η−η′ mixing from U(3)L⊗U(3)R chiral perturbation theory

Herrera-Siklody, Paula; Latorre, José I.; Pascual, P.; Taron, J.

doi:10.1016/s0370-2693(97)01507-4

Cited by 69 publications

(69 citation statements)

References 27 publications

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“…Nevertheless, the slope of the form factor for small values of Q 2 is altered significantly by the next-to-leading-order corrections, as it is also borne out by evaluating Eq. (17). We find…”

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confidence: 73%

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New insights into the neutron electric dipole moment

Ottnad¹,

Kubis²,

Meißner

et al. 2010

Physics Letters B

136

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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 .

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confidence: 73%

“…Finally, we can expressθ in terms of measurable quantities. For m u,d ≪ m s , to lowest order in the quark angles, and neglecting numerically small corrections to the value of V (2) 0 [17] this relation reads (in what follows, we set…”

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confidence: 99%

New insights into the neutron electric dipole moment

Ottnad¹,

Kubis²,

Meißner

et al. 2010

Physics Letters B

136

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“…They do, however, give rise to specific nonmultiplicative renormalizations of the couplings occurring in L (2) (see section 17).…”

Section: Kaplan-manohar Transformation At Large N Cmentioning

confidence: 99%

Large $N_ c$ in chiral perturbation theory

2000

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The construction of the effective Lagrangian relevant for the mesonic sector of QCD in the large N c limit meets with a few rather subtle problems. We thoroughly examine these and show that, if the variables of the effective theory are chosen suitably, the known large N c counting rules of QCD can unambiguously be translated into corresponding counting rules for the effective coupling constants. As an application, we demonstrate that the Kaplan-Manohar transformation is in conflict with these rules and is suppressed to all orders in 1/N c . The anomalous dimension of the axial singlet current generates an additional complication: The corresponding external field undergoes nonmultiplicative renormalization. As a consequence, the Wess-Zumino-Witten term, which accounts for the U(3) R ×U(3) L anomalies in the framework of the effective theory, contains pieces that depend on the running scale of QCD. The effect only shows up at nonleading order in 1/N c , but requires specific unnatural parity contributions in the effective Lagrangian that restore renormalization group invariance.

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“…In this section we will first briefly outline the method of extending the SU(3) R × SU(3) L chiral rotations of the effective Lagrangian in conventional ChPT to U(3) R × U(3) L in a more generalized framework including the η ′ [6,8]. Within this approach the topological charge operator coupled to an external field θ is added to the QCD Lagrangian…”

Section: Wess-zumino-witten Termmentioning

confidence: 99%

“…In order to investigate systematically the effects of mixing and loops for the two-photon decays of π 0 , η and η ′ , we include the η ′ explicitly within the combined framework of chiral perturbation theory (ChPT) and the 1/N c expansion, so-called large N c ChPT [6,7,8]. 2 In this theory, the η 0 is combined with the octet of pseudoscalar mesons (π, K, η 8 ), since in the large N c limit the axial U(1) anomaly vanishes and the η ′ converts into a Goldstone boson.…”

Section: Introductionmentioning

confidence: 99%

The number of colors in the decays ${\pi^0, \eta, \eta' \rightarrow \gamma\gamma}$

Borasoy

2004

Eur. Phys. J. C

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The decays π 0 , η, η ′ → γγ are investigated up to next-to-next-to leading order in the framework of the combined 1/N c and chiral expansions. Without mixing of the pseudoscalar mesons the N c independence of the π 0 and η decay amplitudes is shown to persist at the one-loop level, although the contribution of the Wess-Zumino-Witten term to the pertinent vertices is not canceled by the N c dependent part of a Goldstone-Wilczek term. The decay amplitude of the singlet field, on the other hand, depends strongly on N c and yields under the inclusion of mixing also a strong N c dependence for the η decay. Both the η and η ′ decay are suited to confirm the number of colors to be N c = 3.

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η−η′ mixing from U(3)L⊗U(3)R chiral perturbation theory

Cited by 69 publications

References 27 publications

New insights into the neutron electric dipole moment

New insights into the neutron electric dipole moment

Large $N_ c$ in chiral perturbation theory

The number of colors in the decays ${\pi^0, \eta, \eta' \rightarrow \gamma\gamma}$

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