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The comparison of the theoretical and experimental determinations of the anomalous magnetic moment of the muon (g − 2) µ constitutes one of the strongest tests of the Standard Model at low energies. In this article, we compute the leading hadronic contribution to (g − 2) µ using lattice QCD simulations employing Wilson quarks. Gauge field ensembles at four different lattice spacings and several values of the pion mass down to its physical value are used. We apply the O(a) improvement programme with two discretizations of the vector current to better constrain the approach to the continuum limit. The electromagnetic current correlators are computed in the time-momentum representation. In addition, we perform auxiliary calculations of the pion form factor at timelike momenta in order to better constrain the tail of the isovector correlator and to correct its dominant finite-size effect. For the numerically dominant light-quark contribution, we have rescaled the lepton mass by the pion decay constant computed on each lattice ensemble. We perform a combined chiral and continuum extrapolation to the physical point, and our final result is a hvp µ = (720.0 ± 12.4 stat ± 9.9 syst ) · 10 −10 . It contains the contributions of quarkdisconnected diagrams, and the systematic error has been enlarged to account for the missing isospin-breaking effects.

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 .

We present a lattice QCD computation of η and η ′ masses and mixing angles, for the first time controlling continuum and quark mass extrapolations. The results for Mη = 551(8)stat(6)sys MeV and M η ′ = 1006(54)stat(38)sys(+61)ex MeV are in excellent agreement with experiment. Our data show that the mixing in the quark flavour basis can be described by a single mixing angle of φ = 46(1)stat(3)sys• indicating that the η ′ is mainly a flavour singlet state.