Note on Weinberg operators in the standard model

Booth, Michael J.

doi:10.1103/physrevd.48.1248

Cited by 8 publications

(9 citation statements)

References 20 publications

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“…We shall prove that in the absence of QCD radiative corrections the same mechanism leads to the cancellation of induced θ-term. In contrary to the recent claim that the Weinberg operator is zero to this approximation [7], we find that all operators of dim≥6 acquire non-vanishing values.…”

Section: Introductioncontrasting

confidence: 99%

“…The expression for the Weinberg operator (37) parametrically coincides with the effective magnetic quadrupole moment of W -boson [6] appearing in this model in the same fourth order in semi-weak constant. The attempt to prove the exact cancellation of the Weinberg operator using the external field technic [7] seems to be incorrect. The author of this work believes that antisymmetrizations of the amplitude (8) in m 1 , m 3 and m 2 , m 4 should be imposed independently and both procedures increase the effective dimension.…”

Section: Discussionmentioning

confidence: 99%

“…The trivial average over the direction of p produces three different field operators of the dimension 6. By virtue of equations of motion for the external field (7) they can be transformed to the standard form of Weinberg operator. Finally, we get J-H and J-F contributions to the Weinberg operator in the form:…”

Section: Schwinger Operator Methods For Calculating Cp-odd Lagrangianmentioning

confidence: 99%

“…As far as we are interested in pure gluonic operators we can omit quark currents in the r.h.s. of(7) …”

mentioning

confidence: 99%

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CP-odd effective gluonic Lagrangian in the Kobayashi-Maskawa model

Pospelov¹

1994

Physics Letters B

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Schwinger operator method is applied for studying CP-odd pure gluonic effective Lagrangian in the Standard Model at three-loop level. The induced θ-term vanishes by the same reasons as EDMs of quark and W-boson to two-loop approximation. A simple way is found to demonstrate these cancellations. All other terms of the effective Lagrangian acquire non-vanishing contributions. The effective operator of dimension six, Weinberg operator, is calculated explicitly. The corresponding contribution to the EDM of neutron is much smaller than that comes from large distances.

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Section: Introductioncontrasting

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Schwinger Operator Methods For Calculating Cp-odd Lagrangianmentioning

confidence: 99%

“…As far as we are interested in pure gluonic operators we can omit quark currents in the r.h.s. of(7) …”

mentioning

confidence: 99%

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CP-odd effective gluonic Lagrangian in the Kobayashi-Maskawa model

Pospelov¹

1994

Physics Letters B

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“…The Weinberg operator is relevant in many candidates of new physics beyond standard model such as the Higgs-doublet models [49,[53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69], supersymmetric models [70][71][72][73][74][75][76][77][78][79][80], and other models [81][82][83][84][85][86][87]. The SM contribution generated by the CP phase of the CKM matrix [88] is negligibly small due to suppression by the GIM mechanism [89][90][91].…”

Section: Introductionmentioning

confidence: 99%

Weinberg operator contribution to the nucleon electric dipole moment in the quark model

Yamanaka,

Hiyama

2020

Preprint

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We evaluate the contribution of the CP violating gluon chromo-electric dipole moment (the so-called Weinberg operator, denoted as w) to the electric dipole moment (EDM) of nucleons in the nonrelativistic quark model. The CP-odd interquark potential is modeled by the perturbative one-loop level gluon exchange generated by the Weinberg operator with massive quarks and gluons. The nucleon EDM is obtained by solving the nonrelativistic Schroedinger equation of the three-quark system using the Gaussian expansion method. It is found that the resulting nucleon EDM, which may reasonably be considered as the short-distance effect, is smaller than the long distance one obtained after "γ 5 -rotating" the anomalous magnetic moment using the CP-odd mass calculated with QCD sum rules. We estimate the total contribution to be d n = w × 20 e MeV and d p = −w × 18 e MeV with 60% of theoretical uncertainty.

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Contribution of the Weinberg-type operator to atomic and nuclear electric dipole moments

Osamura

Gubler

Yamanaka

2022

J. High Energ. Phys.

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The contribution of the CP violating three-gluon Weinberg operator, $$ \frac{1}{3!}w{f}^{abc}{\epsilon}^{\nu \rho \alpha \beta}{G}_{\mu \nu}^a{G}_{\alpha \beta}^b{G}_{\rho}^{c\mu} $$ 1 3 ! w f abc ϵ νραβ G μν a G αβ b G ρ cμ , to the atomic and nuclear EDMs is estimated using QCD sum rules. After calculating the transition matrix element between the pion and the vacuum through the Weinberg operator, we obtain the long-range CP-odd nuclear force by determining the isovector CP-odd pion-nucleon vertex, using chiral perturbation theory at NLO. The EDMs of 199Hg, 129Xe, and 225Ra atoms, as well as those of 2H and 3He nuclei are finally given including comprehensive uncertainty analysis. While the leading contribution of the 199Hg EDM is given by the intrinsic nucleon EDM, that of 129Xe atom may be dominated by the one-pion exchange CP-odd nuclear force generated by the Weinberg operator. From current experimental data of the 199Hg atomic EDM, we obtain an upper limit on the Weinberg operator magnitude of |w| < 4 × 10−10GeV−2 if we assume that it is the only source of CP violation at the scale μ = 1 TeV.

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Note on Weinberg operators in the standard model

Cited by 8 publications

References 20 publications

CP-odd effective gluonic Lagrangian in the Kobayashi-Maskawa model

CP-odd effective gluonic Lagrangian in the Kobayashi-Maskawa model

Weinberg operator contribution to the nucleon electric dipole moment in the quark model

Contribution of the Weinberg-type operator to atomic and nuclear electric dipole moments

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