading one-loop accuracy in chiral SU (2), thus in that calculation the form factor originates entirely from the pion cloud. The strength of the form factor was shown to be proportional to a non-derivative, time-reversal-violating pion-nucleon couplingḡ πN N that could only be estimated from dimensional analysis. Furthermore, the leading contributions to the nEDM at finite volume and in partially-quenched calculations were considered in [11], and in [12] the leading order extrapolation formula using a mixed action chiral Lagrangian is given. In this Letter, we extend the results of [7,10] to higher order based on a covariant version of U (3) L × U (3) R baryon chiral perturbation theory. This allows to make contact to the lattice QCD results from [4] and by matching, we can also get more insights into the nucleon electric dipole form factor and the size of the coupling constantḡ πN N .

Nuclear electric dipole moments in chiral effective field theory

“…The only other relevant EDM contribution up to NLO (i.e. contributions suppressed by a factor of ∼ M π /m N ) is the isoscalar sum of the single-nucleon EDMs [15,16,56,57]. In this combination, the large isovector loop contribution to the single-nucleon EDM cancels [58].…”

Nucleon electric dipole moment with the gradient flow: Theθ-term contribution

“…However, already at the physical pion mass, the nucleon Schiff moments obtain O(60%) next-to-leading-order corrections that scale as ∼ M π [6,5]. Considering the large pseudoscalar mass used in our calculation, the discrepancy is not very worrisome.…”

“…Nucleon EDMs arising from the QCD θ-term or BSM physics have been calculated both in models [4] and in chiral perturbation theory [5,6]. In the latter approach, the nucleon EDMs are calculated in terms of effective CP-odd hadronic interactions that have the same symmetry properties as the underlying CP-odd sources at the quark level (for a review, see [7]).…”

“…This calculation has been done up to next-to-leading order (NLO) in both SU (2) [18,19,6] and SU (3) [21,20,5] χPT. Focusing here on the two-flavored theory, the neutron (d N ) and proton EDM (d P ) are given by: 5) in terms of g A 1.27 the strong pion-nucleon coupling constant, F π 92.2 MeV the pion decay constant, M π and M N the pion and nucleon mass respectively, e > 0 the proton charge, and, in principle, three low-energy constants (LECs) of CP-odd chiral interactions:ḡ θ 0 andd N,P . The first one,ḡ θ 0 , is not free as discussed below (see eq.…”

Anomalous decays ofη′ andηinto four pions

“…Note, however, that the current limits on the QCD vacuum angle derived from neutron electric dipole moment measurements,θ 0 10 −11 [19], bound these branching fractions beyond anything measurable. Still, for η → 4π 0 , the suppression of the CP-conserving D-wave mechanism, see Eq.…”